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 University Library 
 University of California • Berkeley 
 
Geodetic Instruments of Precision 
 
 — AT THE — 
 
 Paris Exposition and in European 
 Workshops. 
 
 DAVIDSON. 
 
'I III |;/-'i ' fH 'I I H;UA 
 
 J)3 
 
 [Read before the National Academy of Sciences, November, 1878, at New York, by Prof. 
 George Davidson, A. M., D. Ph., United States Coast Surrey.] 
 
 Geodetic Instruments of Precision at the Paris Exposition 
 and in European Workshops. 
 
 It is a fact familiar to those who have occasion to make use of instrumental 
 contrivances, that novel methods are constantly being devised to meet new 
 requirements or to lessen existing defects. As the delicacy and importance of 
 any given work is increased, the observer soon discovers sources of error that 
 had not been suspected, and finds errors that were veiled by the disposition 
 of the relative parts of the instruments. Instruments of the higher class are 
 too frequently at fault, but the ingenious observer is soon led to investigate the 
 sources of trouble, and either to obviate them or to seek for the best instru- 
 ments suited to his particular and peculiar duties. In the broadest view ot 
 the case we must not be confined to individuals or to nationalities, but aim only 
 to obtain the highest mechanical design and workmanship. In the progress of 
 the geodetic work of the United States, stretching from the Pacific to the At- 
 lantic, and also northward and southward along the Pacific coast, there was 
 furnished to me, among other instruments, one theodolite, of large size, which 
 was subjected to the most rigid scrutiny to determine the flexure of the pillar 
 plate, of the microscope arms, and of the telescope; also, the character of the 
 graduation of the 20-inch circle, and various other points involving accuracy. 
 Under ordinary circumstances the instrument would have passed muster for 
 lines of moderate extent, but when lines of 160 miles in length were involved, 
 it was essential to the integrity of the undertaking, that errors of even a second 
 of arc should be avoided. At the distance of 160 miles one second of arc 
 subtends four feet: a skilled observer can measure a much less quantity than one 
 second, and certainly the instrument should afford the means of his measuring 
 what he can see. 
 
 Fully alive to the importance of the subject, the Superintendent of the U. 
 S. Coast Survey had determined that there should be made a careful examina- 
 tion and study ot the instruments of precision, exhibited at the Paris exhibition 
 for geodetic and astronomical work, topography and hydrography, for the tele- 
 graphic determination of longitude, etc. And, moreover, that the examination 
 should be extended to the first-class workshops of Europe, where instruments 
 of this character are manufactured. 
 
 It was desired to ascertain, if practical, whether the productions of European 
 manufacturers were superior to our own; wherein lay any superiority, if found 
 to exist; and in what consisted the peculiar merit of the work of any particular 
 manufacturer. 
 
 As a mechanician seeking merely the trade secrets of the makers, I could 
 not have expected to enter into any sanctum sanctorum; but upon a candid ex- 
 planation of my purpose and instructions, I found nearly every workshop 
 
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 opened to me, and Ml and free explanations made to my inquiries. It would 
 therefore be unjust to these manufacturers to severely criticise in public the 
 character or even the minor defects of their instruments, or to make known the 
 methods of their processes. These I received for the benefit of the Govern- 
 ment, and whenever I mention any names here, it will be to commend their 
 work; although many are officially commended that are not now referred to. 
 
 In previous experiments upon the larger and finer instruments, I have dis- 
 covered errors of graduation and flexure of parts much greater than I had 
 any reason to suspect; and I believe much greater and more serious than the 
 makers had thought possible. This latter is the more readily understood 
 when we reflect how few mechanicians are actually observers; and that it 
 really requires long practice for the most skilled observer combined with 
 fair mechanical instincts to discover and measure the minute and conflicting er- 
 rors which are resultants of diflferent infinitesimal, and perhaps unsuspected 
 causes. As a rule, the observer makes his measures upon objects subject to many 
 extraneous and disturbing causes, and whenever unsatisfactory results are ob- 
 tained, he is very apt to attribute them to the unfavorable conditions of the 
 atmosphere or to his own condition and temperament at the time; generally 
 overlooking the fact that the instrument maker was quite as liable as himself lo 
 errors of judgment in the proportions and workmanship of the instrument used. 
 
