ACSM Bulletin | December 2008 | #230
Triangulation Adjustments in Buenos Aires
A long time ago, 40 years precisely, a colleague and a friend, Alfredo V. Elias, and I worked on the adjustment of the triangulation known as the Argentinean Fundamental Network (RFA for the Spanish “Red Fundamental Argentina”).1 I don’t know of any publication other than an out-of-print chronicle2 that fully covers the 40 or so years during which the RFA adjustments were made. In particular, nothing has been written about a tight race between two methods and the lives of their champions. Missing are also detailed accounts of the successful (or not so successful) adjustments carried out by hand or by computer. So I decided to put into writing not a history of those years but my memories of what I had witnessed or heard, with the hope that the result might be of interest to the readers of the ACSM Bulletin. The RFA project, which was made possible by the efforts of Dr Fischer and Mr. Byars at the Army Map Service, brought Elias and myself to the U.S. in August 1968 with a double purpose: to assist the old Americas Division of the Army Map Service in the adjustment of the RFA sections completed at that time, and to develop our own adjustment program. In time, I will say a few words about the project and what followed upon our return to Buenos Aires. But first I will describe some of the circumstances and facts which shaped the adjustment problem, and the contest alluded before—both of which long preceded our trip to the U.S.
The Act of the Chart and Argentina’s Military Geographical Institute
The work on RFA started in the early 1940s, thanks to the enactment of the federal Act of the Chart. That doesn’t mean that before that time Argentina had not done any geodetic or cartographic work. On the contrary. But all that work by the Argentinean Military Geographic Institute (IGM in Spanish) led to disconnected systems, was measured at diverse times with non-uniform equipment and procedures, and covered less than 10 percent of Argentina’s territory. Under the aegis of the IGM, a group of enlightened statesmen—a breed in progressive extinction since then—gave final form to, and voted for, the Act. The work legalized by the Act was entrusted to IGM, to be completed in 30 years.
From early in its history, IGM drew its senior civilian personnel mostly from two excellent national universities—Buenos Aires and La Plata—as well as from the vast German pool of highly trained professional geodesists.3 Although all of that happened long before my time and I could meet face-to-face with only Herr Linder, the last of them, occasionally, I would find their traces in the IGM archives or hear of them from old-timers.
In the early years of IGM, not only the geodesists were of German 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 by E. Jäderin, a Swedish instrument maker, for measuring geodetic bases with invar wires manufactured by the mini Aciérie d’Imphy. Argentina purchased four Jäderins in 1904, with the first ever calibration certificates (Nos. 1 to 4) issued by the Bureau International de Poids et Mesures. Another exception, and a most impressive one, was a four-meter comparator manufactured by the Société Genévoise d´Instruments de Physique, for the calibration of wires and other devices.4
The influx of German geodesists ceased some time before the onset of WW II. After the war, IGM again welcomed a number of European scientists and engineers. None from Germany, though.
In the 1940s, with a workforce that numbered in the thousands, IGM was fully committed to implement, in 30 years, the tasks enunciated in the Act of the Chart, and so cover Argentina with 1:50,000 cartography (1:100,000 in mountainous areas). In 1952, when I started working at the Computing Division, the funds for the Act retained a good part of its original value, and the work didn’t seem to be lagging behind schedule. The project of interest to my group at the Computing Division—RFA—was well on its way, with the triangulation accurately measured and scrupulously marked and documented.
Argentinean (pre-GPS) horizontal geodetic networks
Argentina is covered by a hierarchy of geodetic networks, at the top of which lays the RFA, a framework made of chains of quadrilaterals with double diagonals running roughly every two degrees of latitude and two degrees of longitude, plus a chain of triangles.5 On flat areas, the quadrilaterals look very much like squares but they’re nothing like those in hilly 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 a base—its expansion parallelogram—and a Laplace station. Laplace stations could also be found in the middle (more or less) of every meridian section. At each station, RFA directions were measured with a relative weight of 18 and designated as First Order chains. The base expansion parallelogram was measured with weight 24.
This fundamental framework supports four lower orders of triangulations:
• Filling nets made of directions measured with weight 9 (Filling Net First Order) inside each RFA loop
• Second Order triangulations inside each chain and filling net, measured with weight 6.
• Third and Fourth Order triangulations.
