landmarks. of gravity and the plane of the horizon are the axis and

466 J. Physiol. (1962), 163, pp. 466-502With 2 plates and 8 text-fitguresPrinted in Great Britain

SOME QUANTITATIVE ASPECTS OF THE CAT'S EYE:AXIS AND PLANE OF REFERENCE, VISUAL FIELD

CO-ORDINATES AND OPTICS

BY P. O. BISHOP, W. KOZAK* AND G. J. VAKKURtFrom the Brain Research Unit, Department of Physiology,

University of Sydney, Sydney, Australia

(Received 25 April 1962)

The present study grew out of an investigation into the projection of thevisual fields on the lateral geniculate nucleus (LGN) in the cat. The newmethods we have developed for studying this projection using single-unitrecording and the precision we have found in the projection itself directedour attention to many of the basic problems inherent in the idea of topo-graphical localization in the visual system. The present paper is concernedwith an examination of these problems particularly as they pertain to theeye. The nature of the projection of the visual fields on the LGN will bedescribed in the following paper (Bishop, Kozak, Levick & Vakkur, 1962).In order to describe a direction in the visual field a suitable system of

co-ordinates is required, the direction being defined in terms of angles froma reference axis and plane. Under experimental conditions the visual fieldwill consist of a tangent screen or perimeter. In addition, the referenceaxis and plane of the visual field co-ordinate system must be defined inrelation to the projection of retinal landmarks into the visual field. Unlessthis is the case the nature of the projection of the visual fields on to thebrain centres will vary with the position of the eyes. Thus the orientationof the eyeballs should be known and for this purpose an axis and plane ofreference for the eye must be defined in relation to appropriate retinallandmarks.Even before the development of vision the direction of gravity provided

the vertical co-ordinate as the basic reference for the orientation of theorganism in its environment. The development of vision, particularlybinocular vision, has added a second fundamental reference, namely thehorizontal co-ordinate determined visually from the horizon. The directionof gravity and the plane of the horizon are the axis and plane of referenceused by the animal in its interpretation of the visual world. If our system

* Fellow of the Ophthalmic Research Institute of Australia-on leave from NenckiInstitute of Experimental Biology, Warsaw, Poland.

t Fellow of the Post-Graduate Medical Foundation of the University of Sydney.

*QUANTITATIVE ASPECTS OF CAT'S EYE

of visual field co-ordinates is to have significance from a behavioural pointof view, its axis and plane of reference should be conceived in terms of thedirection of gravity and the plane of the horizon. In human perimetrythe choice of a system of spherical polar co-ordinates and. its particularorientation were determined by the needs of clinical neurology withoutthought as to its suitability for describing the projection of the visual fieldson to the centres in the brain. We have found it necessary to consider otherorientations of the spherical polar system as well as other systems ofco-ordinates.The establishment of a plane and axis of reference for the eye has pre-

sented problems of a different kind. It is important to appreciate thatalthough the planes and axes of reference used for the human eye areusually described to a large extent in anatomical and physiological terms,they are, in the final count behaviourally defined and their determinationrequires the co-operation of the subject. As far as we are aware nosystematic formulation has yet been attempted of the problems inherentin the definition and determination of corresponding planes and axes inthe normal unrestrained animal. Co-operation is obviously difficult toachieve in the conscious animal and impossible during anaesthesia andparalysis.

Since the present paper is to a large extent preparatory to our investi-gation on the projection of the visual field on the LGN it should be read inconjunction with the subsequent paper (Bishop et al. 1962). This parti-cularly applies to the analysis of the various systems of visual-field co-ordinates, and the reasons that have dictated our choice of references.

METHODSFull details of the methods used are described in the next paper (Bishop et al. 1962).

Brief mention will, however, be made of those aspects which are essential for an under-standing of the present paper. Cats, 2-5 kg weight, were anaesthetized with allobarbitoneand sodium pentobarbitone together with atropine sulphate, all given intraperitoneally.The animals were fully paralysed with continuous intravenous infusion of gallamine tri-ethiodide and maintained with artificial respiration. The cat's head was rigidly fixed in aHorsley-Clarke (H-C) type stereotaxic apparatus specially constructed so as not to obstructthe visual field. A tangent screen parallel to the H-C frontal plane was placed at 1 m beforethe cat's eyes.The pupils were fully dilated with 1 % atropine sulphate and 10% phenylephrine

(Neosynephrine; Winthrop). Phenylephrine obviates the need for mechanical retractionof the nictitating membrane and eyelids. A range of plastic contact lenses was speciallyconstructed (Corneal Lens Corporation, Sydney) having inner radii of curvature of 8-0,8.5 and 9 0 mm and with three optical powers (OD, + 1D and + 2D) for each radius of curva-ture. From this limited range lenses were selected to match the corneal curvature but usuallythe zero optical power was chosen. Cat's eyes are usually 1D-2D hypermetropic whenatropinized. The correction necessary to focus the eyes at 1 m is usually difficult, however,because of the residual dissimilarity between the curvatures of the lens and cornea. Ourexperiments have not, as yet, seemed to warrant a more detailed attention to the refractive

467

468 P. O. BISHOP, W. KOZAK AND G. J. VAKKURstate of the eye. Krebs's solution was found to be quite satisfactory for irrigating the eyesbefore the application of the lens. After the application of the lens no further attention wasrequired, the lens being removed only for cleaning, usually at the beginning of each day inexperiments that continued for 2 or 3 days. The corneae remain translucent even after3 days. Complete paralysis obviates the need for mechanical fixation of the eyes.The projection of the various retinal landmarks on the tangent screen was carried out by

means of a narrow-beam (< 10) reversible ophthalmoscope (Text-fig. 1). The ophthalmo-scope was usually placed at a distance of about 40 cm from the cat's eye and so arranged

Zeromeridian

-~ -Optic diskVjN D Iri~~~ ~~~~ Lig~~~~~~ht spot

Tapetum

Optic disk

C

A

Text-fig. 1. Diagram showing the method used for plotting retinal landmarks (C)on a tangent screen (A) by means of a narrow-beam reversible ophthalmoscope(B). P, perpendicular projection of the centre of the pupil on the tangent screen;F, presumed fixation point obtained by plotting the estimated centre of the areacentralis on the tangent screen; B, blind spot. D, view of the pupil and fundusobtained through the ophthalmoscope mirror showing light beam centred on thelower margin of the optic disk and at the same time in the middle of the pupil.

that the retinal landmark appeared to be in the centre of the entrance pupil when the smallspot of light was focused upon it by the dioptrical mechanisms. The central hole in theophthalmoscope mirror enabled the observer's visual axis to coincide with the beam of light.By swinging the ophthalmoscope head round 1800 the beam could be directed on thetangent screen and the point plotted. The principle of this method of plotting retinal featureson a tangent screen is briefly mentioned by Talbot & Marshall (1941) and described some-what more fully by Hubel & Wiesel (1960). Since the experiments described here were com-pleted we have used two narrow-beam retinoscopes placed back to back for the purpose ofplotting retinal points on the tangent screen. The retina can be observed through the com-bined retinoscopes but light may be projected from each independently.

RESULTS

Axis and plane of reference for cat's eyeAs pointed out above, we have attempted not only to define our visual-

field co-ordinate system in terms of anatomical and physiological land-

QUANTITATIVE ASPECTS OF CAT'S EYE

marks, but also to choose these landmarks in the eye so that the axis andplane of reference are those which the cat itself uses for visual orientation.Since we do not know how closely our references are in accord with thosewhich might be determined by behavioural methods we use the term'presumed' in respect to them.

Visual axis. The new term 'visual pole' will be used for the point wherethe behaviourally determined visual axis intersects the retina. The term isappropriate since a similar term (posterior pole) is already in use in relationto the optical axis of the eye. In the cat retina a central area has beenspecially developed for acute vision. It is generally assumed that thevisual pole lies in the centre of the area centralis, but the position of thearea of specialized rods and cones (Chievitz, 1889) and the degenerationexperiments at present in progress in this laboratory suggest that thevisual pole may be close to the lateral margin of the area centralis. Never-theless, in this paper the term 'presumed visual pole' will be used to referto the centre of the area centralis as estimated from retinal features (i.e.blood vessels) observed by ophthalmoscopy before histological confirma-tion. We are careful to define our reference point on the retina in this way,since non-behavioural studies can only provide presumptive evidence forthe location of the true visual pole. Furthermore, the same term (pre-sumed visual pole) may still be used as more satisfactory methods becomeavailable in the future for locating the visual pole. It is, of course, impera-tive that, in each report, the expression 'presumed visual pole' should begiven a precise definition in operational terms. In keeping with the aboveargument we may now define the presumed visual axis as the line passingthrough the presumed visual pole and the nodal point of the eye. The pointin the visual field conjugate with the presumed visual pole is the presumedfixation point (F).

Fixation plane. The fixation plane is usually defined in man as thehorizontal plane containing the visual axis when the head is vertical andthe eye is looking straight ahead (e.g. Emsley, 1955, 1957). The human eyesare said to be in their primary position when the visual axes are directedupon the same fixation point situated infinitely far away; correspondingretinal points are similarly orientated and the plane of fixation containsthe two visual axes. In man the visual axis and fixation plane are simplydetermined by giving the subject suitable instructions regarding fixation.In the anaesthetized and paralysed cat we define the presumed fixationplane as the plane which contains the presumed visual axis and intersectsthe H-C frontal plane along a line parallel to the H-C horizontal plane.There are only two conditions which must be fulfilled if this presumedfixation plane is to coincide with the true fixation plane, namely: the pre-sumed visual axis must coincide with the true visual axis and there must

30 Physiol. 163

469

P. O. BISHOP, W. KOZAK AND G. J. VAKKUR

be no rolling of the eye around this axis as a result of the anaesthesia andparalysis. The presumed fixation plane cuts the H-C frontal plane (e.g.the tangent screen) along a line parallel to the H-C horizontal plane,whether the F is directed straight ahead or not, provided there is no rollingof the eye.When Fs are both straight ahead, the cat's eyes are probably very close

to the position equivalent to the primary position of the eyes in man, sincewe have good reason to believe that the anaesthesia and paralysis causevery little change in the elevation of the eyes or rolling of the eyes aroundthe visual axes. The position assumed by the eyes during combinedanaesthesia and paralysis will be referred to as the position of anatomicalrest (cf. Emsley, 1955, 1957).