 Setting aside for the present the peculiar adaptness and fitness of the 
 observer for his business, we are necessarily interested in the requirements of 
 geodetic operations and especially in the duties of the instruments by which 
 these are satisfied. In all geodetic work, portability, accuracy and mainte- 
 nance of instrumental adjustment are essential to rapidity of progress,to economy 
 of expenditure in money and in personnel, and to precision in the results. 
 Experience and theory teach us that in any given instrument, such as a theodo- 
 lite for geodetic purposes, we need simplicity of design; fewness of pieces; 
 harmony in the proportion of parts; accuracy of workmanship; superior gradu- 
 ation with adequate microscope micrometers; micrometer screws free from 
 mechanical defects; commensurate optical conditions of penetration and power; 
 sensitive and trustworthy levels; and the highest precision in all the bearings of 
 the moving parts. Moreover, the general disposition of the parts should be such 
 as to oflfer the greatest facilities to the observer, in order that he may make the 
 necessary observations without fatigue or nervous strain. 
 
 Guided by these general considerations, I examined the fine collection of 
 geodetic instruments exhibited by the Minister of War, many of the exhibits 
 of private exposants, and some of the workshops of the manufacturers in Paris. 
 After this I visited the principal manufactories of Geneva, Neuchatel, Munich, 
 Vienna, Dresden, Berlin, Hamburg, Cassel, London and York. At the exposi- 
 tion I did not have the fullest facilities afforded me, and not only was I unable 
 to get into one of the principal cases, but I was positively forbidden to con- 
 tinue my drawings; whilst one well known maker would not only not permit 
 me to make any tests of the graduation of his theodolite, but would not allow 
 me see his graduating engine. Outside of Paris I was permitted to see every 
 graduating engine of the noted manufacturers, and afforded facilities for the ex- 
 aminations of their productions. But on account of the commercial depression 
 which was overshadowing all business in Europe, as well as the United States, 
 the number of the larger instruments on hand was very few. In some work- 
 shops I found that not over 20 per cent, of the usual number of workmen were 
 employed. 
 
 Besides the mechanical construction of the instruments, I was particularly 
 anxious to study the capacities of the different graduating engines, in order 
 to judge, in a measure, of the probable value of the results. The graduating 
 engine is simply a mechanical tool with which we should expect to divide a circle 
 of say 20 inches in diameter in 360 parts, with no greater an error than the 
 1-50,000 part of an inch or 4-10 of a second of arc in any one degree. The 
 probable error of an experienced observer in reading the five minute gradu- 
 ations of such an instrument is about 1-10 of a second of arc, or the 1-200,000 
 of an inch. It is usually assumed that the graduation errors are not over one 
 
3 
 
 second of arc, and this is what the majority of instrument makers suppose 
 or assert to be their average error in each degree graduation; but I am per- 
 fectly satisfied that even this limit of accuracy is rarely if ever reached. As a 
 matter of fact I failed to learn from any manufacturer that he had ever tested 
 a theodolite after graduation by measuring every five minute space on the circle, 
 or even every degree; whereas in my previous testings of a 20-inch theodolite 
 I had detected differences of 15 seconds between whole degrees, and errors of 
 5, 6 and 7 seconds in contiguous five minute spaces. 
 
 You can readily understand the almost multitudinous sources of error 
 against perfecting a graduating engine; and the most skilled mechanicians find 
 that it requires persistent labor and experiment for two, three or more years 
 to approximately effect their purpose. Yet until we get a reliable graduation 
 it is futile to seek for final accuracy in our measures; nevertheless all other 
 sources of error should be reduced to minima, and the perfection of graduation 
 persistently attempted. After a graduating machine has been made as nearly 
 perfect as the means and skill of the mechanician can effect it, he carefully meas- 
 ures the different degrees, tabulates the errors, and generally constructs an 
 error circle whose circumference is irregular in a certain proportion to the 
 errors determined. This circumference is so connected with the tangent screw 
 moving the graduate circle as to advance or retard the screw the exact amount 
 of the error at any given point. This is one way of effecting the necessary cor- 
 rection, and i3 mentioned merely to serve as an illustration; yet in this method 
 it must be evident that the retarding of a screw brings into operation any 
 backlash that may exist even if it be almost practically infinitesimal. 
 