All the First and Second Order triangulation were placed, marked, and measured by geodetic field parties. The Third and Fourth Order triangulations were measured by topographic field parties. Needless to say, GPS points appeared long after the facts I am going to describe here.
The computations race
In 1952, both fieldwork and the data reduction for the RFA were well on their way—to everybody’s satisfaction. But the computation of RFA didn’t look so good, because the method for solving the normal equations (a critical step in the RFA adjustment) was still undecided. The Computing Division had discussed, for months on end, two radically different methods—with no conclusion in sight. To put an end to the impasse, Guillermo Riggi O’Dwyer, the Division Chief, proposed a controlled and clocked competition [from here on the “contest”] between the two methods and their champions.
Unfortunately I did not witness the contest for I came to work at the IGM one or two years later. There are no written reports that I know of, not even in Spanish, of this unique event, and all eyewitnesses have long since passed away. Here is an account based on my recollections of the comments and stories I heard about the contest. Not all will be hearsay evidence, though, for I can attest to the consequences of the contest—the smoldering resentment that persisted to the very end between the champions and their supporters, and the successes the winner enjoyed and the problems he faced while implementing his method.
The contestants
To implement the tasks mandated by the Act, the Military Geographic Institute of Argentina needed people with first-hand experience in highly complex technical procedures. Nothing scared IGM more than the prospect of adjusting the RFA without such expertise, and, because there were no such experts to be found in Argentina, IGA set its eyes on Europe. A commission travelled to Europe with a mandate to find and engage experts in various mapping disciplines.
Among the scientists they found were such giants as Nikolai Beljajew, a mathematician with a PhD in Celestial Mechanics from an imperial university the name of which I cannot remember, and Alexandre Corpaciu, from Romania, of whose existence before his arrival to Argentina I knew nothing about. Stjepan Horvat, an engineer from Zagreb [Yugoslavia], who had considerable experience in geodetic computations—and was my mentor on Geodesy—arrived about the same time as 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 to his attention a system of differential equations I could not solve. Without pausing to think about the problem, Beljajev wrote down, at full speed, six or seven solutions. Granted, some of them were similar, but at the time, I could not hit on even one—and I considered myself to be quite good in math! Next class, the tutor announced that we need not submit the homework because, “that particular differential system had no solution.” “C’mon”—I objected—“not only is there a solution, there are more than one!” and I gave him my sheet. Needlessly to say, I couldn’t claim authorship; the solutions were well above my head … and our tutor’s as well.
In something else could I never measure up to Beljajew—his taste in shoes! Candidate6 Beljajew was an expert shoe maker, and he always wore only shoes that he himself had made. That skill helped him keep body and soul together during the 1921 calamitous Russian famine; nobody needed a mathematician but everybody needed shoes.
Beljajew’s method for solving the normal equation in a geodetic adjustment yielded a good number of long, complex calculations. Sometimes, when a verification failed, we would spend hours trying to locate the source of the error, until, frustrated by our fumbling, Beljajew would unfold a king-size sheet of paper, and with his eyes very close to the form but his thick eyeglasses on his forehead, he would scan the sea of numbers as a bloodhound. Then, suddenly, he would raise his head, point at a value, and say, “check this!” He was right on the mark most of the times.
Like Beljajew, Stjepan Horvat also had a vocation. He chose cooking and became an artist in the kitchen. Those of us who had tasted his hors d’oeuvres believed he could have earned ten times his IGM salary as a chef—and his pay at IGM was by no means insignificant. Because his family remained in Yugoslavia (those who survived the war), and because Horvat preferred to dine in company, he used to regale his young Argentinian colleagues with exquisite dinners that began with slibovitz and ended with barackpálinka.
Horvat studied Engineering at Zagreb University but he had long working experience in geodesy and cartography. Many times he went over and above his responsibilities to correct field and office procedures, which, if left uncorrected, might have seriously embarrassed IGM scientists and staff. He had a knack of instantly perceiving weaknesses that the theoreticians did not see. And, he was always ready to give advice and help if the party in charge of certain procedures was ready to listen.
Needless to say, that was not always the case, as the resentments born from the contest shut the ears of many of my colleagues for a long time to come. Horvat was one of the protagonists in the contest for better procedures, taking a middle position in both its genesis and aftermath.