Reference axis and plane derived from the H-C co-ordinate system.Although the presumed visual axis and presumed fixation plane are theprimary references as far as the eye is concerned, for special purposes anaxis and plane of reference derived from the Horsley-Clarke system ofco-ordinates will also be used, namely the line of intersection between theH-C horizontal and parasagittal planes through the nodal point of the eyeand the H-C horizontal plane through the nodal point of the eye.

A B¢X j D C E

Meridians Parallels Axis Axis Axis throughvertical horizontal the ref. point

Spherical polar co-ordinatesmeridians + parallels

Text-fig. 2. Possible systems of co-ordinates for defining directions in the visualfield. For details see text.

Co-ordinate system for visual fieldWe considered a number ofpossible systems of co-ordinates (Text-fig. 2).

Co-ordinate system C was finally chosen as being the best approximationto the ideal from the point of view of expressing the projection of thevisual field on the LGN. Details concerning the reasons for this choice aregiven below (see Discussion). System E, which is used in human peri-metry, and system D will, however, be used for special purposes. On aspherical surface the co-ordinate lines of the four systems, A, B, C and Dcan be either meridians or parallels. In respect to a tangent screen themeridians become straight lines and the parallels become conic sections(they can be circles, ellipses, hyperbolas or parabolas).

470

QUANTITATIVE ASPECTS OF CAT'S EYEIt should be emphasized again that the reference axes and planes of the

various visual-field co-ordinate systems do not have any necessary orunique relationship to the axis and plane of reference used for the eye.Thus systems C, D and E are all systems of spherical polar co-ordinatesdiffering only in respect to the orientation of their polar axis in relation tothe eye references. In each case we have made the axis of the co-ordinatesystem pass through the nodal point of the eye but variously in the threeinstances. System C is defined to be such that the polar axis is at rightangles to the presumed fixation plane, while in System E the polar axisand presumed visual axis are made to coincide with one another. System Dis defined to be such that the polar axis lies in the H-C horizontal plane atright angles to the line of intersection of the H-C parasagittal and H-Chorizontal planes through the nodal point of the eye. Thus the letters C,D and E refer to the orientation of the polar axis in relation to eye re-ferences rather than to the co-ordinate system as such.

Formal definition of termsFormal definitions of the terms presumed visual axis and presumed fixation plane have

already been given above.Line of 8ight is the line passing through any given point in the visual field and the nodal

point of the eye.Receptive axi8 is the line of sight passing through the centre of the receptive field of a

lateral geniculate (or other) neurone.Blind axi8 is the line joining the centre of the optic disk to the nodal point of the eye and

passing through the centre of the blind spot in the visual field.Azimuth (m) is the angle between the projection of a given line of sight on the presumed

fixation plane and the presumed visual axis (positive to the right, negative to the left of thevisual axis).

Elevation (E) is the angle between a given line of sight and the presumed fixation plane(positive upwards, negative downwards from the presumed fixation plane).

Deviation (w) is the angle between the given line of sight and the presumed visual axis.Position angle (tlr) is the angle between the plane containing both the given line of sight and

the presumed visual axis and the presumed fixation plane.Declination (8) is the angle between the given line of sight and a H-C parasagittal plane

(e.g. the H-C parasagittal plane through the nodal point of the eye).Inclination (y) is the angle between the projection of a given line of sight on an H-C

parasagittal plane and an H-C horizontal plane (e.g. the H-C planes through the nodal pointof the eye).

The following clarifying comments can be made. The above definitionsdo not refer to any of the visual-field co-ordinate systems in Text-fig. 2.Nevertheless, a particular system of co-ordinates is implicit in the defini-tion of the various angles, i.e. oc and e in system C, 8 and y in system D andw and b in system E. The reference direction and plane for the particularco-ordinate system is also implicit in each case, i.e. cx, E, c and 0, the pre-sumed visual axis and the presumed fixation plane; 8 and y, the line ofintersection between the H-C horizontal and parasagittal planes through

30-2

471


the nodal point of the eye and the H-C horizontal plane. In practice theangles are measured with respect to the centre of the entrance pupil of theeye rather than the nodal point. It is assumed that the centre of theentrance pupil of the fully dilated eye lies on the presumed visual axis.The definitions refer to any line of sight. However, it will be convenient

to adopt the convention that unless otherwise specified the line of sight is areceptive axis. If the line of sight is other than a receptive axis, qualifyingletters will be added, e.g. B, blind axis and OA, optic axis, thus ocB, EOA,etc. The further qualifying subscript, letters R and L will be used toindicate to which eye, right or left, the angle refers, thus YR, YL OA, etc.

In the preparation of our projection maps the direction of a receptivefield of a geniculate neurone will be defined by means of the two angles, xand E. Note that the definitions of these angles are not similar. The termsazimuth and elevation have meanings similar to their use in astronomy,and are appropriate since they convey the idea of the visual field as theinner surface of a large hollow sphere akin to the celestial sphere.

CL

Texfi..Darm.osowhw.esreetweemd. fxn.oatoso.

4 e

(r,f in frn of;the nda pon0. P, pepnIcua prjcion of th cetr

of theppl on,the.screnF, preume fixto pont R, cetefrcetveaeofa geclt,ern. Fr fute detal se tet

Tex fiur 3will+4 assis ina nestnigo oreprmetlpo

cedureA tangent screen, whichcouldbereadilychangedtobeei..ther-.

N ...........

,:.::~~~~~~..:..-.,''-.'_..:::::::: e':'.'*.::......... , , , ,>~~~~~~~~~~~..St,-,........,,........ iU.-.::.: ._ :,_,:*~~~~~~~~~~~~~~~~~~~~~~~~~~~ ?. -. .. :: ::: . :: .:: ....

?:--~~~~~~~~~~~ ...:- .': .::.:::::j.:_:.:.:::::::.::::. ..v.::.: .::+.::. .. .. ..

.:::: ::: .:: ::: .:::... I.......

.'-.'. ..:::.. :::-::::..:~~~~~~~~~~~~~~~~.............. ......._

Text-fig. 3. Diagram to show how measurements were made fixing locations on a

tangent screen placed parallel to a Horsley-Clarke (H-C) frontal plane at a distance(r) of I m in front of the nodal point (O). P, perpendicular projection of the centreof the pupil on the screen; F, presuimed fixation point; R, centre of receptive area

of a geniculate neurone. For further details see text.

Calculation of co-ordinates

Text-figure 3 will assist in an understanding of our experimental pro-cedure. A tangent screen, which could be readily changed to be either

472


black or white, was placed parallel to an H-C frontal plane at a distance of1 m in front of the cat's eyes, and parasagittal tangent screens were usedfor the peripheral parts of the visual field. During the experiment theposition of the centre of a receptive field (R) on the tangent screen wasmeasured in terms of Cartesian co-ordinates (a, e) from the perpendicularprojection (P) of the centre of the pupil of the corresponding eye on to thescreen. The Cartesian co-ordinates of the presumed fixation points (F) andof the blind spots (B) with respect to P are also checked about three timesa day.

It is a straightforward procedure to transform these Cartesian co-ordinates to system C co-ordinates with respect to P as zero. Under thesecircumstances the reference plane is parallel to the H-C horizontal planeand the co-ordinates ofP are both 00. As far as the projection of the visualfields on to the LGN is concerned, however, we require the system Cco-ordinates of R with respect to the presumed fixation point (F) as zero.Although the co-ordinates of both F and R with respect to P are easilycalculated, the co-ordinates of R with respect to F cannot be obtainedfrom these values simply by subtraction. The error is appreciable becausethe inclination of visual axis OF (angle DOF) is about 130.The system C co-ordinates of R with respect to the F are given by the

following formulae:

azimuth (a) = arctan aV(r2+i2) 8azimuth(cc) = r2+ei

elevation (E) = arctan [cos (cc + 8) tan (6-y)],where a, e = Cartesian co-ordinates of R with respect to P on a screen

parallel to the H-C frontal plane;

d, i = Cartesian co-ordinates of F with respect to P on the samescreen;

r = distance OP between node and the same screen;

y = inclination of visual axis (yF = POD) = arctani/r;

1/\ ~~d8 = declination of visual axis (8F = DOF) = arctan J(r2+ '2);

and

0 = inclination of receptive axis (yR = POS) = arctane/r.In the above calculations no simplifying assumptions have been made. Itshould be noted that the meridian plane through R (which is perpendicular

473

474 P. O. BISHOP, W. KOZAK AND G. J. VAKKUR

to the presumed fixation plane) cuts the vertical screen along a straightline which forms an angle, T with the vertical line, where

T= arctan (sinytanoc).

The angle T has been exaggerated in Text-fig. 3.The laborious calculations involved in the use of the above formulae can

be avoided in the following way. Transformations from one direction ofreference to another can be carried out, to a good approximation, by simplesubtractions, provided the respective reference points are sufficiently closeto one another. The angle between the presumed fixation plane and theH-C horizontal plane through the node (y) has a mean value of about 130(see below). By means of the above formulae we constructed a grid,

0Zero ,

meridian

400 200 00 + 200 + 400 + 500 + 700 + goo Azimuth

Fixation 00. + 200

HorizontalPthrough pupil O

100 cm 50 0 50 100 50 0 50cmA Frontal screen B Parasagittal screen

Text-fig. 4. A, grid corresponding to meridians and parallels of spherical polarco-ordinate system C (Fig. 2) with respect to F as zero as they appear on a verticaltangent screen parallel to the H-C frontal plane. F is situated in the H-C para-sagittal plane through the node and 130 vertically above P. The lines of isoelevationland isoazimuth are drawn for both eyes if the FR and FL are regarded as coincidingin F. The two small ovals represent the blind spots averaged over 20 cats. Theupper pair of lines (continuous and interrupted) represent the lower boundaries ofthe tapetum in the two eyes of the one cat. The dotted line represents the projectionof the whole tapetum of the right eye shown in Plate 1. The lower boundary of thetapetum in the left eye of this cat is also shown (- --- -). B, corresponding grid asit appears on a vertical screen parallel to the H-C sagittal plane. For the purposesof the diagram the two screens have been made coplanar. In both A and B pointP is the perpendicular projection of the node on the respective screen, P being1 m from the node in each case. The scale at the bottom of the grids measuresdistance in the plane of the respective screens. For further details see text.


similar to Text-fig. 4A, representing the meridians and parallels of theco-ordinate system C as they would appear on the vertical tangent screenwith respect to a point FN as zero (see below), where FN is situated in theH-C parasagittal plane through the node and the angle yFN is 130 (i.e.FN is 13° vertically above P). In Text-fig. 4A it is important to appreciatethat the lines of isoelevation and isoazimuth have been drawn in for oneeye only, and in order to make the diagram more generally useful the zeropoint has been labelled F instead of FN. For the other eye all the lineswould be displaced laterally by the interpupillary distance, i.e. about 4 cm.During an experiment we obtain co-ordinates with respect to P both ofthe presumed fixation points (F) and of all the receptive fields (R) that weinvestigate. The grid mentioned above is then used as a nomogram toconvert these Cartesian co-ordinates to system C co-ordinates with respectto FN as zero. Since F lies close to FN (see below) and the values of theco-ordinates ofF with respect to FN are therefore small, the transformationof the co-ordinates of R from FN as zero to F as zero can now be carriedout by simple subtraction of angles, without making any significant error.An example will make the method clearer. The various steps can be

readily checked by recourse to the formulae.