 Among the instrument makers I found the most positive and opposite 
 views of practice; for instance, one believes wholly in automatic moving parts 
 in the graduating engine, and makes every effort to secure uniformity of tem- 
 perature, etc.; another scouts the automatic movement and does everything 
 by hand, with or without much attention to change of temperature; ore party 
 believes in a steel cutting tool; another pins his faith upon his diamond cutter, 
 etc. Many of the observers implicitly receive the dicta of the instrument 
 makers, and but few make any exhaustive examiaations for themselves. Among 
 the tests which had been made by the Chief of the Prussian Geodetic Survey, 
 between theodolites of a few of the best makers, there was a very close agree- 
 ment in the probable error of the systematic errors, but the probable error of 
 the irregular errors was only half as great for the Wanschaff circles as for the 
 others. Without here mentioning the rames, I may. state that from the charac- 
 ter of the instruments examined, I recommended the Superintendent of the 
 Coast Survey to have circles graduated by five of the best makers, and test 
 them as I had tested the 20-mch theodolite referred to. For where mechanical 
 si^ill is good and apparently nearly equal, it would be vain to attempt to 
 decide by simple inspection or upon a maker's repatation, although upon these 
 merits alone awards were made at the exposition. 
 
 After the instrument maker has efTected the division of the graduating 
 circle into degrees, the sub-division into 2-minute, 4-minute, 5-minute, or 10- 
 minute spaces is sometimes made by verniers suitably divided, but frequently 
 the coincidence of the lines of the vernier and the circle is determined by 
 bringing the ends of the lines together, and judging by the eye whether one is 
 truly a prolongation of the other. The Kepsolds certainly appreciated this source 
 of error and had in a great measure successfully overcome it. Some of the 
 graduating engines examined had been made and in use from thirty even to 
 fifty years; now considering the great advance in the construction of instru- 
 ments of precision in that time, it is hardly too much to ask that this special 
 mechanical tool should be perfected. Of course there are more recent efforts 
 but not yet notably perfected. It offers to our younger skilled mechanicians a 
 very delicate problem upon which to try their ingenuity, skill and patience; 
 with such a tool superior to those of their competitors, they may be assured of 
 a fair income from its work alone, and an enviable reputation. 
 
 Of the larger theodolites which I had an opportunity of examining, the 
 best was by Brunner. It combined fewness and simplicity of parts, and fair 
 
harmony of proportion, yet I should certainly doubt the adequacy of its opti- 
 cal power for long lines; it reads by four verniers instead of three, involving 
 more labor, and less reading points on the circle; whilst the observer must 
 be placed in a constrained position because the horizontal plane ofthe ;ele- 
 scope is only about two inches above the reading microscopes. Moreover, the 
 circle (instead of the whole instrument) is changed for new positions and 
 clamped by three screws in each position. Should the surface planes of con- 
 taot be warped, this clamping would warp the circle in each new position and 
 thereby introduce error. This method was devised about 20 years since, and 
 soon abandoned; it is now the fashion. 
 
 In the evident desire to obtain compactness and simplicity, the instru- 
 ment is not adapted to the observing of azimuths by means of a close cir- 
 cumpolar star, because the telescope cannot be ele/ated. Instead, the transit 
 instrument w isi replace the theodolite for that purpose, whereby the possibility 
 of error is introduced in occupying the identical station; and even it this be 
 granted, the labor is increased and extra time consumed. 
 
 Fashions prevail among instrument makers and observers just as we find 
 a change of opinion upon the question of refractors and reflectors. At one time 
 it seemed as it the prismatic telescope was to carry everything before it, and 
 I find many manufacturers and observers yet strongly in favor of that form. 
 It certainly has the dec'ded advantage of comfort to the observer; but from 
 personal experience, and from conferring with such observers as Plantimour, 
 it seems that the system ncessarily in/olves "flexure" or deformation of the 
 prism, notwithstanding the njmerous and ingenious efforts made to secure it 
 properly in position. Of course some manufacturers insist that their special 
 methods of securing the prisms are infallible; but the observer is the final 
 jtt^ge of their failures. In the highest character of wo ^k I should certainly not 
 use them; whilst for the secondary works it seems hardly necessary to increase 
 the number and Intricacy of the parts. 
 