Lastly, I must mention a native talent—Guillermo Riggi O’Dwyer, the formidable former chief of the Computing Division. A graduate of the School of Engineering, Buenos Aires University, O’Dwyer was a real “polymath;” he taught Mathematics, Physics, and Geodesy at universities and military schools and lectured on Fine Arts at Argentina’s National Academy. More often than not, O’Dwyer found himself acting as the ombudsman in the not infrequent disputes among the senior members of his staff. The contest was born out of one those disputes.
The need for geodetic adjustment
There are two reasons for a geodetic adjustment: to ensure the geometric “perfection” of the adjusted network, and to localize and reduce error in the measured values. In a perfect or consistent network, no matter what path is followed to compute any one property, the resultant value will be the same.
The general method to be used for the RFA adjustment was least-squares adjustment with condition equations, and by 1950, procedures were set up for the use of this method. But, the method for resolving the normal equations continued to be a source of heated discussion.
The need for an efficient method was crucial because, in principle, the complexity and time of an adjustment grows with the square of the number of condition equations. Precisely how to reduce that growth to something more manageable than a square was at the heart of the contest.
The IGM had already set thousands upon thousands of permanent trigonometric markers across Argentina. It was desirable that for each of these monuments, the discrepancy in distance was no more than 10 cm to the nearest monument. That presupposed a network of perfect geometry. However, achieving this goal proved illusive, as all the established horizontal networks (between five and ten percent of the planned total), were hung from unadjusted RFA sections.
Ideally, the adjustment should have been executed on the complete RFA. Being realistic, however, IGM had to compromise with something less than ideal, in order to satisfy users who couldn’t wait until the whole RFA would be completed (30 years at best). The compromise consisted of a gradual annexation and adjustment of sizable chunks of new loops to the previously adjusted RFA core—very much in the manner of the [then] Geodetic and Coast Survey adjustments in the States. The annexation procedure had to be designed in such a way as to save as much of the previous computations as possible.7
From the practical point of view, and in order to minimize the time spent on the solution of the normals, the workload needed to be organized in such a manner that multiple teams would be able to work simultaneously on different areas of the network. Imagine applying the divide-and-conquer principle to a tightly linked and complex set of thousands of normal equations (between 4000 and 5000 for the completed RFA).
Electronic computers powerful enough for that task were long in coming to Argentina. It was therefore impossible to avoid gross errors, although a great deal of time and ingenuity was spent attempting to correct for them. Especially devastating was the omission of terms in the block eliminations of the normals during the compilation of the “common” forms (Figure 2).
The proposed solutions
Corpaciu’s solution
Alexandre Corpaciu proposed the use of Hans Boltz’s (1923) procedure for the adjustment of geodetic networks using least squares. The reason being (as stated by Boltz), that through partial and gradual adjustments, “the results would coincide with those of a simultaneous adjustment of the completed network.” Given the stated outcome, the Boltz method would have been particularly apt had the IGM stuck to its original plans to provide adjusted chunks of RFA apace with advances in measurement.
But, IGM didn’t really want to keep delivering different coordinates every time a new adjustment was carried out, because the new adjustments would be forced to accommodate old conditions.
In reality, Boltz’s description refers to the partial additions of equations carried out within the same or successive adjustments, which would change the positions already delivered to users.
Corpaciu proposal could not have been backed by more authoritative sources and facts: according to Otto Eggert (Travaux de l’Association Internationale de Geodesy, v15), Boltz’s method was successfully put to use in one of the early German adjustments. I understand that the same could be said of a later (ca. 1950) adjustment of a European triangulation.
I never did any work with Boltz’s procedure; the events I will soon narrate will explain why. Those readers with more than an historic interest on Geodesy can find an explanation and example of Boltz’s method in Jordan and Eggert (1961, § 114).
Beljajew’s solution
Nikolai Beljajew proposed his “Linking Shapes (LS) method (“Figuras de Enlace” in Spanish”), which combined Helmert’s (1880) block elimination method with Pranis-Pranevich ideas on the simultaneous elimination of unrelated blocks of unknowns. The “shapes”—quadrilaterals (or pairs of adjacent triangles) at the intersections of RFA chains (Figure 1)—were entered in the adjustment as blocks of three (or two) triangle equations, and one side equation (none in the case of two triangles) were formulated at every one of those intersections. A block of unknowns was that set of unknowns directly related to a block of equations.
