the act of the chart and argentina’s military...to think about the problem, beljajev wrote down,...

- Bueno Aires at night [Source: http://earthohservatory.nasa.govJ.

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Triangulation adjustments in Buenos Aires—by Albert H J Christensen

A long time ago, 40 years precisely, a colleague and a friendAifredo V Elias, and 1 worked on the adjustment of the triangulation known as the Argentinean Fundamental Network (RFAfor the Spanish “Red FundamentalArgentina”). 1/don’t know ofany publication other than an out-of-print chronicle2 that fullycovers the 40 or so years during which the RFA adjustmentswere made. In particulai nothing has been written about a tightrace between two methods and the lives of their champions.Missing are also detailed accounts of the successful (or notso successful) adjustments carried out by hand or by computerSo I decided to put into writing not a history of those yearsbut my memories of what I had witnessed or heard, with thehope that the result might be of interest to the readers of theACSM Bulletin. The RFA project. which was made possible bythe efforts of Dr Fischer and Mr Byars at the Army Map Service, brought Elias and myself to the U.S. in August 1968 with adouble purpose: to assist the old Americas Division of the ArmyMap Service in the adjustment of the RFA sections completedat that time, and to develop our own adjustment program. Intime I will say a few words about the project and what followed upon our return to Buenos Aires. But first I will describesome of the circumstances and facts which shaped the adjustment problem, and the contest alluded before—both of whichlong preceded our trip to the U.S.

The Act of the Chart and Argentina’s Militarygeographical InstituteThe work on RFA started in the early 1 940s, thanks to theenactment of the federal Act of the Chart. That doesn’t meanthat before that time Argentina had not done any geodetic orcartographic work. On the contrary. But all that work by theArgentinean Military Geographic Institute (1GM in Spanish) led

to disconnected systems, was measured at diverse times withnon-uniform equipment and procedures, and covered less than10 percent of Argentina’s territory. Under the aegis of the 1GM,a group of enlightened statesmen—a breed in progressiveextinction since then—gave final form to, and voted for, theAct. The work legalized by the Act was entrusted to 1GM, to becompleted in 30 years.

From early in its history, 1GM drew its senior civilian personnelmostly from two excellent national universities—Buenos Aires andLa Plata—as well as from the vast German pool of highly trainedprofessional geodesists.3 Although all of that happened long beforemy time and I could meet face-to-face with only Herr Under, the lastof them, occasionally, I would find their traces in the 1GM archivesor hear of them from old-timers.

In the early years of 1GM, not only the geodesists were ofGerman origin; most field and office procedures and equipment were also German. There were exceptions, of course:among them it is worth mentioning the apparatus designed byE. Jäderin, a Swedish instrument maker, for measuring geodetic bases with invar wires manufactured by the mini Aciéne d’lmphy. Argentina purchased four Jäderins in 1904, withthe first ever calibration certificates (Nos. 1 to 4) issued bythe Bureau International de Poids et Mesures. Another exception, and a most impressive one, was a four-meter comparatormanufactured by the Société Genévoise U ‘Instruments de Physique, for the calibration of wires and other devices.4

The influx of German geodesists ceased some time before theonset of NVI II. After the war, 1GM again welcomed a number ofEuropean scientists and engineers. None from Germany, though.

In the 1 940s, with a workforce that numbered in the thousands, 1GM was fully committed to implement, in 30 years, thetasks enunciated in the Act of the Chart, and so cover Argentina with 1:50,000 cartography (1:100,000 in mountainous

16 I ACSM B’JLLETIN I OEcEMBER 2007

TRIANGULATING ARGENTINA

areas). In 1 952, when I started workingat the Computing Division, the funds forthe Act retained a good part of its original value, and the work didn’t seem tobe lagging behind schedule. The projectof interest to my group at the Computing Division—RFA—was well on itsway, with the triangulation accuratelymeasured and scrupulously marked anddocumented.

Argentinean (pre-OPS) horizontalgeodetic networksArgentina is covered by a hierarchy ofgeodetic networks, at the top of whichlays the RFA, a framework made ofchains of quadrilaterals with double diagonals running roughly every two degreesof latitude and two degrees of longitude,plus a chain of triangles.5 On flat areas,the quadrilaterals look very much likesquares but they’re nothing like those inhilly zones, near or in the Andes.

The RFA can also be described as consisting of 50 or so loops of chain sections.At each crossing of the chains there is abase—its expansion parallelogram—anda Laplace station. Laplace stations couldalso be found in the middle (more or less)of every meridian section. At each station, RFA directions were measured witha relative weight of 18 and designatedas First Order chains. The base expansion parallelogram was measured withweight 24.

This fundamental framework supportsfour lower orders of triangulations:• Filling nets made of directions mea

sured with weight 9 (Filling Net FirstOrder) inside each RFA loop

• Second Order triangulations insideeach chain and filling net, measuredwith weight 6.

• Third and Fourth Order triangulations.All the First and Second Order triangula

tion were placed, marked, and measured bygeodetic field parties. The Third and FourthOrder triangulations were measured bytopographic field parties. Needless to say,GPS points appeared long after the facts Iam going to describe here.

The computations raceIn 1952, both fieldwork and the datareduction for the RFA were well ontheir way—to everybody’s satisfaction.

But the computation of RFA didn’t lookso good, because the method for solvingthe normal equations (a critical step inthe RFA adjustment) was still undecided.The Computing Division had discussed,for months on end, two radically differentmethods—with no conclusion in sight. Toput an end to the impasse, Guillermo RiggiO’Dwyer, the Division Chief, proposed acontrolled and clocked competition [fromhere on the “contest”] between the twomethods and their champions.

Unfortunately I did not witness thecontest for I came to work at the GMone or two years later. There are nowritten reports that I know of, not evenin Spanish, of this unique event, and alleyewitnesses have long since passedaway. Here is an account based onmy recollections of the comments andstories I heard about the contest. Notall will be hearsay evidence, though, forI can attest to the consequences of thecontest—the smoldering resentmentthatpersisted to the very end between thechampions and their supporters, and thesuccesses the winner enjoyed and theproblems he faced while implementinghis method.

