no JOURNAL OF THE 



From [S) a = ; hence <? in eqs. (14) and (15; is 



1 8oo6-- 



given (in length of arc on a unit circle) by 



a = as'- ^ ar N" = N^ == .001745329 N^; 



1800 



.-. log a = 7.2418774 — 10 + log (N^) (16). 



The above value of a can be obtained likewise from eq. 

 (7). It is independent of <f, as in fact was assumed from 

 the first; but since s = Nc^ the values of both x and r 

 above, vary directly as c. 



Therefore if we compute from (14) and (15) successive 

 values of x and y for c = 100, corresponding to N = i, 

 2, 3, 4, . . . , 15, and denote these values by, 

 Xi, X2, X3, . . . . , X^5, 

 Y Y' Y Y 



the subscripts denoting the station to which they refer; 

 then when c has any other value than 100, we have by (14) 



and (15), 



Xc 0.2 NX 



^r = = (17), 



100 D° 



Yc 0.2 NY 



y = — = (18); 



100 D° 



the last forms being derived by substituting for c its value 



20 N 



given by (12). 



The results of the computation are given in the adjoin- 

 ing table under the corresponding values of N given at the 

 tops of the columns. 