Beljajew’s proposal included ingenious ways of arranging equations and expressions. One of them, perhaps an original by Beljajew, was an improvement on the Gauss-Doolittle’s method for solving sets of linear equations. The most distinct improvement was the usage of “accordions”—forms folded along columns of values—to facilitate multiplications by columns.
The successive block eliminations were structured as sets of formulae, all hand-written and easily understood in the context of global adjustments. However, annexation of terms and equations from new RFA loops could be a headache and a source of confusion for those of us not fully in command of the method.
A good example of those critical formulae was the “III Common” (Figure 2) which incorporates coefficients and independent terms from other forms. To outline and complete the adjustment forms we were provided with very strong, 48 x 36 cm paper, gridded at two lines/cm. Some forms were so large—we called them “bed sheets” or “sábanas” in Spanish—that we had to glue two sheets together to fit them in.
As in all adjustment forms, the number of rows and columns of matriz III Common was variable. I still have a complete specimen. I rescued it from the fire following an order, given in anticipation of a naïve computer solution of the normals, that all paperwork created by the manual RFA adjustments should be burned. The form is 44 columns wide (56 cm) and 30 cm high. The number of rows varies between 40 and 60. It still shows the folds we made to turn it into an accordion. Figure 2 shows a small part (18 cm square) of the left side of the matrix as it looked after the resolution of loops 4H and 5H and the annexation of loop 6H. More columns and rows were appended with loops 4G and 5G9. The additions were made as soon as corresponding fieldwork and preliminary computations were completed.
Elimination of unrelated blocks
of unknowns
If we arrange the normal equations corresponding to a number of RFA loops without regard to sparseness and solve them with the original Gauss method, we will end up filling most of the originally empty positions. Part of the filling can be avoided by arranging the unknowns in blocks that can be resolved in terms of other unknowns in the manner suggested by Helmert.
The Helmert process can be improved considerably for matrices derived from triangulation chains in loops by applying the ideas of Pranis-Pranievitch. A matrix conformed to those ideas would show “Helmert blocks” grouped into “orders” in such a way that blocks belonging to the same order would be unrelated to each other.
The arrangement was highly beneficial in the pre-computer age because it facilitated the distribution of the workload to staff: blocks of the same order could be resolved by more than one person working on the adjustment—simultaneously and yet independently. Today, the same benefit could be derived from using parallel processors.
Either way, fewer matrix positions to fill translates into shorter processing times and—especially important in the manual mode—in smaller round-off errors. The combined Helmert/Pranis-Pranievitch approach thus enables better allocation and utilization of resources.
An illustration by example
To better explain the mechanics of the Helmert/Pranis-Pranievitch approach, the reader is directed to a group of diagrams in Figure 3, which illustrate the solution of a set of 9 loops with 24 chain sections (CS) and 16 Linking Shapes (LS) (Figure 3a). Variation of coordinates is assumed to be the general method of adjustment in use. As the orientation unknowns are supposed to have been eliminated before the formation of the normals, the LS in Figure 3a are more inclusive than those in Figure 1.
The diagrams in Figures 3b to 3e show the sorting of CS and LS blocks in nine orders of elimination. The nine-order arrangement is optimal as regards efficiency (there are other optimal arrangements). The worst—consisting of 17 orders of elimination—does not conform to Pranis-Pranievitch’s ideas.
Figure 3b represents the state of the network after the elimination of the 1st order unknowns (CS): 16 LS pairs were selected by that elimination. Thick lines represent pair relationship or connectedness. Out of the 16 LS, four (in turquoise) were selected for the 2nd order of elimination.
The next network configuration is represented in Figure 3c with three sets of blocks, each made of four LS unrelated to each other. One set (light brown) is chosen for the 3rd block elimination.
In Figure 3d, the 3rd order unknowns have vanished. One of the two (in orange) remaining orders of four blocks each is selected for the 4th order elimination. This operation connects each of the remaining four LS blocks (in violet, see Figure 3e,) to the other three. They will be eliminated in four steps. Three blocks are arbitrarily assigned orders from 5th to 7th. The first numerical values of unknowns obtained are those from the 8th order LS. The rest of the unknowns are computed during the process known as the backward solution.
An experiment conducted in 1972 illustrates the advantage of the Pranis-Pranievitch/Helmert approach (Process A) over the plain Helmert method (Process B). Both processes used the variation of coordinates method with the same data: three RFA loops with 177 trigonometric points organized into 10 CS and 8 LS, with 886 observations and 354 normal equations (the orientation unknowns were eliminated from the observations).