The contestantsTo implement the tasks mandated by theAct, the Military Geographic Institute ofArgentina needed people with first-handexperience in highly complex technicalprocedures. Nothing scared 1GM morethan the prospect of adjusting the RFAwithout such expertise, and, becausethere were no such experts to be foundin Argentina, IGA set its eyes on Europe.A commission travelled to Europe with amandate to find and engage experts invarious mapping disciplines.

Among the scientists they found weresuch giants as Nikolai Beljajew, a mathematician with a PhD in Celestial Mechanics from an imperial university the nameof which I cannot remember, and Alex-andre Corpaciu, from Romania, of whoseexistence before his arrival to ArgentinaI knew nothing about. Stjepan Horvat, anengineer from Zagreb [Yugoslavia], whohad considerable experience in geodeticcomputations—and was my mentor onGeodesy—arrived about the same timeas Beljajew and Corpaciu, but via a different route.

Beljajew was hired to help develop algorithms for solving large equation systems;there was probably nobody else better qualified for the job. I remember bringing once tohis attention a system of differential equations I could not solve. Without pausingto think about the problem, Beljajev wrotedown, at full speed, six or seven solutions.Granted, some of them were similar, but atthe time, I could not hit on even one—andI considered myself to be quite good inmath! Next class, the tutor announced thatwe need not submitthe homework because,

“that particular differential system had nosolution.” “C’mon”—l objected—”not onlyis there a solution, there are more thanone!” and I gave him my sheet. Needlesslyto say, I couldn’t claim authorship; the solutions were well above my head ... and ourtutor’s as well.

In something else could I never measure up to Beljajew—his taste in shoes!Candidate5 Beljajew was an expert shoemaker, and he always wore only shoesthat he himself had made. That skillhelped him keep body and soul togetherduring the 1921 calamitous Russian

From left to right: G. Riggi O’DwyeiNikolai Beljajew, and Stjepan Horvat.

OECEMBER 2007 I ACSM BULLETIN I 17


famine; nobody needed a mathematicianbut everybody needed shoes.

Beljajew’s method for solving the normalequation in a geodetic adjustment yieldeda good number of long, complex calculations. Sometimes, when a verification failed,we would spend hours trying to locate thesource of the error, until, frustrated by ourfumbling, Beljajew would unfold a king-sizesheet of paper, and with his eyes very closeto the form but his thick eyeglasses on hisforehead, he would scan the sea of numbers as a bloodhound. Then, suddenly, hewould raise his head, point at a value, andsay, “check this!” He was right on the markmost of the times.

Like Beljajew, Stjepan Horvat also had avocation. He chose cooking and becamean artist in the kitchen. Those of us whohad tasted his hors d’oeuvres believedhe could have earned ten times his 1GMsalary as a chef—and his pay at 1GM

followed to compute any oneproperty, the resultant valuewill be the same.

The general method tobe used for the RFA adjustment wasleast-squares adjustment with conditionequations, and by 1950, procedures wereset up for the use of this method, But, themethod for resolving the normal equationscontinuedto beasourceof heated discussion.The need for an efficient method wascmcial because, in principle, the complexityand time of an adjustment grows with thesquare of the number of condition equations.Precisely how to reduce that growth tosomething more manageable than a squarewas at the heart of the contest.

The 1GM had already set thousands uponthousands of permanent trigonometricmarkers across Argentina. It was desirablethat for each of these monuments, thediscrepancy in distance was no morethan 10 cm to the nearest monument. Thatpresupposed a network of perfectgeometly.However, achieving this goal proved illusive,as all the established horizontal networks(between five and ten percent of theplanned total), were hung from unadjustedRFA sections.

Ideally, the adjustment should havebeen executed on the complete RFA. Beingrealistic, however, 1GM had to compromisewith something less than ideal, in order

21iito satisfy users who couldn’t wait untilthe whole RFA would be completed (30years at best). The compromise consistedof a gradual annexation and adjustmentof sizable chunks of new loops to thepreviously adjusted RFA core—very muchin the manner of the [then] Geodetic andCoast Survey adjustments in the States.The annexation procedure had to bedesigned in such a way as to save as muchof the previous computations as possible.7

From the practical point of view, andin order to minimize the time spent onthe solution of the normals, the workloadneeded to be organized in such a mannerthat multiple teams would be able towork simultaneously on different areas ofthe network. Imagine applying the divide-and-conquer principle to a tightly linkedand complex set of thousands of normalequations (between 4000 and 5000 for thecompleted RFA).

Electronic computers powerful enoughfor that task were long in coming toArgentina. It was therefore impossible toavoid gross errors, although a great deal oftime and ingenuity was spent attemptingto correct for them. Especially devastatingwas the omission of terms in the block

LT°f -°

IPhysics, and Geodesy atuniversities and militaryschools and lectured on FineArts at Argentina’s NationalAcademy. More often thannot, O’Dwyer found himselfacting as the ombudsman inthe not infrequent disputesamong the senior membersof his staff. The contestwas born out of one thosedisputes.

The need for geodeticadjustmentThere are two reasons fora geodetic adjustment: toensure the geometric “perfection” of the adjusted network,and to localize and reduceerror in the measured values.In a perfect or consistent network, no matter what path is

I5H

56

132

n - I.f7’(lFA )7fLin1dng T7 \_.- 70I X I 2nd Ordnr I X I Fi1ai, ..4st C)rdnr / 2nd O,do,

onnued],_) j,/ Filling ont

- / Filling n,t 12 Qondinlatmts

Figure 1. Unit 4H of Argentina’s geodetic network.

was by no means insignificant. Becausehis family remained in Yugoslavia (thosewho survived the war), and becauseHorvat preferred to dine in company, heused to regale his young Argentiniancolleagues with exquisite dinners thatbegan with slibovitz and ended withbarackpálinka.

Horvat studied Engineering at ZagrebUniversity but he had long workingexperience in geodesy and cartography.Many times he went over and above hisresponsibilities to correct field and officeprocedures, which, if left uncorrected,might have seriously embarrassed 1GMscientists and staff. He had a knack ofinstantly perceiving weaknesses that thetheoreticians did not see. And, he wasalways ready to give advice and help ifthe party in charge of certain procedureswas ready to listen.