Cartesian co-ordinates with respect to P (by direct measurement; r =100cm), F:a, +6cm; e, +24cm.

R:a, +36cm; e, +10cm.System C co-ordinates with respect to FN (by using nomogram),

F: 'a', + 3.30; Cc, +0.50.R: 'a', +19.90; c'e, -6 8.

System C co-ordinates with respect to F (by subtraction),

R: oc, + 16.60; c, -7 3°

(The symbols ' a' and 'c' are used because the reference direction passesthrough FN and not through F.)

Transformation of co-ordinatesThe following formulae are valuable for the purpose of transforming

spherical polar co-ordinates (system C) to their corresponding Cartesianco-ordinates. The isoazimuth lines in system C as they appear on thetangent screen (Text-fig. 4A) are straight lines and the distance, a, of anypoint on an isoazimuth line from the vertical line through P (Text-fig. 3) isgiven by

(r2+ ei)tan(o + 8)a=

(r2 +i2)

475


The isoelevation lines are hyperbolae and the distance, e, of any point onan isoelevation line from the horizontal line through P is given by

e = rtan(arctanotanE )+

The following formulae enable transformations to be made from systemC to system E, provided the axis and plane of reference remain unchanged.namely:

tan Etan+= s and

sin ax

tan octanw

t= cosVOn a screen perpendicular to the visual axis

tan = -l and tanc =-,{(a')2+(e)2}a/ ~~~~~~r

where a' and e' replace a and e (the latter being Cartesian co-ordinates on atangent screen parallel to the H-C frontal plane).

Parasagittal tangent screenThe above treatment applies to any tangent screen parallel to the H-C

frontal plane. Such a tangent screen obviously becomes impracticablefor the large values of azimuth which may be encountered, since we havefound single geniculate units whose receptive fields have values of a up to+ 900. This difficulty can be overcome by using a screen parallel to theH-C sagittal plane, the procedure being analogous to the one describedabove. During the experiment the Cartesian co-ordinates are measuredin centimetres from P (sagittal) and later converted by means of anomogram to cx and E with FN as zero, and then by subtraction trans-formed to a and E with F as zero.The method of construction of the nomogram is indicated in Text-

fig. 4B, which has been constructed for FN as zero (i.e. SFN = 00,yFN = + 130). The anterior edge of the parasagittal screen abuts theright-hand edge of the frontal screen and corresponding lines are seen to becontinuous. For the purposes of illustration the two screens have beenplaced in the one plane. P is the perpendicular projection of the nodalpoint of the eye on to the parasagittal screen. The method of constructionis indicated by

x = rtan (90-oc),

rtanecos (900-a)'

476

QUANTITATIVE ASPECTS OF CAT'S EYEwhere r is the distance from the nodal point to the screen. Note thatalthough the distance r is different for the two eyes, this does not causeany difficulties provided that the parasagittal screen is outside the field ofbinocular vision. For the purpose of illustration the frontal screen onlyextends 1 m laterally from the zero meridian; in practice we have made thisdistance 15 m with corresponding alterations in isoazimuth and isoele-vation lines on the parasagittal screen.

Fundus of the eyePlate I has been obtained by piecing together a large number of fundal

photographs of the right eye in the one cat to give a composite picture ofthe region of the retina occupied by the tapetum. Because of the very highabsolute reflectivity of the cat's tapetum (about 44 %; Weale, 1953) andof its relative reflectivity in relation to the surrounding pigmented retina,considerable difficulty was experienced in obtaining satisfactory photo-graphs. The marked difference in reflectivity caused the area surroundingthe tapetum to appear black in the composite fundal photograph. Thegreatly increased brightness of the cat's tapetum in comparison with thehuman fundus for a given level of illumination is indicated by the factthat the intensity of the light source used for photography had to bereduced by a factor of 130 times for the cat. Although the compositephotograph has been fairly extensively retouched, every attempt has beenmade to retain accuracy consistent with the two-dimensional reproduc-tion of a spherical surface. The two radial 'cuts' which allow the com-posite photograph to be artificially flattened have been hidden by suitableinserts and these are indicated by the two arrows. Plate 2, A, B and C, has,however, not been retouched in any way. The method used for determin-ing the presumed fixation plane and zero meridian will be described below.The extent of the tapetum in relation to the retina as a whole is shown

in Text-fig. 4A where the margins of the tapetum in Plate 1 have beenprojected on to the tangent screen. It should be emphasized that thetapetum in Plate 1 is somewhat smaller than usual, the optic disk beinggenerally inside the tapetum and clear of the pigmented portion of theretina. The nasal portion of the tapetum is larger than the temporalportion, the margin extending about 400 on the nasal side but only about250 on the temporal side. Hence the projection is eccentrically placed inthe visual field. The centre of the tapetum is much closer to the posteriorpole of the eye than to the centre of the area centralis (presumed visualpole). Thus when the whole retina of the excised eye is examined the tape-tum appears to be symmetrically located in the fundus.There are usually three main arterio-venous bundles which issue from

the periphery of the optic disk, one proceeding upwards and medially and

477

P. O. BISHOP, W. KOZAK AND G. J. VAKKURthe other two downwards (Plate 2). These arteries are derived from theciliary system, the central artery of the retina being vestigial in the cat(Davis & Storey, 1943). Owing to the fact that the lower horizontalboundary of the pigmented retina reaches higher than usual in Plate 1,only one of the large arterio-venous bundles is visible passing upwardsacross the tapetum. The more usual level for the lower boundary of thetapetum is shown by the upper lines in Text-fig. 4A, and in Plate 2 thepigmented retina is just visible at the left lower edge of the field of view.In their early course two of the arterio-venous bundles, the upper one andthe lateral of the lower pair (Plate 2A), are approximately in line immedi-ately above and below the disk at an angle of about 300 to the vertical.These two bundles, however, soon sweep laterally in a wide arcuate courseabove and below the area centralis. This is particularly the case with thelower lateral bundle, which finally curves round in an upward directionon the far side of the area centralis near the temporal edge of the tapetum(Plate 1). In contrast to man, and unlike the veins they accompany, thearteries in the cat pursue a very tortuous course.By careful ophthalmoscopic observation correlated with subsequent

examination of the excised eye we have been able to recognize features ofthe retina which localize the centre of the area centralis ophthalmo-scopically with an accuracy of probably better than 0 5 mm. The centreof the area centralis lies about one-and-a-half disk diameters above andthree-and-a-quarter disk diameters lateral to the centre of the optic disk.A quick guide to its location is the fact that the line joining the centre ofthe disk to the centre of the area centralis roughly bisects the anglebetween the two arterio-venous bundles which issue in line above andbelow the disk (Plate 2A). Furthermore, some small vessels always runfrom the temporal side of the disk in a fairly direct line to the medial sideof the central region of the area centralis. The central region itself is freeof visible blood vessels and can be distinguished, as in Plate 2A, by reasonof the fact that the arterioles and venules converge radially upon it fromall directions. Occasionally, also, the area centralis is differentiated by itscolour, which may take on a greenish hue in faint contrast to the moregolden colour of the surrounding tapetum. The presumed visual pole isestimated ophthalmoscopically by choosing the spot on the retina atwhich all the incoming blood vessels would converge. The area freeof visible blood vessels is somewhat smaller than the optic disk. Thepresumed visual pole in Plate 2A is indicated by the intersection of linesX - X' (presumed fixation plane) and Y - Y' (zero meridian). The threeblack spots in vertical line immediately to the right of the presumed visualpole in Plate 2A are due to the stop placed in the fundal camera to eliminatethe corneal reflex. On the far side of the area centralis in Plate 1 both the

478


arteries and veins meet along a 'watershed', the line of division in eachcase curving sharply upwards and laterally from the area centralis, thevenous division lying above the arterial. The field of view in Plate 2Ais about 300 in the X - Xl plane.The area centralis can be identified with certainty in the excised eye by

methylene-blue staining of the intact retina. Following whole-head per-fusion with 10% formalin saline, the eyeball was excised, cornea, lens andvitreous removed and the cavity of the eyeball filled with a 1:2000solution of methylene blue in normal saline for 5-10 min. With the dis-secting microscope ( x 10- x 40) the area centralis can be easily identified.It appears as a dark spot in the centre of Plate 2B, the optic disk beingsituated in the lower right-hand corner. In Plate 2B and C the blurringtowards the edges of the photographs is due to the marked curvature ofthe retinal surface. The area centralis appears as a dense collection ofganglion cells less than 1 mm in diameter with a less dense temporo-superior extension. Often the main collection of cells forms a smallmound but this is probably an artifact due to retinal detachment in theregion of the area centralis during the staining procedure. The circle aroundthe point F in Text-fig. 4A indicates the probable area of acute visioncorresponding to the region of the retina where there is a two- to fourfoldlayering of the ganglion cells (Ganser, 1882 a, b). The nerve fibres will stainif the head is not perfused and if the methylene blue is applied for aboutone minute only. In the whole-mount preparation these stained fibrescan be seen to form a 'watershed' curving upwards and laterally from thetemporal side of the area centralis in a manner analogous to the arteriesand veins described above.The optic disk as seen in the excised eye may be circular or elliptical in

outline, the long axis in the latter case being variably placed with respectto the fixation plane. The disk has a mean diameter of 0 93 mm (8 cats).No significant difference was found between measurements made in theexcised eye with or without prior whole-head perfusion with 10% formalinsaline. By contrast to the area centralis the disk is marked by a shallowdepression.