Both adjustments considered the CS as 1st order unknowns. Their elimination (Figure 3b) left all LS connected. Thereafter, the processes diverged. In process A, the LS blocks were optimally grouped into four (from 2nd to 5th) orders of elimination. While in process B, the LS blocks were not associated in any way, as befits the Helmert method. Instead they were eliminated one at a time, in eight steps.
An IBM /360 Model 50 was used for the experiment. The CPU times for the solution of the normals were 115 sec for Process A and 175 sec for Process B, proving conclusively the benefit of utilizing Pranis-Pranievitch’s ideas in block elimination. The difference in CPU times would have been much larger if, in the course of process B, sections of chains were assigned orders 1st to 10th, thus increasing to 18 the total number of orders of elimination.
The outcome of the contest
The contest took place in 1950 or 1951—regrettably before my time. Otherwise I would have been able to instill in this account some of the suspense and drama felt by the two scientists whose very contracts depended on the outcome of the contest.
Each of the contestants was assigned a pair of the best human “calculators” the IGM employed. Their task was to solve a set of 134 normal equations for loop 4H (Figure 1), two of which were polygonal, four base, six Laplace, 28 side, and 96 triangle.
The day was won by Beljajew and his linking shapes. His computing team (two enthusiastic and reliable ladies) solved, with his method, the 134 equations in two hours, using only on four pages for his clever schemes. In comparison, Corpaciu’s application of the Boltz method took days of filling endless columns of values—sixty pages of them (Beljajew 1953). According to one of the staff assigned to the Boltz solution, Corpaciu’s effort was doomed from day one; he had entered independent terms with the wrong sign, so his sixty pages only led to correlatives that diverged more and more from the correct solution. I never found out whether the solution was attempted again with the correct signs.
After the contest, and as expected, the judges, under Riggi O’Dwyer’s leadership, decided in favor of Beljajew version of the block elimination method which uses Pranis-Pranievitch’s ideas. This was a great win for Beljajew; his contract with the IGM was no longer on the block. But, Corpaciu never saw his renewed. He vanished—later I heard that he had emigrated to the States—but not without a parting shot at his opponent.
In his paper entitled “Contribution a l’étude de la compensation de la triangulation fondamentale argentine,” Corpaciu wrote: The method of the linking figures expounded by N. Beljajew” (Bulletin Géodésique, no 28, 1953) for the adjustment of large triangulations runs the risk of being incomplete (deficient, defective) and difficult to take to a proper conclusion.” Not fair! Two years before Corpaciu’s prediction, with Beljajew’s method and without a hitch, we did complete the adjustment of three RFA loops.
Manual and partial FFA adjustments
As soon as the method to be used was identified, about 30 new staff were recruited (I being one of them) and trained on the many separate tasks in which the adjustment process had been organized. The work was always carried out in the “dual calculation mode,” a necessary if expensive precaution to preclude ordinary mistakes. However, there were setbacks, due to the inexperience of the new staff, myself included; none of us was as experienced and attentive as the four calculators who had taken part in the contest.
Thankfully, some of the gross errors made in the solutions of the normals were prevented from spreading by the internal checks instituted by Beljajew, and others would have been corrected in time had the simple mechanism recommended by Horvat been adopted. The procedure, always used in Europe, resorted to an extra column to receive the sum of all rows in each form, later to be treated as an ordinary column. The procedure would have added some time to the computations, but it would have been worth it. But, as with many other Horvat’s suggestions, it was ignored.
From the already adjusted 4H loop, the manual adjustments proceeded as gradual annexations of new loops, to culminate in the adjustment of ten loops. This operation called for the formation and solution of 1121 equations and took so long to complete that when this actually happened there were only two of the original thirty or so staff left. Fortunately for Beljajew, they were the two ladies who helped him win the contest back in the early 1950s.
The 1121 normals verified and so did the condition equations. Regrettably, one of the last and definitive checks, the transport of geographic coordinates across the adjusted loops, did not verify for one of the loops. Presumably the error was in the computation of preliminary positions by the Schreiber method. The precise location was never found, and no correction was ever made.
The error did not discredit the feat of having solved rigorously a set of 1121 equations with the sole help of MADAS electromechanical desk calculators. On the contrary, the successful completion of the task was the ultimate and an apt rebuttal of the missive delivered by Corpaciu in the Bulletin Géodésique in 1954.