Needless to say, that was not alwaysthe case, as the resentments born fromthe contest shut the ears of many ofmy colleagues for a long time to come.Horvat was one of the protagonists inthe contest for better procedures, takinga middle position in both its genesis andaftermath.

Lastly, I must mention a native talent—Guillermo Riggi O’Dwyer, the formidableformer chief of the Computing Division. Agraduate of the School of Engineering,Buenos Aires University, O’Dwyer was areal “polymath;” he taught Mathematics,

18 I ACSM BULLETIN I DECEMBER 2007

IN PERSUIT OF GEOMETRIC PERFECTION

Alexandre Corpaciu proposed the use ofHans Boltz’s (1923) procedure for theadjustment of geodetic networks usingleast squares. The reason being (asstated by Boltz), that through partial andgradual adjustments, “the results wouldcoincide with those of a simultaneousadjustment of the completed network.”Given the stated outcome, the Boltzmethod would have been particularly apthad the 1GM stuck to its original plansto provide adjusted chunks of RFA apacewith advances in measurement.

But, 1GM didn’t really want to keepdelivering different coordinates everytime a new adjustment was carried out,because the new adjustments would beforced to accommodate old conditions.

In reality, Boltz’s description refers to thepartial additions of equations carried outwithin the same or successive adjustments,which would change the positions alreadydelivered to users.

Corpaciu proposal could not have beenbacked by more authoritative sources andfacts: according to Otto Eggert (Travauxde l’Association Internationale de Geodesy,vi 5), Boltz’s method was successfully put touse in one of the early German adjustments.I understand that the same could be said ofa later (ca. 1950) adjustment of a Europeantriangulation.

I never did any work with Boltt’sprocedure; the events I will soon narrate willexplain why. Those readers with more thanan historic interest on Geodesy can find anexplanation and example of Boltt’s methodin Jordan and Eggert (1961, § 114).

Beijajew’s solutionNikolai Beljajew proposed his “LinkingShapes (IS) method (“Figuras de Enlace”in Spanish”), which combined Helmert’s(1880) block elimination method withPranis-Pranevich ideas on the simultaneouselimination of unrelated blocks of unknowns.The “shapes”—quadrilaterals (or pairs ofadjacent triangles) at the intersectionsof RFA chains (Figure 1)—were entered

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Figure 2. Section of Ill Common form.The key to the figure: Equations are read in columns. Rows list coefficients. Figure 1 should be consultedto better understand what follows. The letters A and B in column headings respectively designateLaplace and base equations; ‘2 and 13 point to three sections of the horizonal chain I. So letterA withthe subscript I designates the Laplace equation formulated from chain section I,. The letter E identifiesthe linking shapes (IS). Four pairs of columns without headings are shown. The columns on the left ofeach pair list RFA members (chain sections, quadrilaterals and linking shapes). The columns on the rightlist correlative designations in the equations associated with the RFA members listed in the adjacentcolumn. The correlatives (K) for side equations are superscripted with the quadrilateral number (Arabicnumerals). 1(11 designates the side equation derived from quadrilateral 11 (the IS in the Southeastcorner of Figure 11. The same applies to triangle correlatives, with the addition of a subscript that pointsto the particular triangle within a quadrilateral. Thus 1(211 designates the equation derived from the 2’triangle inside quadrilateral 11. For chains of triangles (Chain section 4, part of the Meridian Arc project)the superscripts are Roman numerals; in Figure 3 there is only one: K’, the correlative associated withlinking shape II (Southwest intersection in Figure 1). Not all the other triangle unknowns belonging to ISappear: they were eliminated in computations preceding the compilation of form III Common. Dependingon their configurations, unknowns from triangle shapes were eliminated by had-hoc procedures. One ofthose unknowns was K. The rows labeled as co contain the independent terms for each of the equationsnamed in the heading.

eliminations of the normals during the in the adjustment as blocks of three (or Beljajew’s proposal included ingeniouscompilation of the “common” forms two) triangle equations, and one side ways of arranging equations and(Figure 2). equation (none in the case of two triangles) expressions. One of them, perhaps an

were formulated at every one of those original by Beljajew, was an improvement

Th , •. intersections. A block of unknowns was on the Gauss-Dooliffle’s method foriiit proposeu SO UiIOflS that set of unknowns directly related to solving sets of linear equations. The most

Gorpaciu’s solution a block of equations. distinct improvement was the usage

DECEMBER 2007 I ACSM B’JLL[TIN I 19


of “accordions”—forms folded alongcolumns of values—to facilitatemultiplications by columns.

The successive block eliminationswere structured as sets of formulae,all hand-written and easily understoodin the context of global adjustments.However, annexation of terms andequations from new RFA loopscould be a headache and a source ofconfusion for those of us not fully incommand of the method.

A good example of those criticalformulae was the “III Common” (Figure2) which incorporates coefficients andindependent terms from other forms. Tooutline and complete the adjustmentforms we were provided with verystrong, 48 x 36 cm paper, gridded attwo lines/cm. Some forms were solarge—we called them “bed sheets” or

“sábanas” in Spanish—that we had toglue two sheets together to fit them in.

As in all adjustment forms, thenumber of rows and columns of matrizIII Common was variable. I still have acomplete specimen. I rescued it fromthe fire following an order, given inanticipation of a naïve computer solutionof the normals, that all paperwork createdby the manual RFA adjustments shouldbe burned. The form is 44 columns wide(56 cm) and 30 cm high. The number ofrows varies between 40 and 60. It stillshows the folds we made to turn it intoan accordion. Figure 2 shows a smallpart (18 cm square) of the left side of thematrix as it looked after the resolutionof loops 4H and 5H and the annexationof loop 6H. More columns and rowswere appended with loops 4G and 5G9.The additions were made as soon ascorresponding fieldwork and preliminarycomputations were completed.

Elimination of unrelated hocksof unknownsIf we arrange the normal equations corresponding to a number of RFA loops withoutregard to sparseness and solve them withthe original Gauss method, we will end upfilling most of the originally empty positions.Part of the filling can be avoided by arranging the unknowns in blocks that can beresolved in terms of other unknowns in themanner suggested by Helmert.