Histological section of the retina shows that the single layer of ganglioncells, which is characteristic of the retina generally, becomes four to fivecells thick at the area centralis (Ganser, 1882 a, b; Chievitz, 1889). It is thisdense condensation of ganglion cells which causes the appearance of a darkspot in Plate 2A. The two classes of ganglion cell, large and small, can bequite clearly made out in the photographs. Except for the area centralisboth types of cell seem to be fairly uniformly distributed in the fundus, thesmall cells being much more numerous than the large. Towards the peri-phery of the retina, however, the density of ganglion cells is markedly

479

P. O. BISHOP, W. KOZAK AND G. J. VAKKURreduced. In Plate 2C it can be seen that the condensation at the centre ofthe area centralis is predominantly made up of small cells.

Actually the structural differentiation seen in Plate 2B and C is almostentirely due to the selective staining of the ganglion cells by the methyleneblue. This is indicated by our degeneration experiments involving sectionof an optic tract in new-born kittens. Under these circumstances Ganser(1882 a, b) has shown that the degeneration is limited to the ganglion-celllayer of the corresponding hemiretinae. In our methylene-blue-staineddegenerated retinae virtually no cells were visible in the hemiretinaecorresponding to the severed optic tract. The ganglion cells tend to bearranged in rows orientated in the direction taken by the nerve fibres asthey sweep round, above and below, the area centralis. In Plate 2B somethick bundles of nerve fibres can actually be seen sweeping outward fromthe edges of the disk and covering any underlying ganglion cells. In thephotographs the presence of small blood vessels is indicated by theirregular white lines which result from the absence of ganglion cells alongtheir course. The width of these spaces (down to 1O p) indicates that thesevessels are probably pre-capillaries and capillaries. According to Duke-Elder (1958, p. 481) the capillaries in the cat penetrate only to the ganglioncell layer, but Prince, Diesem, Eglitis & Ruskell (1960) report that theymostly occur in the inner plexiform layer and can be seen in almost anylayer of the retina anterior to the outer nuclear layer.

Location of presumed visual poleSince the ophthalmoscopic determination of the visual pole depends very

largely on the arrangement of the visible blood vessels, it is important toestablish that the centre of the area centralis can be localized in the fundusby observing the arrangement of the identical blood vessels in the excisedeye. In one cat a tracing of all the blood vessels in the region of the diskand presumed visual pole was obtained by a point-by-point projection onto the tangent screen with the reversible ophthalmoscope. Point F wasalso defined in relation to these blood vessels. The eye was then excisedand the appropriate small portion of the retina was carefully stripped offand laid flat on a microscope slide. The vascular system was then outlinedon paper by means of a microprojection apparatus. Very good agreementwas obtained between the two methods, the same vessels being traced towithin 0*5 mm of the presumed visual pole on the one hand and the areacentralis on the other. Furthermore, when the methylene-blue-stainedfundus is observed under the dissecting microscope, the radial arrange-ment of vessels in the region of the area centralis is readily observed(Plate 2B) and the fine terminal capillaries can be traced almost to thecentre of the area centralis.

480

QUANTITATIVE ASPECTS OF CAT'S EYEThe degree of coincidence between the presumed visual pole and the

centre of the area centralis is also indicated by measurements of the angle,cwB, which the blind axis makes with the presumed visual axis. Thefollowing procedure was carried out. Nine cats were aligned in the stereo-taxic apparatus and the positions of the points F and the blind spots wereplotted on the tangent screen and the angle coB measured for each eye.The mean value for coB was 16.10 (S.D. 1.70, range 13.4-18-50). Then,after whole-head perfusion with 10% formalin saline, the retina of theexcised eye was stained with methylene blue. The distance between thecentre of the optic disk and the centre of the area centralis (c, Text-fig. 5)was then measured by the aid of a dissecting microscope, the mean valuebeing 3-42 mm (S.D. 0-28 mm, range 3 0-4 0 mm). Taking 4.40 of visualangle as equivalent to 1 mm on the retina (Vakkur, Kozak & Bishop,unpublished; cf. Barlow, Fitzhugh & Kuffler, 1957), the angular distance,coB = 16- 10, would give a retinal distance of 3 66 mm between the centreof the disk and centre of the area centralis, in good approximation to themeasured distance of 3x42 mm.On the basis of the various lines of evidence described above it is pro-

bable that the ophthalmoscopically determined visual pole coincides withthe centre of the area centralis to within 0-5 mm (= 2.2°). We are atpresent attacking this problem by placing very small, sharply definedlesions around the presumed visual pole by means of a Zeiss photo-coagulator. It is important to bear in mind that the centre of the areacentralis may not be the true visual pole (see above).

Does rolling of the eye occur?The absence of any precise knowledge about the orientation of the

retinal landmarks when the cat's eyes are in the primary position makes itdifficult to estimate any changes that may occur as a result of anaesthesiaand paralysis, even although we now have an accurate account of theorientation of these landmarks under the latter circumstances. The onlyangle about which a clear statement can be made is the declination (8F)since by definition the visual axis lies in a parasagittal plane when the eyeis in the primary position. During anaesthesia and paralysis the meandeclination of the presumed visual axis is 2.60 giving a mean divergence ofthe two axes of 5.20. It is possible however that, under these conditions,the true visual axis is more nearly parallel to the H-C sagittal plane, sincethe centre of the area of specialized rods and cones is approximately0-S-1 mm lateral to the central of the area centralis of accumulatedganglion cells (Chievitz, 1889).The details that we have about the other angles indicate the degree to

which the two eyes behave symmetrically but they do not, in themselves,

481

P. O. BISHOP, W. KOZAK AND G. J. VAKKURprovide any information in relation to the primary position of the eyes.Fortunately our lack of knowledge about the divergence of the yF fromthat characteristic of the primary position is of no consequence as far asthe projection of the visual field on the LGN is concerned, provided thereis no rolling of the eye. It is therefore of considerable importance to deter-mine whether or not rolling of the eye occurs as a result of the anaesthesiaand paralysis. If rolling does occur, the magnitude of the expression(ORB -kLB) is a good guide to the symmetry of the rolling. The expression(kRB-OLB) ranged from -8 5° to 7.5 (mean -0 4°; S.D. 4.5°). Move-ments of the eyes during the course of an experiment have not proved tobe a problem. These movements are readily detected, they are alwayssmall and due allowance can be made for them by appropriatecomputations.While there are many indications that little if any rolling occurs the

evidence that we have been able to obtain is unfortunately not sufficientlyprecise to exclude rolling as a significant variable in the preparation of ourprojection maps. This evidence is as follows:

Slit pupil. The slit pupil of the cat provides a guide to the orientation ofthe eyeball. An attempt was made to measure the slope of the pupil-slitin the normal unrestrained animal by taking frontal photographs of aseries of cats. Photographs in which the cat appeared to be looking at thecamera were selected for measurement. The line of the slits converge inan upward direction to form an angle between the slits of 110 (mean of12 cats, S.D. 2-5', range 7°-14-5°) without any consistent asymmetry withrespect to the sagittal plane. In anaesthetized and paralysed cats thedirection of the pupils can be measured, if all the atropine is withheld atthe beginning of the experiment and only neosynephrine drops are in-serted until after the measurements have been made. Only four cats haveso far been investigated, measurements on two of these being made bothbefore and during anaesthesia and paralysis. In these 4 cats the averageconvergence upwards was 210 but there was a consistent asymmetry: themean direction of the left pupil being 80 to the sagittal plane while that ofthe right pupil was 130. In the two cats in which measurements were madein the normal unrestrained state the average convergence was 80 and sym-metrical but during anaesthesia and paralysis the mean convergenceincreased to 200 and became asymmetrical: left 80, right 15°. We can offerno explanation for this asymmetry, particularly since measurements of theblind spots described above do not reveal a comparable asymmetry. Wefeel that this approach is unlikely to provide a satisfactory answer to theproblem of rolling. The measurements cannot be made with any precisionand there is the additional uncertainty concerning the constancy of therelationship of pupil-slit to retina when subjected to anaesthesia and

482

QUANTITATIVE ASPECTS OF CAT'S EYEparalysis. The use of tattooed spots on the cornea seems a more promisingexperimental approach.Lower boundary of tapetum. The dense black pigmentation of the sur-

rounding parts of the retina provides a fairly distinct boundary to thetapetum. For a distance of about 7 mm on the temporal side of the opticdisk this boundary is approximately horizontal and hence parallel to thepresumed fixation plane (Plate 1). The orientation of this part of theboundary is probably related to the visual horizon and the mitigation ofthe glare from the sky. If the shape of the tapetum and its orientation inthe fundus are of functional significance, then under normal conditions it isa reasonable assumption that the projections into the visual field of the'horizontal' parts of the lower boundaries of the right and left tapetashould coincide with one another, provided the visual axes are directedupon a common fixation point. This is particularly likely to be the casewith those parts of the projections which fall between and just above thetwo blind spots, since they are here so close to the fixation point. As canbe seen from Plate 1 the boundary in this region ofthe fundus is not entirelystraight and the transition from tapetum to pigmented retina is somewhatindefinite. Nevertheless, by projecting a sufficiently large number of'points' of transition and using common criteria of identification for thetwo eyes the mean line ofthe boundary for each eye can be established withreasonable confidence. In Text-fig. 4A the mean line of the lowerboundaries of the tapeta in two cats have been plotted, the two upper linesbeing from the one cat and the two lower from another. It was from thelatter cat that the composite fundal photograph of the eye shown inPlate 1 was prepared and the entire boundary of the tapetum of this righteye has been plotted in Text-fig. 5. It can be seen that the portions of theboundaries between the two blind spots correspond closely in the oneanimal. While these findings argue against the presence of rolling they arenot entirely convincing, since they depend upon the assumption that theportions of the lower boundaries which project between the blind spots arenormally horizontal.Medial borders of homonymous hemi-fields and zero meridian. Work is at

present in progress in this laboratory (Sefton, Stone & Vakkur) aimed todefine the medial borders of the ipsi- and contralateral hemi-fields in agiven cat. Two approaches are being used, namely (1) by studying thepattern of the retinal ganglion-cell degeneration following optic-tractsection in kittens (cf. Ganser, 1882 a, b) and (2) by plotting on the tangentscreen the receptive fields of as many single lateral geniculate neurones aspossible in the region of the zero meridian recording from the nuclei on bothsides. In the normal unrestrained animal the medial borders of the homo-nymous hemi-fields are presumably parallel and also vertical when the

483


eyes are in the primary position, thus coinciding with zero meridian. Anydeviation from this condition would therefore indicate rolling of the eyes.Our repetition of the degeneration studies of Ganser (1882a, b) has

revealed a sharp line of division between nasal and temporal hemi-retinaeand, on the assumption that this line is vertical, measurements on tworetinae have given a value for bB of about 25°, which is very close to themean value found by projection on the tangent screen of the presumedvisual pole and optic disk for the series of cats reported in this paper(Table 3). In two electrophysiological experiments the receptive fields ofover 100 geniculate units per cat have been plotted. Such a number ofunit-fields, however, have not been sufficient to provide a clear definitionof the medial borders of the hemi-fields. Nevertheless, when allowance ismade for the separation of the eyes and divergence of the visual axes thesefindings indicate that the medial borders probably abut on one anotherwithout overlap along a vertical line through F, with an experimentalerror of about 2° or 3°. Details of these investigations will be publishedelsewhere.