 A prevailing fashion at present is to introduce reversing apparatus and 
 counterpoises, even in theodolites with circles of eight inches in diameter. 
 This is as complete a wandering from simplicity as can well be imagined, and 
 must certainly lead to grave errors. It is well known that by moving a tele- 
 scope in altitude by means of the usual slow-motion screw, the tendency is to 
 raise the transit axis pivots, but as the weight of the telescope is too great to be 
 lifted clear of the Y's, the pivot is moved up one side of the sloping Y, and 
 the telescope thereby changed in azimuth. Now, if the weight of the telescope 
 be counterpoised by springs, the pivot is lifted still higher and the resulting 
 change in azimuth becomes greater. Not only that, but the intricacy of the 
 adjustment thereby introduced, conflicts very much with the bearings of the 
 vertical axis. I saw no form of reversing, that should be applied to any first- 
 class theodolite, or to any theodolite which might be used at a distance from 
 the workshop of a skilled mechanic. The same amount of labor otherwise 
 expended upon the same instrument, would largely increase its value for honest 
 work. This form, as well as the prism telescope, must however be demanded 
 by observers or the makers would hardly continue their manufacture. 
 
 Another fashion that seems to prevail is the use of microscope micrometers 
 upon small theodolites of eight inches diameter, and even in some cases of only 
 six inches. These microscope micrometers read the circle to one or to two 
 seconds; but in every such case the telescopic power and the transit axis level 
 were vastly inferior to such delicacy, and therefore the contradiction existed 
 that the instrument maker expected the observer to measure what he could not 
 see. In fact, I think it may be safely asserted as a rule that the telescopic power 
 of all the instruments examined was inferior to the other parts. 
 
 And still another fashion is in the use of the universal or Altazimuth in- 
 strument. The combination of two or more instruments for differeut purposes 
 into one instrument for all the required purposes is difficult and doubtful even 
 in machines of industry; but when every new piece and movement introduces 
 a fresh source of error into a delicate instrument where the constant-study 
 should be really to decrease them, the combination must be clearly shown not 
 
only to possess freedom from additional errors, but to give better results or 
 as good results as two different and separate instruments at less cost of con- 
 struction, less weight for transportation and mounting, and greater rapidity of 
 manipulation. For certain classes of work, the universal instrument has, with- 
 out doubt, some decided advantages; but for such work as is demanded in the 
 primary and main triangulation of the United States they are essentially un- 
 suited. Nor would our surveys willingly adopt the eccentrically placed tele- 
 scopes of the theodolites used in the Prussian Geodetic Survey, although the 
 character of that wcrk stands very high; if any series of observation is broken 
 it cannot be utilized without extra calculation; and a loss of time means a loss 
 of money. The multiplicity of parts in some of the instruments on exhibition 
 was astonishing. I was attracted by the complication of an instrument having 
 a circle of about eight inches diameter, and although I could see little more 
 than one side of the instrument I counted no less than 93 screws of all kinds, 
 whilst others seemed evolved and contrived from the inner consciousness of 
 some closet professor. 
 
 In one large combination instrument in the exhibition, there were, among 
 other curious features, two small lamps for illuminating the horizontal circle 
 under the three microscopes; one for the telescope, and one for reading the 
 level and the two microscopes for the vertical circle, together with a multipli- 
 city of mirrors to reflect the lights. No matter howsoever small the heat ot the 
 flames might be, here was the introduction of souces of error that wou'd tend 
 to complicate and mask the other defects of the instrument. 
 
 I had the opportunity of studying many of the recent and varied forms of 
 portable transit instruments. Some there were that never should have been 
 permitted to leave a workshop; others aiming at great stability by the use of very 
 heavy cast-iron stands, yet introducing an element of error in having their ad- 
 justments for level and azimuth at the base. This seems very much like 
 erecting a great solid building upon a movable foundation. It is granted that 
 in the usual form of movable Y's tor the adjustment of the transit axis level 
 and of azimuth, two fertile sources of error exist, but many years since I 
 readily and successfully overcame the difficulty by tightly clamping either mov- 
 able Y alter the last mechanical correction has been made to the adjustments. 
 Troughton and Simms have in part since used a similar application. The frames 
 of the later Coast Survey transit instruments are emphatically portable from 
 their form and weight of metal ; their telescopes have generally greater light- 
 collecting power than the portable transits examined, whilst the character of 
 the results is fully established by the rigorous method of discussing them. By 
 the adoption of four foot-screws 1 have secured remarkable firmness; whilst the 
 double frame gives no ,only great facilities for preliminary adjustments in the 
 meridian, but enables the trans" t to be used for a latitude instrument by the 
 Talcot method. Some of the portable transits in Europe hardly bear out that 
 character, and would not be adopted in the mountains where our geodetic 
 work is being carried; it was very evident that cast-iron was cheap, transpor- 
 tation easy, and time no object. And I found severer criticisms than mine 
 passed upon particular instruments (designed for great surveys) by some whose 
 opinions have much weight in the geodetic world; whilst one well known 
 observer confessed, that were he to design a new instrument it would not have 
 the form of that which he had planned, constructed and already used. 
 