The Helmert process can be improvedconsiderably for matrices derived fromtriangulation chains in loops by applyingthe ideas of Pranis-Pranievitch. A matrixconformed to those ideas would show

“Helmert blocks” grouped into “orders” insuch a way that blocks belonging to thesame order would be unrelated to eachother.

The arrangement was highly beneficialin the pre-computer age becauseit facilitated the distribution of theworkload to staff: blocks of the sameorder could be resolved by more thanone person working on the adjustment—simultaneously and yet independently.Today, the same benefit could be derivedfrom using parallel processors.

Either way, fewer matrix positionsto fill translates into shorter processing times and—especially important inthe manual mode—in smaller round-offerrors. The combined Helmert/PranisPranievitch approach thus enables betterallocation and utilization of resources.

Au illustration hy exampleTo better explain the mechanics of theHelmert/Pranis-Pranievitch approach, thereader is directed to a group of diagramsin Figure 3, which illustrate the solutionof a set of 9 loops with 24 chain sections(CS) and 16 Linking Shapes (IS) (Figure3a). Variation of coordinates is assumedto be the general method of adjustmentin use. As the orientation unknowns

©

are supposed to have been eliminatedbefore the formation of the normals, theLS in Figure 3a are more inclusive thanthose in Figure 1.

The diagrams in Figures 3b to 3e show thesorting of CS and LS blocks in nine ordersof elimination. The nine-order arrangementis optimal as regards efficiency (there areother optimal arrangements). The worst—consisting of 17 orders of elimination—does not conform to Pranis-Pranievitch’sideas.

Figure 3b represents the state of thenetwork after the elimination of the 1st orderunknowns (CS): 16 IS pairs were selectedby that elimination. Thick lines representpair relationship or connectedness. Out ofthe 16 IS, four (in turquoise) were selectedfor the 2nd order of elimination.

The next network configuration isrepresented in Figure 3c with three setsof blocks, each made of four IS unrelatedto each other. One set (light brown) ischosen for the 3rd block elimination.

In Figure 3d, the order unknownshave vanished. One of the two (in orange)remaining orders of four blocks eachis selected for the 4th order elimination.This operation connects each of theremaining four IS blocks (in violet, seeFigure 3e,) to the other three. They willbe eliminated in four steps. Three blocksare arbitrarily assigned orders from5th to 7th The first numerical values ofunknowns obtained are those from the8t order IS. The rest of the unknowns

•i •

_

I1 l •

©ORDERS of ELIMINATION

I1st 2nd 3rd 4th 5th to 8th

Figure 3. Elimination of unrelated blocks of unknowns.


GEOMETRIC GEODESY

are computed during the process knownas the backward solution.

An experiment conducted in 1972illustrates the advantage of the PranisPranievitch/Helmert approach (ProcessA) over the plain Helmert method(Process B). Bath processes used thevariation of coordinates method withthe same data: three RFA loops with 177trigonometric points organized into 10CS and 8 IS, with 886 observations and354 normal equations (the orientationunknowns were eliminated from theobservations).

Both adjustments considered the CSas order unknowns. Their elimination(Figure 3b) left all IS connected. Thereafter, the processes diverged. In processA, the IS blocks were optimally groupedinto four (from 2nd to 5th) orders of elimination. While in process B, the IS blockswere not associated in any way, as befitsthe Helmert method. Instead they wereeliminated one at a time, in eight steps.

An IBM /360 Model 50 was used forthe experiment. The CPU times for thesolution of the normals were 115 secfor Process A and 175 sec for ProcessB, proving conclusively the benefit ofutilizing Pranis-Pranievitch’s ideas inblock elimination. The difference in CPUtimes would have been much larger if,in the course of process B, sections ofchains were assigned orders 10t to1 0h, thus increasing to 18 the totalnumber of orders of elimination.

The outcome of the contestThe contest took place in 1950 or1951—regrettably before my time.Otherwise I would have been ableto instill in this account some of thesuspense and drama felt by the twoscientists whose very contractsdepended on the outcome of thecontest.

Each of the contestants wasassigned a pair of the best human

“calculators” the 1GM employed. Theirtask was to solve a set of 134 normalequations for loop 4H (Figure 1), twoof which were polygonal, four base,six Laplace, 28 side, and 96 triangle.

The day was won by Beljajew andhis linking shapes. His computingteam (two enthusiastic and reliableladies) solved, with his method, the

134 equations in two hours, using onlyon four pages for his clever schemes. Incomparison, Corpaciu’s application of theBoIt2 method took days of filling endlesscolumns of values—sixty pages of them(Beljajew 1953). According to one ofthe staff assigned to the Boltz solution,Corpaciu’s effort was doomed from day

with the wrong sign, so his sixty pagesonly led to correlatives that divergedmore and more from the correct solution.I never found out whether the solutionwas attempted again with the correctsigns.

After the contest, and as expected, thejudges, under Riggi O’Dwyer’s leadership,decided in favor of Beljajew version of theblock elimination method which uses Pranis

Pranievitch’s ideas. This was agreat win for Beljajew; his contractwith the GM was no longer on theblock. But, Corpaciu never sawhis renewed. He vanished—later Iheard that he had emigrated to theStates—but not without a partingshot at his opponent.

lnhispaperentitled”Contributiona I’étude de Ia compensation de Iatriangulation fondamentale argentine,” Corpaciu wrote: The methodof the linking figures expounded byN. Beljajew” (Bulletin Geodésique,n° 28, 1953) for the adjustment oflarge triangulations runs the riskof being incomplete (deficient,defective) and difficult to taketo a proper conclusion.” Not fair!Two years before Corpaciu’s prediction, with Beljajew’s methodand without a hitch, we did complete the adjustment of threeflEA loops.

T3 Wild, Heerbmgg (Switzerland), theodolitewith which the 1st order triangulation wasmeasured [Source: http://www.gmat.unsw.edu.au].