This notwithstanding, the mistakes made on the way proved that, in particular, the formation of the condition equations would have greatly benefited from the attention of an experienced geodesist—which Beljajew was not. He was so preoccupied with the solution of the normals that others soon started equating the adjustment project with this one step within the project. This misconception resurfaced during the first attempt—a too charitable term for that venture—to program the adjustment for an early electronic computer.
Following the solution of the 1121 equations, a few loops were adjusted forcibly to ten polygons. All manual adjustment work ceased around 1960 when IGM adopted electronic computing.
Computerizing the RFA adjustment
Around 1960, IBM offered IGM time in its model 650 computer. Part and parcel of the offer was a programming course—the best I have ever attended—on the SOAP language, a kind of a simple Assembler for the 650, with which we programmed a couple of tasks, the first being the arc-to-chord corrections for directions in the filling nets. The results were so good that IGM decided to purchase the next IBM machine suitable for technical tasks. “Suitable” must be qualified with a strong emphasis on “relatively,” for that machine was a bare-essentials 1620—to wit, comprising only 20000 digits of magnetic core storage, a typewriter, and a card reader/punch. The languages were an early and simple FORTRAN and SPS, an exiguous Assembler. FORTRAN, in a machine as puny as our 1620, was practical only for the simplest programming.
Yet, little by little, we programmed for the 1620 a handful of the heaviest Computing Division’s tasks. Despite the injunction of military chiefs, we always programmed in SPS. However, we didn’t do anything directly to resolve the adjustment quandary, which, by the early seventies, had frankly become grievous. Beljajew’s team of lady computers had retired, and he had not been given any replacements; meanwhile, newly measured RFA loops kept arriving from the field.
The programming of the RFA adjustment was assigned the highest priority. IGM assigned the task to an Army officer, with Beljajew acting as instructor and counselor. The 1620 and FORTRAN were the means, and after uncountable numbers of boxes of Hollerith cards had been punched and reread many times, the programming of the adjustment was declared complete. However, the “program”—only the kind-hearted would mistake it for that—covered only the solution of the normals, which, in itself, would have been valuable in alleviating the headache the RFA was giving IGM. But, as some of us had feared, the “program” turned out to be unworkable.
At about the same time we’re trying to come to terms with the botched adjustment, the Computing Division was dismantled, Riggi O’Dwyer passed away, and some of us went to work for the Geodesy Division, with Horvat as advisor. And Computer Center was organized around the IBM 1620 and placed under the supervision of an Army officer.
Finally we could try to do what made sense, that is, to start at the beginning of the adjustment and program the formation of the condition equations. Some readers will surely wonder why did we persevere in following this approach instead of the more computer-tractable variation of using coordinates. In fact, we discussed the latter at length and, although we understood the benefits, we decided to stay with condition equations because of our experience and the numerical results we had to verify the programming.
This time we were going to program in SPS. I started with the polygonal equations and, after a couple of months, I had a program working that yielded the differential expressions of length and azimuth with minimal manual data entry, Concurrently, two colleagues “attacked” the other conditions. But, we did not go any further.
Programming at the Army Map Service and its use in Buenos Aires
The reason why we didn’t was an offer from the Army Map Service (see Fischer’s Memoirs in the ACSM Bulletin) to assist IGM with programming for the RFA adjustment. My friend and colleague Alfredo V. Elías and I travelled to the U.S. and, this time, we programed using coordinates—to the satisfaction of everybody in AMS and IGM. (More on this can be read in “Two Argentineans in the Army Map Service,”July/August 2005 issue of the ACSM Bulletin.)
We returned to Buenos Aires with the programs and the preliminary design of an archival system for geodetic data, as well as a reduction of 1st order astronomic observations. The adjustment of 19 polygons of the RFA that AMS had carried out as part of an agreement arranged by David Byars (Fischer 2005) had previously been shipped to IGM. According to Jack Reynolds, Mr Byars’ appointee to handle the data preparation, “No other work that AMS had ever processed had a quality that approached that of the RFA, be it in documentation, field procedures, measurements, or data reduction.” Indeed, the r.m.s of that adjustment was 0.4 arc seconds.
In Buenos Aires, I undertook the implementation of the adjustment program, with the Burroughs 3500 installed at the DISCAD (as the computer center of the Joint Chief of Staff was called), while Alfredo worked on the reduction of the astronomical observations and the adjustment of filling nets using conjugate residuals.
