354. Mr. Nixon on the Measurement {hy Trig07wmetry) of the 



stituted in the register for an actual observation of the signal 

 B. When A and B had been seen also from D (or any other 

 station), two or more values of the required reading were pro- 

 cured by the same process of calculation, of which the mean 

 was adopted. 



When the distance between two signals (E, A) has been 

 measured from several 

 bases (C, B, &c.), the 

 claim to accuracy of 

 each measurement has 

 been considered, in the 

 determination of the 

 proper mean, to be in- 

 versely as the greatest 

 error to which, limiting 

 the uncertainty of ob- 

 servation to one minute, 

 it may be deemed liable. 

 This 7naximwn error of 



the distance in logarithms [x) was calculated by the following 

 formulae, in which d denotes the difference between the log. 

 sine of the angle D, and that of the same angle +1', and a 

 the corresponding difference for the angles A and A + 1'. 



Class I. — Given the observed angles E, A, D, each corrected 

 by one-third of the difference of their sum and 180°. 



Case 1. — D and A being acute. 



X =. d + a, when a = d; 



X = — ^ — -, when a exceeds d; 



X = — - — -, when d exceeds a. 

 Case 2. — When either D or A is obtuse. 



2d +2a , ^ , , 



X = — , when a = 2d, or d = 2a ; 



X = — ;; , when d exceeds 2 a ; 



.r = -^ — , when a exceeds 2 d. 



Class II. — Given the observed angles D and A only. 



x = a + d; D and A being both acute, or either of 

 them obtuse. 



Class III. — Given the observed angles E antl A only. 



Case 