This Wild T4 theodolite and the Askaniameridian circle were essential for theLaplace stations [Source: http://www.ryerson.ca/archives/1.

one; he had entered independent terms

MADAS 2OATG electromechanical calculator withits extra second register for geodetic adjustment computations was an expensive ($3000 in 1952) but indispensable piece of equipment for the team. It was alsonoisy too—multiplying ten nines by ten nines createdsuch a ratchet that nobody could accuse us of beingidle. [Source of the image: http://www.rechenmaschinenillustrated.com/].



Manual and partial FEA adjustnientsAs soon as the method to be used wasidentified, about 30 new staff wererecruited (I being one of them) and trainedon the many separate tasks in which theadjustment process had been organized.The work was always carried out in the

“dual calculation mode,” a necessaryif expensive precaution to precludeordinary mistakes. Howeve there weresetbacks, due to the inexperience of thenew staff, myself included; none of uswas as experienced and attentive as thefour calculators who had taken part inthe contest.

Thankfully, some of the gross errorsmade in the solutions of the normalswere prevented from spreading by theinternal checks instituted by Beljajew,and others would have been correctedin time had the simple mechanismrecommended by Horvat been adopted.The procedure, always used in Europe,resorted to an extra column to receivethe sum of all rows in each form, laterto be treated as an ordinary column. The

procedure would have added some timeto the computations, but it would havebeen worth it. But, as with many otherHorvat’s suggestions, it was ignored.

From the already adjusted 4H loop,the manual adjustments proceeded asgradual annexations of new loops, toculminate in the adjustment of ten loops.This operation called for the formationand solution of 1121 equations andtook so long to complete that whenthis actually happened there were onlytwo of the original thirty or so staff left.Fortunately for Beljajew, they were thetwo ladies who helped him win thecontest back in the early 1 950s.

The 1 121 normals verified and so didthe condition equations. Regrettably,one of the last and definitive checks,the transport of geographic coordinatesacross the adjusted loops, did not verifyfor one of the loops. Presumably the errorwas in the computation of preliminarypositions by the Schreiber method. Theprecise location was never found, and nocorrection was ever made.

The error did not discredit the feat ofhaving solved rigorously a set of 1121equations with the sole help of MADASelectromechanical desk calculators. On thecontrary, the successful completion of thetask was the ultimate and an apt rebuttalof the missive delivered by Corpaciu in theBulletin Geodésique in 1 954.

This notwithstanding, the mistakesmade on the way proved that, inparticular, the formation of the conditionequations would have greatly benefitedfrom the attention of an experiencedgeodesist—which Beljajew was not. Hewas so preoccupied with the solutionof the normals that others soon startedequating the adjustment project withthis one step within the project. Thismisconception resurfaced during the firstattempt—a too charitable term for thatventure—to program the adjustment foran early electronic computer.

Following the solution of the 1121 equations, a few loops were adjusted forcibly toten polygons. All manual adjustment workceased around 1960 when 1GM adoptedelectronic computing.

Computerizillg the BFA adjustmentAround 1960, IBM offered 1GM time inits model 650 computer. Part and parcelof the offer was a programming course—the best I have ever attended—on theSOAP language, a kind of a simpleAssembler for the 650, with which weprogrammed a couple of tasks, the firstbeing the arc-to-chord corrections fordirections in the filling nets. The resultswere so good that 1GM decided topurchase the next IBM machine suitablefor technical tasks. “Suitable” must bequalified with a strong emphasis on

“relatively,” for that machine was a bare-essentials 1620—to wit, comprisingonly 20000 digits of magnetic corestorage, a typewriter, and a card reader!punch. The languages were an early andsimple FORTRAN and SPS, an exiguousAssembler. FORTRAN, in a machine aspuny as our 1620, was practical only forthe simplest programming.

Yet, little by little, we programmedfor the 1620 a handful of the heaviestComputing Division’s tasks. Despite theinjunction of military chiefs, we alwaysprogrammed in SPS. However, we

fl 650 computer. [Source: http.//www.computer-history.com.]


GEOMETRIC GEODESY

adjustment quandary, which, by the earlyseventies, had frankly become grievous.Beljajew’s team of lady computershad retired, and he had not been givenany replacements; meanwhile, newlymeasured RFA loops kept arriving fromthe field.

The programming of the RFA adjustmentwas assigned the highest priority. 1GMassigned the task to an Army officer, withBeljajew acting as instructor and counselor.

The 1620 and FORTRAN were the means,and after uncountable numbers of boxesof Hollerith cards had been punched andreread many times, the programming ofthe adjustment was declared complete.However, the “program”—only the kindhearted would mistake it for that—coveredonly the solution of the normals, which, initself, would have been valuable in alleviatingthe headache the RFA was giving 1GM. But,as some of us had feared, the “program”turned out to be unworkable.

At about the same time we’re tryingto come to terms with the botchedadjustment, the Computing Division wasdismantled, Riggi O’Dwyer passed away,and some of us went to work for the Geodesy Division, with Horvat as advisor. AndComputer Center was organized around theIBM 1620 and placed under the supervisionof an Army officer.

Finally we could try to do what madesense, that is, to start at the beginning ofthe adjustment and program the formation

will surely wonder why did we perseverein following this approach instead of themore computer-tractable variation of usingcoordinates. In fact, we discussed the latterat length and, although we understood thebenefits, we decided to stay with conditionequations because of our experience andthe numerical results we had to verify theprogramming..

This time we were going to program inSPS. I started with the polygonal equa

tions and, after a couple ofmonths, I had a programworking that yielded thedifferential expressions oflength and azimuth withminimal manual data entry,Concurrently, two colleagues “attacked” the otherconditions. But, we did notgo any further.

Programming at the ArmyMap Service and its usein Buenos AiresThe reason why we didn’twas an offer from the ArmyMap Service (see Fischer’sMemoirs in the ACSM Bulletin) to assist 1GM withprogramming for the RFA

adjustment. My friend and colleagueAlfredo V. Ellas and I travelled to the U.S.and, this time, we programed using coordinates—to the satisfaction of everybodyin AMS and 1GM. (More on this can beread in “Two Argentineans in the ArmyMap Service,”July/August 2005 issue ofthe ACSM Bulletin.)