It took me a month or so to confirm the uselessness of the B3500 for complex technical tasks, so I installed the programs on an IBM /360, which, under OS, proved to be the ideal computer for our work. With it I adjusted many RFA sections. My friend and colleague Rubén Rodríguez continued the good work when I left the country in 1975.
Before that, in 1973, and without IGM assistance, Alfredo and I traveled to Oxford, U.K., to attend the International Meeting on Computational Methods in Geometrical Geodesy, convoked by the International Association of Geodesy. We wrote a report entitled “Programs for the Adjustment of the IGM Nets,” part of which I read at the meeting. Readers with more than a passing interest on the history of Geodesy could apply to the IGM for a copy. If unsuccessful, I’d be pleased to send them a scanned copy.
Final words
Geometric geodesy and particularly triangulation adjustment has made great strides since the 1960s, the time frame of this paper. Over the years, GPS has pushed traditional triangulation adjustments out of the classrooms and textbooks and into the field. No doubt, that deserves celebration, but for us who now look back more often than ahead, it also evokes regret. In that spirit I put together these pages, hoping that they will ease the way for RFA and the toils of its makers into the chronicles of traditional Geodesy.
Footnotes
1 In 2005, the ACSM Bulletin published an abridged version of Dr. Irene Fischer’s memoirs entitled “Geodesy? What’s that?” The parts of interest in the context of this article are those appearing in ACSM Bulletin nos 213 and 215.
2 100 años en el quehacer cartográfico del país 1879-1979 (100 years of cartographic work in the country 1879-1979) Instituto Geográfico Militar, Buenos Aires, 1980, 304 pp. The Library of Congress holds a copy.
3 I was told more than once that German was heard oftener than Spanish in the old Geodesy Division. Also, that the European oaks in the IGM 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.
4 Those circumstances tell a lot about Argentina in the early 1900s—projects of infrastructure, made possible by a sound economy, were then seen as essential by scientists, engineers, and authorities educated 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.
5 Chain of triangles that traverses Argentina, mostly along the W64° meridian, established by the National Committee for the Measurement of a Meridian Arc. The Committee was created in 1936 by instigation of Felix Aguilar, Civil Engineer (La Plata University, 1910), memorable author, educator, 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, commoner candidates had to undergo long apprenticeships under the supervision of the guilds. Candidate Beljajew chose shoe-making and, until his death, wore only the excellent shoes he had himself made.
7 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, corrections to the directions would be only somewhat different. However, with each addition of forced RFA members, the new partial adjustments would yield corrections that increased m (mean error of the unit of weight) and the deformations in the annexed members. I remember 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 IGM was anticipating the need of an eventual, global, free and simultaneous adjustment of the complete RFA, very much in the manner the USC&GS in the 1970s adjusted the whole main triangulation in the conterminous 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. Moreover, 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, IGM 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.
8 The RFA numbering scheme plus a key to the status of its adjustment can be found in Programs for the Adjustment of the IGM Nets. Perhaps it can still be obtained from the IGM, Cabildo 381, Buenos Aires. Upon request, I can send copies over the Internet.
References
Beljajew, N. 1953. Método de las figuras de enlace para resolver las ecuaciones normales en la compensación de grandes redes. Bulletin Géodésique 27(2).
Boltz, H. 1923. Development procedure for the adjustment of geodetic networks by the least squares method. (In German, Veröffentlichungen des Preußischen. Geodätischen Instituts,) Berlin, Germany.
Corpaciu, A. 1954. Contribution a l’étude de la compensation de la triangulation fondamentale argentine. Bulletin Géodésique 28(4).
Eggert, O. XX Travaux de l’Association Internationale de Geodesy, v15. XXXX,
Fischer, I. K. 2005. Geodesy? What’s That?, Part 10: Focus on the Southern Hemisphere. ACSM Bulletin no. 215 (May/June).
Jordan, W, and Eggert, O. 1961. Handbuch der Vermessungskunde, Vol. 1, §114 . J. B. Metzlersche Verlagsbuchhandlung, Stuttgart.
Helmert, F. R., 1880. Die mathematischen und physikalischen Theorieen der höheren Geodäsie. vol. 1. Leipzig, Germany. 631 pp.
Albert Christensen will answer questions
at ahchris@T-FCO.com