REPETITION OF ANGULAR MEASURES WITH THEODOLITES. 105 



Instability of Instrument. 



Of all sources of error in angular measurement that arising 

 from instability of the instrument is perhaps the most irregular, 

 and the most difficult precisely to ascertain. All results from 

 single series of repeating-measures should be regarded as subject 

 to correction by some undetermined quantity to be ascribed to 

 this cause, which in general will tend to reduce the value of the 

 arc through which the telescope is turned. Hence this element of 

 instability (which appears to be independent of the magnitude of 

 the arc measured and to due what may be called play in the parts 

 of the instrument) may be at least partially eliminated by measur- 

 ing also the complementary arc, to make up 360°, and the half 

 difference of the sum of the measures subtracted from 360° may 

 be taken as the value of the constant for instability. Other causes 

 of movement can only be guarded against by delicate handling, 

 and by protection from the effects of variations of temperature, 

 wind, sun, etc. But for this injurious element, small and easily 

 portable theodolites, properly fitted with large telescopes, might 

 be made to serve every purpose required in geodetic operations 

 of a first class character. 



In conclusion it may be remarked that a rigorous examination 

 of the errors, and an incisive inquiry into the performances of 

 instruments used in surveys of precision, would no doubt lead to 

 more exact opinions as to the possibilities of this branch of the 

 science of physical measurement, than at present exist ; and if 

 this article, which discusses the repeating system so far as the 

 writer is aware on new lines, has aided in any degree the realiza- 

 tion of this end, or contributed any suggestions tending thereto, 

 it has achieved its object. 



Discussion. 

 Mr. J. F. Mann — I think this paper is a most valuable one. 

 In the early days of surveying these transit theodolites were not 

 known, but with the transit and with tape measures the most 

 wonderful results have been obtained. I beg to move a vote of 

 thanks to Mr. Knibbs for his paper. 



Mr. D. M. Maitland — The information conveyed in Mr. 

 Knibbs' paper is of a most valuable and instructive character, 

 especially to those surveyors who have had any experience in the 

 higher branches of the profession. I am tolerably well acquainted 

 with most works on the subject and have had a fair experience, 

 but he has certainly treated the subject in a manner entirely new 

 to me. I think therefore the paper is all the more valuable. 

 From what I know of Mr. Knibbs I feel sure that any theory he 

 has advanced is certainly based upon his own practical experience, 

 and the observations he has made. For that reason I regard his 