We returned to Buenos Aires with theprograms and the preliminary design of anarchival system for geodetic data, as wellas a reduction of 1 order astronomic observations. The adjustment of 19 polygons ofthe RFA that AMS had carried out as partof an agreement arranged by David Byars(Fischer 2005) had previously been shippedto 1GM. According to Jack Reynolds, MrByars’ appointee to handle the data preparation, “No other work that AMS had everprocessed had a quality that approachedthat of the RFA, be it in documentation,field procedures, measurements, ordata reduction.” Indeed, the r.m.s of thatadjustment was 0.4 arc seconds.

In Buenos Aires, I undertook theimplementation of the adjustment program, with the Burroughs 3500 installedat the DISCAD (as the computer centerof the Joint Chief of Staff was called),while Alfredo worked on the reductionof the astronomical observations and theadjustment of filling nets using conjugate residuals.

It took me a month or so to confirmthe uselessness of the B3500 for complex technical tasks, so I installed theprograms on an IBM /360, which, underOS, proved to be the ideal computer forour work. With it I adjusted many RFAsections. My friend and colleague RubenRodriguez continued the good workwhen I left the country in 1975.

Before that, in 1973, and without 1GMassistance, Alfredo and I traveled toOxford, U.K., to attend the InternationalMeeting on Computational Methods inGeometrical Geodesy, convoked by theInternational Association of Geodesy.We wrote a report entitled “Programs forthe Adjustment of the 1GM Nets,” partof which I read at the meeting. Readerswith more than a passing interest on thehistory of Geodesy could apply to the1GM for a copy. If unsuccessful, I’d bepleased to send them a scanned copy.

final wordsGeometric geodesy and particularly triangulation adjustment has made greatstrides since the 1 960s, the time frameof this paper. Over the years, GPS haspushed traditional triangulation adjustments out of the classrooms and textbooks and into the field. No doubt, thatdeserves celebration, but for us whonow look back more often than ahead,it also evokes regret. In that spirit I puttogether these pages, hoping that theywill ease the way for RFA and the toilsof its makers into the chronicles of traditional Geodesy.

Footnotes1 In 2005, the ACSM Bulletin published an

abridged version of Or. Irene Fischer’smemoirs entitled “Geodesy? What’s that?”The parts of interest in the context of thisarticle are those appearing in ACSM Bulletin nos 213 and 215.

2 100 años en el quehacer cartogréfico del pals7879-1979 (100 years of cartographic work in

didn’t do anything directly to resolve the of the condition equations. Some readers

) computer.[hUp://www.floodcontractco.riversde.caus.]

DECEMBER 2007 ACSM BULLETIN 23

the country 1879-1 979) Instituto Geográfico Militar, Buenos Aires, 1980,

304 pp. The Library of Congress holds a copy.

I was told more than once that German was heard oftener than Span

ish in the old Geodesy Division. Also, that the European oaks in the

1GM grounds grew from acorns stowed away by a homesick German

geodesist. As traces go, 45 or so years ago I found, secreted among

the pages of an old survey manual, a score for Bundeslied with the

poem in German cursive script.Those circumstances tell a lot about Argentina in the early 1 900s—

projects of infrastructure, made possible by a sound economy, were

then seen as essential by scientists, engineers, and authorities edu

cated in Western European traditions. All that, as it is well known,

changed a few years after 1940. Capital was wasted on meaningless

ventures, the country turned its eye toward its native and colonial

past, and its mapping, so well conceived and funded by the Act of

the Chart, slowly but steadily screeched to a halt.Chain of triangles that traverses Argentina, mostly along the W64°

meridian, established by the National Committee for the Measure

ment of a Meridian Arc. The Committee was created in 1936 by insti

gation of Felix Aguila Civil Engineer (La Plata University, 1910), memo

rable author, educatot astronomer and geodesist. A section of the Arc

makes the west side of polygon 4H (Figure 1).6 In pre-WW1 Russia, a commoner [from the peasant class) applying to

study at a university had to have a trade. To meet this requirement, com

moner candidates had to undergo long apprenticeships under the supervi

sion of the guilds. Candidate Beljajew chose shoe-making and, until his

death, wore only the excellent shoes he had himself made.Newly measured chain sections and loops were to be adjusted by a

method that maintained fixed the positions of the points in common

with the already adjusted RFA core. The correlatives resulting from

those forced coincidences would certainly be different from those

of a free adjustment, although by not too much. Similarly, correc

tions to the directions would be only somewhat different. However,

with each addition of forced RFA members, the new partial adjust

ments would yield corrections that increased m (mean error of the

unit of weight) and the deformations in the annexed members. Ire-

member to have read the same conclusions about the successive

non-simultaneous adjustments of USC&GS triangulation by Bowie’s

method. In view of those imperfections, in the 1950 1GM was antici

pating the need of an eventual, global, free and simultaneous adjust

ment of the complete RFA, very much in the manner the USC&GS

in the 1 970s adjusted the whole main triangulation in the conter

minous USA. The RFA was completed years ago; however—and to

the regret of us who know how much the RFA cost the country in

terms of money, time and effort, not to forget heated discussions

and the “famous” methods contest—, its final global adjustment has

not been carried out. Moreove as far as I know, it is no longer in

the plans. Some of my readers would dismiss my laments by noting

that economical and precise GPS receivers had greatly decreased

the value of geodesic markers. Granted, Yet they must be keeping

a substantial value. That value, no matter how small, deserves to

be contrasted with the cost of today’s free and global adjustment of the

RFA, which as regards manual work, should be zero because the data,

unadjusted observations, should be accessible in magnetic media. I

myself designed and started loading a tape-based archival system

to store data and results from adjustments. I put the source code,

archival tapes and full documentation in the hands of the Chief, 1GM

Computer Center, right before my emigration from Argentina. As

regards processing time, surely nobody would care about it: today

machines are thousands of times cheaper and more powerful than

the IBM/360 we used to run our partial adjustments 40 years ago.6 The RFA numbering scheme plus a key to the status of its adjust

ment can be found in Programs for the Adjustment of the 1GM Nets.

Perhaps it can still be obtained from the 1GM, Cabildo 381, Buenos

Aires. Upon request, I can send copies over the Internet.

