OF THE UNITED STATES. 3S9 



a smaller diameter, and yet capal)le of givinjj; the same ac- 

 curacy as the lar^c instruniciitr^. thoui:;h at the expense of 

 niore skill, labour, and lime of the observer. It was also 

 di sirable that the same instrument should equally serve for 

 vertical angles, in order to enal)lc tiic ol)server to determine 

 accurately latitudes, times, and tlie angles of elevation of the 

 signals. 



The multiplication of the terrestrial angles in the plane of 

 the horizon was far preferable to that in the plane of the ob- 

 jects, on account of the great influence of lefraction near the 

 sea shore, particularly upon sandy beaches and islands, where 

 it may be considered as varying constantly ; and even a sav- 

 ing of time in the calculations was an object worth conside- 

 ration. 



It was necessary, on this account, that tlie instrunicnt 

 should be of the repeating kind, and a theodolite. 



In planning an instrument to answer thi'se views, the prin- 

 ciples mentioned when treating of the two-feet theodolite 

 and the repeating circle with two telesco|)es, lead me to 

 unite the properties of l)oth these instruments, omitting only 

 the means of measuring ani^les in inclined planes. 



In repeating instruments, tlie main points to ensure accu- 

 racy are, — the exact and steady levelling of the instrument, 

 and the constant parallelism of the motions with respect to 

 each other, in the course of the re|)eatcd measurement of an 

 angle. These being secured, the plane of llie divided circle 

 itself, with its division, serves as a mere indicator of the ope- 

 rations, which has no influence until in the final reading of 

 the stoppins; point, by the amount of the reduction of the dis- 

 tance of it from its intersccti(tn with the real hoii/on and by 

 the accidental erroi- of the division used, which have been 

 shown to be the two smallest errors. The influence of ec- 

 centricity beinja; corrected tiy the indiscrin\inate mean of the 

 three readings, and the instrument admitiina; ;ill the systema- 

 tic coml)ination of the series of ani^les which the two-feet 

 theodolite admits for the siuKh* aniiles. 



The same principles, as far as relates to the mode of mul- 