Ipsilateral and contralateral genicutae neuroneq. Essentially the LGN inthe cat is composed of three cellular layers, A, A1 and B, lying successivelyone below the other. Layers A and B receive axons from the nasal retinaof the contralateral eye and layer A1 receives axons from the temporalretina of the ipsilateral eye. The studies that we have carried out on theprojection of the visual fields on to the LGN (Bishop et al. 1962) indicatethat neurones in layers A and A1, which lie immediately adjacent to oneanother on either side of the interlaminar zone, have receptive fields whichare also close to one another on the tangent screen after due allowance hasbeen made for the separation of the eyes and divergence of the visual axes.Thus as the micro-electrode is inserted down through the nucleus thereceptive fields of successive units have been found to fall along a linewithout any evidence of a sharp discontinuity as the electrode moves fromthe one layer to the next. There are two possible explanations for thisfinding: one is that there is a sharp discontinuity under normal circum-stances but that there is always just sufficient rolling of the eyes as a resultof the anaesthesia and paralysis to eliminate it and the other is that thereis no rolling of the eyes. The latter explanation is obviously the morelikely.

Binocularly-activated geniculate neurones. The great majority of lateralgeniculate neurones respond to stimulation of only the one eye. There are,however, a small number of units which respond to stimulation of eithereye. It is to be expected that the fields of these units will be respectivelyconjugate to corresponding retinal points, so that under normal circum-stances the receptive fields should coincide. Lack of coincidence of the

484

QUANTITATIVE ASPECTS OF CAT'S EYE 485

receptive fields due to eye movements can be avoided by expressing thedirection of the receptive fields in relation to their corresponding presumedvisual axis. Apart from the uncertainty in the localization of the visualpole any residual lack of coincidence is probably due to rolling. While wehave recorded from a number of binocularly-activated units, the conditionsof the particular experiments from the point of view of the location of F,etc., were unfortunately not such that any very precise conclusions can bedrawn. In our future experiments binocularly-activated geniculate unitswill be carefully studied from this point of view, but recording from singlecortical units promises to be a more profitable approach.

All the above evidence indicates that rolling of the eyes, if it occurs, isprobably less than 5° considered as the difference between R and L ofcorresponding retinal points.

IIg

I

I

11 ;F

I

H.-C. ant.50mm

ON ~~~~40

II ~~~30OD

La. 30mm 20 10Text-fig. 5. Scale drawing of a horizontal section of the left eye viewed from above,

giving the respective mean anterior and lateral H-C co-ordinates. AC, area

centralis; OD, optic disk; N, nodal point; F, presumed fixation point; B, blindspot; c, distance between vi&ual pole and blind pole of the retina; w, angle formedat the node by the visual axis and blind axis; v, posterior nodal distance

= (2sinco/2)Physiol. 16331

P.O. BISHOP, W. KOZAK AND G. J. VAKKUR

Horsley-Clarke co-ordinates of eye (nodal point)The approximate H-C co-ordinates of the eye are given in Text-fig. 5,

which is a scale drawing of a horizontal section of the left eye viewed fromabove. It has been prepared to some extent from data in the literature(Hartridge & Yamada, 1922; Duke-Elder, 1958; Marriott, Morris &Pirenne, 1959) but mainly from measurements carried out in this laboratory.For simplification the visual axis, NF, has been drawn parallel to themedian sagittal plane. Distance c between the centre of the optic disk(OD) and the centre of the area centralis (AC) has been measured inmethylene-blue-stained preparations of the whole eye (see above). Thepupil is drawn fully dilated, though the diameter should be about 11-5 mm.The optic nerve should take a rather more medial course than that shownin the drawing.A knowledge of the H-C co-ordinates of the eye and particularly the

nodal point is essential for the design and use of precision ophthalmicequipment such as the tangent screen, perimeter, multibeam ophthal-moscope, etc., especially when these instruments are used in conjunctionwith H-C stereotaxic methods for electrical recording from the brain. Theco-ordinates of the nodal point (N, Text-fig. 5) are of special importance,because through this point passes the axis of the system of spherical polarco-ordinates (system C) which we have adopted in order to describe theprojection of the visual fields on to the LGN. More precisely the co-ordinate system should be centred on the anterior nodal point, but theterm nodal point is used here in respect to the concept of a reduced eye inwhich the anterior and posterior nodal points are replaced by a single inter-mediate point.The H-C co-ordinates of the point on the surface of the cornea inter-

sected by the presumed visual axis (corneal point) are given in Table 1(mean of 5 cats, i.e. 10 eyes).Taking the distance from corneal surface to retina as 21-5 mm and the

posterior nodal distance (v, Text-fig. 5) as 13 mm (Vakkur, Kozak &Bishop, unpublished) the nodal point (N, Text-fig. 5) is situated about8-5 mm from the corneal surface (our recent work has shown a correlationbetween eyeball dimensions and body weight and this should be taken intoconsideration when future determinations are made concerning the H-Cco-ordinates of the nodal point). The H-C co-ordinates of the nodal pointmay now be calculated by taking into account the direction that the pre-sumed visual axis makes with the H-C planes (cf. Table 2). The location ofthe nodal point in the eyeball is unlikely to be far astray. From our measure-ments of the optical constants of the cat's eye and assumptions regardingthe thickness of the lens and its refractive index, Dr W. R. Levick in this

486

QUANTITATIVE ASPECTS OF CAT'S EYElaboratory has calculated the location of the anterior and posterior nodalpoints as 8-13 and 8*63 mm respectively from the corneal surface. Thesecalculations do not involve a knowledge of the distance between thecorneal surface and retina. Uncertainty in the lateral and basi-heightco-ordinates of the nodal point are of no consequence in respect to the useof the ophthalmic instruments referred to above, because in practice they

TABLE 1. H-C co-ordinates

Anterior Lateral Basi-height*

Corneal point 4857 19-3 11X8(44.6-52.0) (16.4-21-2) (9-9-13.6)

Nodal point 40 4 18-9 9.9Visual pole 27-7 18-3 741

* Height above the basi-horizontal plane.

are referenced on the centre of the apparent pupil. In the 10 eyes theanterior co-ordinate of the nodal point varied from 36-4 to 43-7 mm. It isof interest that the level of the node approximately corresponds to themid-horizontal plane (i.e. one third the distance from the basi-horizontalplane to the level of the vertex of the skull (cf. Fig. 1, Bishop et al. 1962)).Also the posterior extension of the presumed visual axis passes very closeto the inter-aural line.

Thus, in the cat, when the eye is in the primary position, the visual axis isinclined to the basi-horizontal plane by an angle of approximately 130.This is in contrast to man, where the visual axis is approximately parallelto the basi-horizontal plane.

Reference points in the visual fieldVisual axis (fixation point). Text-fig. 6B shows the position of the pre-

sumed fixation point (F) in 20 cats (40 eyes) plotted on a tangent screenplaced parallel to a H-C frontal plane. PL and Pp are the perpendicularprojections of the centres of the apparent pupils (0) of the left and righteye, respectively. The way in which the angles 8 and y have been measuredis indicated in the insert Text-fig. 6A and the mean values for the anglesSLF, 8RF, YLF and yRF are given in Table 2. The mean position of F withrespect to P is given by declination (8F) = 2.60 and inclination (yF) = 12.60,without any significant asymmetry between the two eyes. An analysis ofthe scatter of the points F is given below.

Blind axis (blind spot). Successive points round the margin of the opticdisk can be accurately plotted on the tangent screen (Text-fig. 1). Theseplots provide a most valuable guide to the orientation of the eyes and aready index of the constancy with which the direction of the visual axesis maintained during the course of an experiment. After the cat has been

31-2

487

488 P. O. BISHOP, W. KOZAK AND 0. J. VAKKURparalysed the position of the blind spot becomes relatively constant, themovement during the course of 2 days being always less than 40 and usuallyless than 20. It is not significantly altered after temporarily discontinuing

*FA

-F

s

L tR

* 00OO L-5° 00115 O0 + 2r-100 -5F- 0 50 100 do_ 0.1oF____ 0.00 f0 c)F02 0-iI'S--- 06byoR F %R ~0

B [50 0(PL 00 PR PL PR

Text-fig. 6. A, diagram to show how the angles 8 and y (shown for right eye only)have been measured. 0, nodal points of eyes; P, perpendicular projection of nodalpoints oftangent screen; Fe, Fo, respective left and right presumed fixation points.B, portion of tangent screen showing the scatter in the location of the left (*) andright (0) presumed fixation points (F) in 20 cats plotted as they actually appearedon the screen with respect to PL and PR. PL and PR, perpendicular projections ofthe left and right nodes, respectively. C, position of FR in respect to FL in eachcat shown by plotting all the left presumed fixation points at a common point (a)),the latter being the mean location of all the points FL in the 20 cats (i.e. 8L F =-2 5°; YLF = + 12-3°-Table 2). The scatter ofpoints FR in the vertical direction isindicated as degrees above and below the level of FL and in the horizontal direc-tion as degrees to the left and right of the PR vertical.

