of using the Theodolite. 1T7 



In this formula, n is always a very large number, so that the 

 fraction ,- is almost unit ; and thus 



\ = ^1 ^\ "^^^y- 



When the system of three readers is used, the error is of the 

 form 



3 



and thus the entire measure of inexactitude is 



which may be expanded into 



in which jo' will occur in each of the three situations (n — 1) 

 {n — 2) times, that is in all 3 (n — 1) (?* — 2) times; while 

 2;? gr will occur in each place 2 {ii — 2) times. We have, then, 

 for the entire measure of inaccuracy 



i {3(«-l) («-2) 2/>'^ + 12 (m-2) 2i>(?} 

 and for the measure of one chance 



that is {e f 



3 n(n — l) 

 1 » — 3 1 . 



(« — 3)2.^« 



s'' ?t n — 1 3 



_ 1 !izi2 (e Y 



whence e, = e — - — - 



^ 1 \f 3 n — 1 



Putting, in general, i for the number of readers, the form of 

 one error is 



p + q-i-r-i- (» tenns) 



« 



and hence the measure of inaccuracy of an ohservation with t 



readers is 



(eY - 2 . {jt> + g -f r 4- i terms}* 



^ '^ ■" i«.M(» — 1)(» — 2) (n — »+l) 



VOL. XXVI. NO. LI. — JAIJUABY 1839. M 