ReferencesBeijajew, N. 1953. Método de las figures de enlace pare resolver las ecuacio

nes normales en Ia compensación de grandes redes. Bulletin Gdodésique

27)2).Bollz, H. 1923. Developmentprocedure for the adjustment of geodetic net

works by the least squares method. (In German, Veroffentlichungen des

PreuBischen. Geodbtischen Instituts,) Berlin, Germany.Corpaciu, A. 1954. Contribution a l’étude de Ia compensation de Ia triangulation

fondamentale argentine. Bulletin Geodesique 28(4).Eggert, 0. XX Travaux de lAssociation Internationale de Geodesy, vi 5. XXXX,

Fischer, I. K. 2005. Geodesy? What’s That?, Part 10: Focus on the Southern

Hemisphere. ACSM Bulletin no. 275 (May/June).

Jordan, W, and Eggert, 0. 1961. Handbuch der Vermessungskunde, Vol. 1,§114.1. B. Melzlersche Verlagsbuchhandlung, Stuttgart.

Helmert, F R., 1880. Die mathematischen undphysikalischen Theorieen

derhöheren Geodasie. vol. 1. Leipzig, Germany. 631 pp.

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1917—2D1J7BO, historian emeritus at the SmithsonianInstitution and an expert on timekeepingand the history of early American scientificinstruments, died of pneumonia Nov. 14 atSuburban Hospital. He lived in Washington.Silvio Bedini was born in Ridgufield. Conn.,

and attended Columbia University beforejoining the Army Air Forces during WorldWar II. He served in Army intelligenceat Fort Hunt, Vu., part of a top-secretinterrogation center for Cerman prisonersof war. After the war, he returned toConnecticut to run the family’s contractingand landscaping business. In his sparetime, he researched and wrote storiesabout science and technology forelementary schools, encyclopedias, anda hobby magazine before joining theSmithsonian. Bedini was recruited to the

Smithsonian inlBBl and becameassistant, thendeputy. directorof what was thenthe NationalMuseum of Historyand Technology.He wrote morethan 20 books,starting with “EarlyAmerican ScientificInstruments and

for the Historyof Technology, hereceived the Abbott

Payson Usher Prize in I962 and the Leonardo da Vinci Medal in2000. He was a member of the American Philosophical Society.the American Antiquarian Society. the Society of AmericanHistorians, the Washington Academy of Sciences, the SurveyorsHistorical Society. the D.C. Association of Land Surveyors, andthe Cosmos Club. —By Patricia Sullivan

Silvin A. Eedini

Their Makers” (IBB4). followed by “The Life of Benjamin Banneker(lB7l), “Thinkers and Tinkers: Early American Men of Science”(IBTh) and “With Compass and Chain: Early American Surveyorsand Their Instruments” (2001). He also wrote a number ofbooks about Thomas Jefferson and a hook on Hanno, a whiteelephant given to Pope Leo X in l5I4 by the King of Portugal.In 1978. Mr. Bedini became the keeper of rare books at theSmithsonian’s Dibner Library. He retired in 1978 but continuedto work as historian emeritus until his death. From the Society

DECEMBER 2007 I ACSM BULLETIN I 25

WoridView- Ireaches full operational capability

Longmont, Cob., November 26, 2007—DigitalGlobe,provider of the world’s highest-resolution commercialsatellite imagery and geospatial information products,announced in late November that WorldView-1 hascompleted its commissioning and is delivering imagery tothe National Geospatial-Intelligence Agency (NGA) as partof the NextView program. Full Operating Capability (FOC)with NGA began on November 17th. Following a controlledroll-out with NGA, DigitalGiobe will begin taking orders forWorldView-1 imagery from its global resellers, partners,and customers on January 3, 2008. The satellite waslaunched from Vandenberg Air Force Base on September18 and delivered its first sample set of high-resolutionimages on October 15.

“This is truly a fabulous milestone for DigitalGlobe,” said JillSmith, chief executive officer of DigitalGlobe. “We are proud tobe serving the NextView contract and excited to be operatinga new imaging satellite that addresses the worldwide demandfor map accurate satellite imaging capacity.”

WorldView-1 is part of the National GeospatialIntelligence Agency’s (NGA) NextView program, and itwas partially financed through an agreement with the NGA.The majority of the imagery captured by WorldView-1 forthe NGA will also be available for distribution throughDigitalGlobe’s ImageLibrary. Additionally, WorldView-Jfrees capacity on DigitalGlobe’s QuickBird satellite tomeet the growing commercial demand for multi-spectralgeospatial imagery.

WorldView-1 is the first of two new next-generationsatellites DigitalGlobe plans to launch in the near future. Inlate 2008, Ball Aerospace and Technologies Corp. and 1ffCorporation will complete WorldView-2, bringing the totalnumber of satellites DigitalGbobe has in orbit to three andenabling the company to offer a constellation of spacecraftthat will provide the highest commercial collectioncapacity, with more than 1 million square kilometersper day of high-resolution Earth imagery, Additionally,WorldView-2 will provide eight bands of multi-spectral forlife-like true color imagery and greater spectral applicationsin the mapping and monitoring markets.

The company’s updated and growing lmageLibrarycontains more than three hundred million squarekilometers of satellite and aerial imagery suited tocountless applications for people who map, view, navigate,and study the Earth.

Satellite images of lfrom top] Addis Ababa, Ethiopia; Houston, Texas; andYokohama, Japan, taken by DigitialGlobe’s WorldView-1 satellite.


A f• MaCARTOGRAPHIC liCENSE

US, r,,e 0 owa as a

DR.M

In the elementary model of our Earthethere is one simple polar axis around

th The Earth rotates, once a day, 365.25(approx.) times a year. It is located at 90 degreesNorth and 90 degrees South. In reality, however,the pole is more dynamic. The Geographic Northand South Poles are where all those meridiansconverge, but the instantaneous poles are wherethe Earth’s rotational axis meets the Earth’ssurface. Because there is a slight wobble in theEarth’s rotation, this position varies over time; thewobble moves the north instantaneous pole in aclockwise traced circle called the Chandler circle.The North pole of balance is at the center of theChandler Circle, and it apparently moves about 6inches (150 mm) toward North America each year.None of these are the magnetic poles, of course,the place toward which the north- and south-seeking arrows on a compass point. The NorthMagnetic pole is currently near FIlet RingnesIsland in northern Canada, and it is also moving.