TABLE 2. F and B with reference to P (20 cats)

Angle Mean (0) S.D. (0) Range (0)8F Right + 2-7 2-6 - 2-0 to + 9-2

Left - 2-5 1-6 - 5-3 to 0-0yF Right +12-9 2-2 + 8-4to +18-1

Left +12-3 2-0 + 8-1 to +17-0SRF-SLF + 5-2 2-7 - 0-4 to +10-9SRF+SLF + 0-2 3-3 + 7-4 to - 7-3yRF-yLF - + 0-6 0-9 - 1-2 to + 2-0SB Right +16-9 2-6 +10-3 to +23-4

Left -17-0 1-6 -14-2 to -20-0yB Right +19-6 2-5 +15-6 to +25-1

Left +19-3 2-6 + 15-6 to +25-6SRB -LB - + 33-9 2-9 + 28-3 to + 39-8SRB+SLB - 0-1 3-3 - 8-0 to + 7-0YRB-YLB + 0-3 0-9 - 1-6 to + 1-7


the paralysis overnight, by removing the contact lens, by replacing the lenswith one of different power from OD to 2D, or even several hours after thedeath of the animal. If at the beginning of an experiment the position ofthe blind spot diverges from the mean the movement during the course ofthe experiment is nearly always towards the more usual and symmetricalposition. The position of the blind spot is also fairly constant from cat tocat, the mean position of B with respect to P being given by declination(B) = 16-9' and inclination (yB)= 19.50 without any significantasymmetry between the two eyes.

spots(B *20n20as helf n ih lidsosbi lotdwt epc

B~~~

I~~~~~~~~~~~~~C a

to3a50p f -a200p -- +). The way i 150g200 n-100 ~~~~~~~50 -100,

-a 200 LftRiht)

spot \(I, eif0 as helf adrgt Righspts engpote wihrepc

to a common presuimed fixation point (F). Also included are the locations of thecorresponding optical axes (OA, +). The way in which the angles ac, E, w and Vrhave been measured is indicated in the inset diagram. The stippled screen is atright angles to the presumed visual axis (OF). P, perpendicular projection of thenodal point (0) on the plain screen placed vertically behind the stippled screen.

Text-figure 7 shows the relationship of the blind spot to the presumedfixation point in 20 cats. This graph has been prepared by making the rightand left presumed fixation points coincide with a common fixation point(F). The mean location of the blind spot with respect to F is given insystem C co-ordinates by the angles azimuth (aB) = 14-60 and elevation(EB) = 6.50 and in system E co-ordinates by position angle (b) = 24*40and deviation (X) = 16.00 without any significant asymmetry between thetwo eyes (Table 3). The way in which the angles oc, E, co and f have beenmeasured is indicated in the insert in Text-figure 7. An analysis of thescatter of the location of the blind spots is given below.

489

490 P. O. BISHOP, W. KOZAK AND G. J. VAKKURThe diameter of the blind spot, calculated as the angle subtended at the

node, has a mean value of 4-10 (18 cats). The position and dimensions ofthe blind spot are not significantly altered by changing the power of thecontact lens between OD and 2D, or by removing the lens. Taking themean diameter of the disk to be 0-93 mm, 4.40 of visual angle is equivalentto 1-0 mm on the retina. The value given by Barlow et at. (1957) is 4.50/mm.

TABLE 3. B* and OAt with reference to F

Angle Mean (0) S.D. (0) Range (0)aB Right +14-3 1.5 + 11-0 to +16-6

Left -14-8 1.1 -11-9 to -16-7eB Right + 6.4 1-2 + 3-8 to +7-9

Left + 6-7 1-3 + 4-5 to +9-2cuB Right 15-8 1.5 13-6 to 18-5

Left 16-1 1-3 12-9 to 18-6*B Right 24-2 4-5 14-6 to 32-0

Left 24-6 4-0 17-8 to 32-8xRB-aLB +29-0 2-3 25-2 to +33-0cBB+ZLB - 0-4 1-3 - 3-8to +2-1eRB-ELB - 0-3 0-9 - l9to +1-4ORB-wLB - 0-4 0-5 - 29to +1-2IfRB-VfLB - 0-4 4-5 8-6 to +7-4oaOA Right +11 4 + 7 to +18

Left -14 6 - 6 to-25EOA Right - 1 3 - 5 to +2

Left 0 2 - 2 to +1wOA Right 12 4 8 to 18

Left 14 6 5 to 25VkOA Right - 5 12 -19 to +10

Left - 1 6 -lOto+5* Mean of 20 cats; t Mean of 9 cats.

Analysis of factors determining the location of F and B. As indicatedabove, the centre of the area centralis can be estimated ophthalmo-scopically with an accuracy of about 20, and, with respect to the centre ofthe optic disk, the error is much less than this. Apart from these errors,scatter in the location of F and B can be due to a number of factors,namely: (1) variations in the location of the head in the stereotaxisapparatus, (2) the displacement ofthe eyes in their orbits or (3) to anatomicalvariations in the position of the landmarks in the fundus.

It will be convenient to consider first the scatter due to location of thehead in the stereotaxic apparatus. The nodal point of the eye is very closeto the infra-orbital margin (H-C reference level) and separated from itonly by a portion of the eyeball whose over-all dimensions vary less than+ 1 mm (Vakkur, Kozak & Bishop, unpublished). Thus most of thescatter in the direction of the visual and blind axes will be due to changesin the shape and location of the external auditory canals rather thanvariations in respect to the infra-orbital margins. From our measurements


of the accuracy to be expected of the H-C method (Bishop et al. 1962) it islikely that variations in these canals will lead to shifts in this region thatare always less than + 15 mm. Estimating the anterior H-C co-ordinateof the infra-orbital margin to be about 48 mm these shifts would lead to acombined maximum variation in the direction of a visual axis of less than+ 20. Analogous considerations indicate that rotations of the head aroundan anteroposterior axis would lead to a maximum rotation of the planeof fixation with respect to the H-C horizontal plane of less than 3°. Asfar as the centre of the visual field is concerned corresponding variations inthe angles 8, y, a and E would be much less than this. Rotations of the headaround axes other than the anteroposterior lead to displacements of theeyes which are equivalent to the four conjugate movements of dextro-,laevo-, supra- and infra-version.

During paralysis movements of the eyes in their orbits are due to passiveanatomical forces, so that they do not resemble the active movementsrequired for normal binocular vision. Apart from rolling only the foursymmetrical movements are likely to occur, namely supraversion, infra-version, convergence and divergence. Anatomical variations in the funduswill cause a scatter in the points F and B in symmetrical directions in thetwo eyes in a manner analogous to the passive movements described above.From an analysis of the data we have obtained it is possible to get someidea of the scatter that results from the operation of the above factors.Variations due to possible rolling of the eyes round the visual axis cannotbe estimated as such, but will appear as variations in the values of thevarious angles 8, y, oa and e.

Since the H-C variations other than rotations round an anteroposterioraxis always cause conjugate displacements of the eyes they are easilyeliminated from our data by plotting the right-hand points (FR) withrespect to a common left fixation point (FL). In Text-fig. 6C this has beendone by shifting the two points FL and FR so as to make the point FL inall the cats coincide with the mean position &LF = 2.50, YLF = 12-3°.This procedure eliminates the variations due to the H-C method both inthe horizontal and vertical directions and the effect of rotation of the headabout an anteroposterior axis can be neglected in the central part of thefield as far as the angles 8 and y are concerned. In addition the effect ofdisplacements in the vertical direction due to symmetrical anatomicalvariations and symmetrical movements of the eyeballs are eliminated.Thus the vertical scatter shown in Text-fig. 6C (given by the expression,YRF -yLF) represents the combined residual displacements of the pre-sumed visual axis due to inequalities in the anatomical variations and eye-ball movements. In respect to Text-fig. 6B and C it is important toappreciate that declination (8) is measured to the left and to the right of

491

492 P. O. BISHOP, W. KOZAK AND S. J. VAKKUBparasagittal planes passing through PL and PR. The latter are separatedfrom one another by the distance between the nodal points of the twoeyes.The range of the residual displacements of FR in the vertical direction

(Text-fig. 6C) is equivalent to approximately ± 1.60 (S.D. 0 90) for each eye.This scatter approximates the possible experimental error associated withthe location and plotting of F (i.e. about 2°). The location of the centre ofthe blind spot is much less subject to experimental error; nevertheless thescatter in the values of the two expressions (YRB - yLB) and (YRF -yLF)from cat to cat was almost the same, namely 3.30 (S.D. 0-90) and 3-20(S.D. 0 90) respectively (Table 2). Hence this residual scatter, about + 1.60in each eye, is probably mainly due to true anatomical variations andresidual differences between eyeball movements rather than errors in thelocation of the centre of the area centralis. A systematic error in theidentification of the centre of the area centralis would, however, beeliminated in the vertical direction in Text-fig. 6C.The scatter of the points FR in the horizontal direction in Text-fig. 6C

is given by the expression (8RF- 8LF). The apparent increase in scatterin this direction is due to the combined effect of symmetrical anatomicalvariations and the symmetrical movements of convergence and divergence,none of which are eliminated by the method of plotting but are in factadditive in each case (i.e. if the two eyes diverge, then divergences add).The scatter in the values of the two expressions (SRB- SLB) and (8RF -8LF) from cat to cat was almost the same, namely 11-5° (S.D. 2.90) and11.30 (S.D. 2 70) respectively (Table 2). Hence again, errors in the locationof the visual pole are probably not a significant factor as far as scatter inthe horizontal direction is concerned.In the horizontal direction the values of the symmetrical variations can

be calculated in this way because by definition the primary or zero positionof the eyes is known, namely when the true visual axes are directedstraight ahead. The mean amplitude of the symmetrical displacements ofthe eyes in the horizontal direction as a result of anaesthesia and paralysisis given by the mean declination of the presumed visual axis (i.e. 2*60 inboth directions), since all other sources of variation will tend to cancel oneanother. The only uncertainty that remains is the possible discrepancybetween the presumed visual axis and true visual axis. Similar calculationsabout symmetrical variations in the vertical direction cannot be made,because the zero position of the eyes is not known, the angles beingmeasured from the arbitrary zero point P.Assuming that there has been no rolling of the eyes, and apart from

errors in the location and plotting of the points, the scatter in the positionof the blind spots (Text-fig. 7) depends only upon anatomical variations


within the given eye. The mean position of the centre of the blind spot isacB = 14-60, EB = 6.50 with no significant asymmetry between the twoeyes. The pattern of the scatter is approximately symmetrical about themean position in each eye (S.D. 1- -1-5°) and the same for both eyes, therange of the scatter being about + 2.50. Just how relatively small thescatter is can be gauged from the fact that all the centres of the variousblind spots fall within an area very little larger than the size of the blind