 Although I made few efforts to examine the manufacture of lenses for tel- 
 escopes and microscopes, those which I did see were generally of superior 
 character. I was very much impressed with the thorough skill and knowledge 
 of Shroeder, of Hamburg, who was making the lenses for the 15-inch equa- 
 torial of the new Potsdam observatory. An examination of some of his smaller 
 instruments revealed marvelous precision of figure, whilst his means of testing 
 the curvature of the lens was beyond anything I had seen or known. The 
 computations for the curvatures of the lenses are very elaborate and exhaustive. 
 
 Without going into details of telegraphic longitude apparatus, electrical 
 clocks and chronometers, etc., I may mention that I examined the base ap- 
 paratus of Brunner, being constructed for the Spanish Geodetic Survey; and 
 
6 
 
 had the greatest pleasure in examining the original base apparatus of Bessel in 
 the Prussian geodetic office. The Brunner apparatus aims at the simplicity of 
 the Borda thermometer, and is therefore composed of two four-meter bars of 
 different metals, having largely different co-efficients of expansion. The lower 
 bar is platinum; immediately above it is the brass bar of the same cross sec- 
 tion. At one extremity of the compound, or rather composite bar, the two bars 
 are joined, but are free towards the other extremity. At the free ends the 
 upper bar has a slot in it that receives a piece soldered to the lower bar, 
 whereby the upper surface of this piece is flush with the upper surface of the 
 brass bar. Upon one is cut a series of graduated lines; upon the other a 
 vernier. "When the bars expand or contract through increase or decrease of 
 temperature they do so unequally, and the difference of that change is read and 
 is determined by the scale and vernier. 
 
 The base bars of Bessel are four in number, and each composite bar is 
 formed of two bars of different metals of different rates of expansion for equal 
 increments of heat. In this case the lower bar is iron and the upper is zinc. 
 One end of each system is formed by the junction of the two bars, and thence 
 the bars are free. Instead of a scal-» upon one and a vernier upon the other, 
 the zinc bar terminates close to a small projection upon the upper surface of 
 the iron bar, and the difference of expansion was measured by the insertion of 
 long graduated wedges of glass in the space between the end of the zinc bar and 
 the iron stud. 
 
 Either of these forms of apparatus has great merit in the extreme simplicity 
 of the form and fewness of parts, and it appears to me that with thorough skill 
 in the observer, accuracy of comparison with the given standard bar, simplicity 
 and stability of the supporta, and the proper means of effecting the contacts, 
 the method is susceptible of great accuracy. But I was very far from being 
 satisfied with the character of the supports and the methods and appliances of 
 measurement. These, however, I discuss fully in my official report to the Su- 
 perintendent of the Coast Survey. 
 
 Without detaining the attention of the Academy any longer, I may mention, 
 in brief, the general conclusion to which I arrived. While I saw much of deep 
 interest, there was no single instrument that 1 would unreservedly recom- 
 mend for adoption in its entirety. What I principally learned was really wJiat 
 not to copy. And whilst awarding high credit to the instrument makers of 
 Europe, and keenly alive to their courtesy, I am convinced that we do not 
 need to go to Europe for geodetic instruments, although we should possess 
 copies of their finest efforts for comparison with our own. With our own ob- 
 servers and mechanicians working in harmony and striving to attain the highest 
 excellence, I firmly believe that we are fully competent to lead in this scien- 
 tific effort. Both parties fully appreciate the fundamental requisites to success, 
 and the character of the geodetic work of the United States demands that the 
 mechanical means shall be adequate to the delicate manipulation and require- 
 ments of the most skillful observers. 
 
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