of the Trajectories of Shot. 283 

 "With Mr. Bashforth's law substituted, this is 



-^(1000) 3 ET4 = w Dsec0 (a) 



*J qsec<p 



Now the quantity 



180g 



7T 



can be calculated for every 10 feet, by giving K its mean value over the 

 10 feet, beginning with 1700 for ogival-headed shot and with 2150 for 

 spherical. Supposing this were done, and the results for all the compo- 

 nents of 10 feet added together, the number opposite any velocity v would, 

 for example, in the ogival-head-shot tables, be the value of 



*1700 t\j 



dV 

 KY 4 



If we denote this quantity by V„, the equation (a') may be written 



d 2 — 



"V 2 sec^ — Vp gec( p = — D sec^>, ....... (a') 



which may be regarded as an equation for the determination of q. 



The distance-ordinates and time may be found in a similar manner. 

 They are given by 



s%p sec <p 

 _ X = p.ns fh 1 



w 



r X=co S *l _ K | 2 , (b') 



%) ffsec © 



d 2 - C 



seccp 



r sec ^Tooo^,^v 



"> (C) 



KY 



2 seccp 

 v q sec <p 



If we denote by S„ and T v the two integrals 



■ 1700 ■ /ww o o 7TT ^1700 



KY 3 ' 



the equations (b'), (c'), and (d') become 

 d 



W 



X = COS^(S ?8eccp -S^sec^), (fr) 