WLB

wOAf 1724(L

16

20 ~~15 * *B1 4

18 F- 116,, 1

1 A 131415161718192001 B12 - 90 LB108.6 7 6

42 6-

014 1516 17 18192005.'B

440 50 60 70 80eRB

Text-fig. 8. A, correlation between the angle wB of the blind axis and the angle wOAof the optic axis in the same eye in a series of 9 cats. +, 0)LOA against WLB;ED, GROA against WR B. B, correlation between the angle X for the blind axes insame cat (i.e. wcLB against WRB) for a series of 20 animals. The line of symmetry isshown on the graph. C, correlation between the elevations of the blind axes in thesame cat (i.e. eLB against ERB) for a series of 20 animals. The line of symmetry isshown.

spot itself. No doubt much of this variation is due to the uncertainty in thelocation and plotting of the presumed fixation point F, the scatter beingsubsequently transferred to the blind spot in Text-fig. 7 because, in theplotting, all the points F have been made to coincide. Nevertheless, theuncertainty in the location and plotting of F is significantly less than thatsuggested by the scatter of the blind spots in Text-fig. 7, because there is acorrelation between the position of the blind spots in the two eyes of agiven cat (Text-fig. 8B and C). The standard deviation of the expressions(OCRB + aLB) and (ERB -'EL B), which are 1-30 and 0.9, respectively, wouldbe 1'9' and 1.80 respectively in the absence of such a correlation.

493

P. O. BISHOP, W. KOZAK AND G. J. VAKKURThe following conclusions can be drawn from the above analysis. The

centre of the area centralis (and hence the point F) can be determinedophthalmoscopically to within about 20. In the anatomical position ofrest the mean location of F with respect to the H-C reference system isgiven by SF = 2 6°, yF = 12'6', the scatter to be expected about thismean position from all causes being about + 5°. By definition the declina-tian of the true visual axis in the primary position is zero. Although thelocation of the true visual axis remains uncertain, its declination probablylies between 0.00 and 2.60 in the anatomical position of rest (cf. Ganser,1882a, b; Chievitz, 1889; Sefton, Stone & Vakkur, unpublished obser-vations). By analogy with the declination value and the fact that thescatter in the location of F and B is small and symmetrical about theirrespective mean positions, it is likely that the inclination (y) of the truevisual axis is also close to that taken up by the presumed visual axis inthe anatomical position of rest. Thus the anatomical position of rest of theeye is probably very close to that of the primary position. Much of thescatter in the location ofF in the anatomical position is due to symmetricalvariations in the two eyes in a given cat so that due allowance can be madefor it.

Optic axisBy using the Purkinje-Sanson images produced by a slightly modified

version of the reversible ophthalmoscope it was possible to get an approxi-mate estimate of the position of the optic axis. The images were observedat a viewing angle of about 100 from the light beam. The contact lenseswere left in place since their removal did not alter the position of the opticaxis significantly (2 cats). The optic axes of 9 cats were projected on to thetangent screen (Text-fig. 7), the mean values for the direction of the axisbeing given in Table 3. There was a fairly wide scatter in the direction ofthe optic axes, partly due, no doubt, to inaccuracies in the method. Mostof this scatter, however, concerned the deviation value (cwOA), since therewas relatively little in the vertical direction. No explanation can be givenfor this pattern of scatter. The optic axes were roughly symmetrical aboutthe zero meridian in a given animal, and there is a fairly linear correlationbetween the angle cuB and cuOA in all the eyes that have been examined(Text-fig. 8A). These correlations presumably indicate that the generalpattern of the scatter is of biological origin.The optic axis lies approximately in the presumed fixation plane and at

an average value of 130 lateral to the visual axis, so that when the pre-sumed visual axes are parallel the optic axes diverge by 260. Thus OA isabout at the level of F and below B. The angle alpha in human ophthal-mology is defined as the angle formed at the nodal point between the visual

494


and optic axes. We have used the symbol ac in a different sense, but whenused with respect to the optic axis the angle designated is virtually thesame whichever sense is intended. This follows from the fact that the opticaxis in the cat lies very close to the presumed fixation plane. Johnson(1901) found the divergence of the optic axes in the cat to vary between 140and 18°, whereas Duke-Elder (1958) gives the divergence as 260; in manthe divergence is 100.

DISCUSSION

Anatomy offunduwThe structure of the subprimate mammalian retina has been little

studied and most of our knowledge dates back to the second half of the lastcentury. Muller (1861) first identified the area centralis in mammals,similar in structure to the macula lutea and recognizable by a similarconfiguration of central blood vessels as in man. The first accounts of thestructure of the cat's retina appear to be those of Ganser (1882a, b) andChievitz (1889), and relatively little has since been added to these earlydescriptions. Ganser described the arcuate course of the optic nerve fibresskirting the conical mound of accumulated ganglion cells formed at thecentral area. The distance from the edge of the optic disk to the peak ofthe mound is given as 2-4 and 2-8 mm respectively in two cats. The regionof two-to-fourfold increase in ganglion-cell number lies within a radius of1-4 mm from the peak of the hillock. No fovea centralis was found.Ganser also made some important observations concerning the degener-ations that follow lesions in various parts of the visual system in kittens.Chievitz (1889) estimated the centre of the area centralis in the cat asbeing 2-5 mm from the centre of the optic disk, the diameter of the areabeing about 1-2 mm. He also noticed that the area of specialized photo-receptors lay 0 5-1 0 mm lateral to the centre of the area centralis, but heregarded this as an artifact resulting from his method of preparation.Chievitz also made quantitative observations on the density of cell nucleiin the three retinal layers, in different regions from the central area to theperiphery. His data show that the greatest density of nuclei in theexternal nuclear layer is about 1 mm temporal to the centre of the area ofaccumulated ganglion cells (i.e. area centralis). Chievitz explains therelatively reduced density of nuclei in the outer nuclear layer oppositethe area centralis as being due to the increased density of cones in this area.The cones have a larger diameter than rods; there are therefore less nucleiper unit area in the outer nuclear layer in this region. Krause (1895)described a slight fovea on the inner aspect of the area centralis, butKolmer & Lauber (1936) were unable to confirm this, using in vivo stainingwith methylene blue. Nor have we seen any evidence of a fovea centralis.

495

P. O. BISHOP, W. KOZAK AND G. J. VAKKURZurn (1902) reported a very small external depression or external fovea onthe tapetal aspect of the retina in dog opposite the area centralis. Camp-bell (1961) has published a brief description of the fundus of the cat's eye.It is clear that a detailed study of the structure of the retina of the cat andother subprimate mammals is required, particularly in respect to thecentral area. The same may be said about the dioptrical mechanisms,since the only papers specifically concerned with the optical propertiesof the cat's eye seem to be those of Hartridge & Yamada (1922), Marg &Reeves (1955) and Marg, Reeves & Wendt (1954). The aim of Lashley'sinvestigation of the structure and dioptrical mechanism of the rat's eye(Lashley, 1932) has much in common with that of the present paper and,similarly, Davis's (1929) study of the rabbit's eye contains much valuableinformation. Parry (1953) has studied the structure of the dog retina, buthis paper does not include much that is relevant to the present study.

Position of the eyeThe main aim of the present paper was to provide the knowledge about

the eye that is necessary in order to determine the projection of the visualfield on to the LGN. Our first consideration was to determine an axis andplane of reference for the eye by which to define location on the retina.The visual axis we have used is probably very close to the true visual axisand our fixation plane is similarly very close to the fixation plane for theprimary position of the eyes in the conscious animal. No precise informa-tion appears to be available in the literature regarding the relationshipbetween the anatomical position of rest and the primary position of theeyes, and only man seems to have been studied in this regard (cf. Cogan,1956). This is somewhat surprising, since the position of the eyes duringanaesthesia is of considerable interest in relation to the surgical correctionof strabismus. In man, after complete ophthalmoplegia or in death, theeyes are directed straight ahead or, more usually, are slightly divergent(cf. Duke-Elder, 1932). During surgical anaesthesia when the extra-ocular muscles are devoid of electromyographic evidence of innervation(Breinin, 1957) or when the muscles have been paralysed by drug action(Duncalf & Jampel, 1961) the position assumed is again usually slightlydivergent and without upward rotation. If the basic anatomical positionis one of divergence, then a basic stress tending towards divergence mustunderlie whatever position the eyes assume in consciousness. With normaltone the position of the eyes when all stimuli but those for binocular visionare present is called the physiological position of rest. In man this positionis usually not far from the anatomical position of rest and both usuallyapproximate, within a few degrees, the primary position of the eyes. It isinteresting that Stutterheim (1934) found that, in the European eye, the

496

QUANTITATIVE ASPECTS OF CAT'S EYEvisual axis in what he called the 'physiological primary position' was 3°divergent. He also studied the force needed to deviate the eye in baboonand monkey from the position taken up during anaesthesia and after death(Stutterheim, 1933). The eyeballs resisted passive movement, springingback to the same position of rest when released. Unfortunately Stutter-heim did not attempt to define the various positions of the eye (anatomicalposition, primary position, etc.) in quantitative terms with respect to thehead. It is possible that the slight divergence of the visual axes that wehave found in the paralysed cat may be due to the release of passive forcesconsequent upon the partial detachments of the jaw muscles in theoperative preparation of the animal. Another factor might be the separa-tion of the jaws required by our design of head holder.