The Earth’s wobble was detected in 1891 byAmerican astronomer Seth Caro Chandler, Jr.,who detected two distinct wobbles, with periodsof 12 and 14 months. The 12-month wobble is aforced motion caused by seasonal variation in theatmosphere, oceans, and water bodies. The 14-month Chandler wobble is a resonant, free oscillation that exists because the Earth is not rotatingabout its ideal axis. The Chandler wobble, whichhas been decaying over about 30-100 years, hasbeen shown to be six different wobbles, not justone, all cyclic, and not all at the same time. It hasbeen suggested that E Nino, volcanic eruptions,and much else are reflected (or caused by) theChandler wobble. Indeed, the amplitude of theChandler wobble has been observed to increaseoccasionally, with no clear cause.

So, a Chandler circle is that figure traced outby the Chandler wobble, a complex series ofmovements in the Earth’s axis of rotation. Thewobble is insufficient to make one fall over, evenafter drinking too much Egg Nogg. However, overmany years, it could confuse Santa Claus and hisreindeer somewhat.

11111999 to 111112005 Grid = .05 ercsecond X(5.1 feet)) —

111112005 to 111712006

Spin Axis spirals unler dodeabe ii this seven year fradc. AUant

Figure source: http://www.michaelmandeville.com/earthmonitor/polarmotion/2006wobbIe_anomaly.htm

C

How long is a year?

A A calendar year is 365 days, with an• extra leap year every four years, making• a year 365.25 days. A day is one revolu

tion of e earth about its axis, including its Chandler wobble.

.

“E pur si muove” (And yet it moves)—Galileo Galilei (1633)

Dear Dr. Map:

• What is the Chandler Circle?

aw HIew He

WobbleTracker . Wobble Pattern


AND YET IT MOVES...

If the transit of a particular staris observed from a fixed point,say through the transit instrument at the Greenwich observatory, it will reappear 24 hourslater. Or rather not, because theEarth itself has also moved abit around the sun during those24 hours, meaning that the starreappears 23 hours, 56 minutesand 4.091 seconds later, about4 minutes shorter than a 24-hourday. As the four minutes getrepeated every day, after a year,the Earth has rotated a wholeday less than we would think bycounting days using the sun.

By formula, this makes a year365.243 days within the measurement accuracy, which comes intoplay, too. With a 365-day year, anda leap year every 4 years, we stillneed to make corrections. Sothree of every four century years(years ending with 00, like 1900and 2000) is not a leap year, subtracting 3 days every 400 years, or.0075 days per year. That gives usayearof365.2425days.

Encounter Canada, Land—People—Environment—Student Book, by Patricia Healy,Kingsley Hurlington, Lisa Mulrine andCathy Costello, Oxford University Press,2007, ISBN-13: 978-0-19-542539-0, Hardcover, 440 p.

Accurate measurements givea year as 365.242198 days, giveor take a leap second or so. Soto answer the question, a yearis about 365.242198 days, or8765.812752 hours, not theexpected 8766, a 0.002% difference. lithe Earth turns through15 degrees of longitude everyhour, and each degree is from111,321 m at the equator and1,949 m at 89 degrees N, whaterror does that cause in location,and does the Chandler wobblematter enough to make yourhead spin?

What is Coriolis, effect?

A, NamedforGaspard-Gus, tave Coriolis, the French

scienti who first described it in1835, Coriolis effect is the apparent deflection of moving objectsfrom a straight path when theyare viewed within a rotating ref

erence frame, namely the Earth,and its latitude/longitude grid.

The effect is noticeable when amoving object (e.g., a rocket or astorm system) is deflected to theright of the direction of travel inthe northern hemisphere, and tothe left of the direction of travelin the southern hemisphere. TheCoriolis effect is caused by theCoriolis force, a fictitious forcewhich results when the reference frame itself is moving, as isthe latitude/longitude grid.

So, for example, a rocket firedat a point would miss the pointunless the movement of thepoint (at 15 degrees of longitudeper hour, give or take 0.002%)during the rocket’s flight is takenalso into account. Coriolis effectis caused by the Earth’s rotation,not by its curvature or shape. Inspite of popular belief, Corioliseffect has nothing to do withhow water goes down plug holesor toilets. That spin is caused bythe Chandler effect (See U.S. Pat.No. 5,504,948).

designed to get the students thinkingabout what they have read.

The book also has a short section onmapping and 615, and one of the illustrations used is “Kayaking in Canada,” animage of a map that won the studentaward for printed map in the 2005 ACSMCaGIS Map Design Competition.

Encounter Canada can be ordered online from Amazon.ca (www.amazon.ca)or Indigo Books & Music (www.chapters.indigo.ca). With time, it may also beavailable at the ACSM eStore.

As one who visits Canada regularly (mywife has French-speaking relatives inOttawa), I enjoyed the book and, by reviewing it, I should be able to converse intelligently about Canada during our next visit.

E. Russell Johnston III, PEMeehan & Goodin, Engineers-Surveyors

Mancheste CT 06042www.meehangoodin.com.

OK REVIEW

I I,,the interest of full disclosure,let me state at the outset thatthis book is a 9Lh grade geog

raphy textbook for Canadian students.With that in mind, anyone interested inquickly learning more about the “land,people, and environment” of Canada willfind this book informative. It covers abroad range of topics from the geologyof the land, its natural resources, thevarious people who live in Canada andwhere they live, and the varying environments across the land. It also touches oncurrent issues such as sustainability andclimate change.

Richly illustrated with photographs,illustrations, graphs, and simple maps,which alone with their captions willprovide a good overview of the material covered by the book. Because thisis a textbook there are many learningactivities, questions, and assignments

28 I ACSM BuLLETIN I OECEMBER 2007

the act of the chart and argentina’s military...to think about the problem, beljajev wrote down,...

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