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 