Visual-field co-ordinate systemsThe co-ordinate systems that we have used to define direction in the

visual field have been fully described. It remains to outline the reasonsthat have dictated our choice of a particular co-ordinate system. Inspeaking of the projection of the visual fields on to the LGN the term' projection' is not used in any mathematical sense, but refers to a relation-ship which is defined by the laws of physiological optics and the histo-logical connexions between the retina and nucleus. The nature of this pro-jection is structurally determined. The system of co-ordinates used todescribe the visual field should be such as to represent or display this pro-jection in as meaningful a way as possible. Certain 'natural distortions'are already known to occur as the visual field is projected on the LGN,such as the relatively large portion of the nucleus concerned with the smallcentral part of the visual field. However, spurious distortions can easilybe introduced by an unwise choice of co-ordinates.The choice of a suitable system of co-ordinates for the visual field is a

difficult one. Ideally it should satisfy the following requirements:(1) It should be possible to measure the co-ordinates directly during the

experiment or easily to calculate them from the experimental data.(2) The transformation from one direction ofreference to another should

be possible by simple calculations. This is desirable because of the un-certainty regarding the precise location of the true visual axis. Shouldfurther evidence become available after the experiment regarding thelocation ofthe visual axis, the transformation to the new reference directionshould be easily carried out. Though these transformations present aproblem even if a perimeter is used to plot the field, further complicationsare, however, added by the use of a tangent screen.

(3) If lengths in the visual field are to be expressed in terms of the anglethey subtend at the anterior nodal point, the co-ordinate system should be

49'

P.O. BISHOP, W. KOZAK AND G. J. VAKKURsuch that the length of a degree of the co-ordinate system is constant overthe surface of the reference sphere and equal in every direction at anypoint. In other words the spaces in the grid of meridians and parallels onthe sphere should be equal everywhere (see below). Although this con-dition is impossible of fulfilment, its approximation is desirable, since anydistortions that occur in the projection maps of the visual fields on to theLGN would, to the extent of the approximation, then reflect the naturaldesign of the visual system rather than the consequences of the systemof co-ordinates.

(4) Every direction in the visual field should have unique co-ordinates.(5) The structure of the co-ordinate system should simulate the

vertical and horizontal structure ofperceptual space. While it is not possibleto infer neural organization from psychological analysis, the precise topo-graphical organization of the visual system becomes intelligible only onthe assumption that the maintenance within the visual system of astructural resemblance to perceptual space is essential for some phase ofthe visual reaction. Furthermore, the patterns of contraction of theextraocular muscles in normal movements of the eye must be referencedon a visual-field co-ordinate system in the brain having componentsrelated to the anatomical arrangement of the muscles themselves. Theextraocular muscles are organized in pairs so that, in general, movementsof the eye are resolved into vertical and horizontal components.

Actually co-ordinate systems A, B, C and D are nearly identical inrespect to the central part of the visual field. In all cases, if both a < 200and E < 20°, their differences are less than 1.10. The principal advantageof system C is that for small elevations above and below the horizontal thespaces in the grid of meridians and parallels are very nearly equal (cf.condition 3 above). This condition no longer applies for larger values ofelevation, but this is largely offset by the fact that visual fields are verymuch more restricted in the vertical direction than they are in the hori-zontal direction. The visual field can be regarded as a horizontal band. Thegreatest distortion in the grid of meridians and parallels occurs round thepoles, and system C is actually the only one in which the poles of thespherical polar system are outside the visual field.

The use of a perimeterWe are attempting to minimize calculations by developing a perimeter

which will enable us to measure the direction of receptive fields directlyin system C co-ordinates with respect to the presumed visual axis andfixation plane. It should be possible to shift such a perimeter readilyfrom one eye to the other and also to provide for an upward tilt of the

498


equatorial plane of the instrument so that it is adjusted to the actualinclination of the Fs in the particular cat. This is necessary, because forceddownward rotation of the eyes so as to make the fixation plane coincide withanH-C horizontal plane would lead to more ofthe visual field.being obscuredby the lower lid and infra-orbital tissue and it would also be extremelydifficult to retain the symmetry of the eyes so accurately achieved bysimple paralysis. Developments in this direction will not, however, greatlyaffect the importance of tangent-screen perimetry in work of this kind.Although our analysis of visual-field co-ordinate systems and eye

references is specifically related to the cat, it is nevertheless immediatelyapplicable to the primates. In the latter the visual-field co-ordinatesystem can be readily centred on the fovea recognizable ophthalmo-scopically although the problem of eye rolling remains. In the sub-primatemammals, however, additional problems arise when the eye becomes morelaterally placed in the head and the point of binocular fixation movesround the temporal retina towards the ora serrata. In the rat Lashley(1932) estimated that the retinal area dominant in binocular fixation wouldlie a little more than half-way between the disk and the temporal marginof the retina and in the rabbit (Thompson, Woolsey & Talbot, 1950) it iseven more laterally placed. Many mammals with laterally placed eyesprobably have two retinal areas specialized for acute vision, an areacentralis situated near the posterior pole for uniocular fixation and asecond area, situated in the temporal retina, for forward binocular fixation(Zurn, 1902; Prince et al. 1960). In some animals such as the rabbit thereis the possibility of a third area for posterior binocular fixation. Manybirds have developed two definite foveae for uniocular and binocularfixation respectively. The problem is still further complicated by Duke-Elder's contention that 'unless there is an area centralis of acute visionthrough which an animal orientates itself towards an object and aroundwhich spatial orientation is centred, the whole concept of fixation along avisual axis is meaningless' (Duke-Elder, 1958: p. 676). It is difficult toknow to what extent such a state of affairs exists, since a retinal area mightwell have some degree of functional (spatial) specialization in the absence ofany distinctive histological structure.

SUMMARY

1. An axis (presumed visual axis) and plane of reference (presumedfixation plane) for the cat's eye have been defined in relation to retinallandmarks and the Horsley-Clarke (H-C) system of co-ordinates.

2. A number of systems of co-ordinates were analysed in respect totheir usefulness for describing direction in the visual field. These co-

499

P. O. BISHOP, W. KOZAK AND G. J. VAKKURordinate systems have been fixed in relation to the axis and plane ofreference for the eye.

3. A system of spherical polar co-ordinates whose polar axis passesthrough the nodal point of the eye is regarded as best suited for describingthe projection of the visual fields on to the lateral geniculate nucleus. Theuse of tangent-screen perimetry in relation to this system of co-ordinatesis described in detail.

4. The fundus of the cat's eye has been studied both opthalmoscopicallyand in the excised methylene-blue-stained whole-mount preparation. Aquantitative description is given of the fundus, particularly the opticdisk, the arrangement of the blood vessels, the position ofthe area centralisand the boundaries of the tapetum in respect to the H-C reference planes.The centre of the area centralis, which can be estimated ophthalmo-scopically to within 0 5 mm, is situated at a mean distance of 3*42 mmfrom the centre of the optic disk.

5. The position of the eye in the paralysed cat has been studied inrelation to the H-C reference system. It is concluded that this positionprobably approximates very closely the primary position in the consciousanimal. A number of lines of evidence indicate thaat anaesthesia andparalysis probably cause little if any rolling of the eye around the visualaxis.

6. The presumed visual axis of the paralysed eye is inclined upwardsand is slightly divergent with respect to H-C horizontal and sagittal planesrespectively. The mean divergence (declination, 8) for one eye is 2.60 andthe inclination (y) is 12.60.

7. The directions of the presumed visual axis and the blind axis havebeen analysed both with respect to each other and to the H-C system ofco-ordinates. The factors determining the direction of these axes havebeen investigated.

8. The H-C co-ordinates of the nodal point of the eye have beendetermined.

9. The optic axis lies approximately in the presumed fixation plane andat an average value of 130 lateral to the visual axis.

This study was aided by grants from the National Health and Medical Research Councilof Australia, from the Ophthalmic Research Institute of Australia and from the Post-Graduate Medical Foundation of the University of Sydney. The views expressed by theauthors are their own and not necessarily those of the bodies mentioned. We wish toacknowledge the skilled assistance given by the technical staff ofthe Physiology Department,particularly Mr J. Stephens, Mr D. Larnach and Mr B. McGee and to express our thanksto Miss S. JphInp, and Miss H. Hunter for much bibliographic and secretarial assistance.

500

QUANTITATIVE ASPECTS OF CAT'S EYE 501

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BREININ, G. M. (1957). The position of rest during anesthesia and sleep. Arch. Ophthal.,N.Y., 57, 323-327.

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uber das Corpus bigeminum anterius. Arch. Psychiat. Nervenkr. Bd. 13: 341-381.HARTRIDGE, H. & YAMADA, K. (1922). Accommodation and other optical properties of the

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KOLMER, WV. & LAUBER, H. (1936). Haut und Sinnesorgane, 2. Teil, Auge. In Handbuchd. Mikroskopischen Anatomie des Menschen, MOLLENDORFF, W. ed., 3 (2).

KRAUSE, W. (1895). Die Retina. VI. Die Retina der Sauger. Int. Monat. Anat. Physiol. 12,46-186. Cited by ZURN, J. in Arch. Anat. Physiol., Lpz., Anat. Abt. Suppl. Bd. 99-146.

LASHLEY, K. S. (1932). The mechanism of vision. V. The structure and image-forming powerof the rat's eye. J. comp. Psychol. 13, 173-200.

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PARRY, H. B. (1953). Degenerations of the dog retina. I. Structure and development of theretina of the normal dog. Brit. J. Ophthal. 37, 385-404.

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EXPLANATION OF PLATES

PLATE 1

Composite fundal photograph of the tapetum of the right eye of a cat obtained by piecingtogether a large number of separate findal photographs. The two radial 'cuts' whichallow the composite photographs to be artificially flattened have been hidden by insertsindicated by the two arrows. The tapetum is smaller than usual. Retouched.

PLATE 2

A. Unretouched fundal photograph of the region containing the area centralis and opticdisc. The estimated centre of the area centralis is indicated by the intersection of linesX-X1 (presumed fixation plane) and Y-YL (zero meridian). The three black spots in thecentre of the photographs are artifacts produced by the fundal camera.B. Photograph of a methylene-blue-stained whole-mount preparation of the right eyeshowing the same region of the fundus but in another cat as in A. The area centralis isindicated by the conglomeration of ganglion cells in the centre of the photograph and theoptic disk is in the bottom right-hand corner. For further details see text.C. Area centrals and surrounding retina as in B but under higher magnification. Largeand small ganglion cells can be distinguished. The clear 'channels' are blood vessels.

The Journal of Physiology, Vol. 163, No. 3

P. O. BISHOP, W. KOZAK AND G. J. VAKKUR (Facing p. 502)

Plate I

The Journal of Physiology, T'ol. 163, NAo. 3 Plate 2

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P. 0. BISHOP, W. KOZAK AND G. J. VAKKUR

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