AND ITS APPLICATION TO MR. B. TOWER'S EXPERIMENTS. 
201 
Eliminating y between equations (70) and (71) 
. K 2 2 sin 6 , 
sm <j) 0 / 2sin 3 # 
iV i c (d -^~-l + i S in 2 # 
(75) 
The equations (74) and (75) suffice to determine a, c, and (f) 0 under the conditions 
/y T and c small so long as </> 0 is not small, in which case the terms retained in the 
equations become so small that some that have been neglected rise into relative 
importance. 
To commence with let 
(Cases 5 and 9, Section III.) 
Then by (72) 
and by (70) 
putting for y its value sin — <£ 0 ’i 
L = 0 
cos <£ 0 =0 
X=~ 
sin 6 X 
XT 
. sin #, 
cos <f>i = — e — 
(76) 
Equation (76) gives two equal values of opposite signs for c f> v These correspond to 
the positions of P 2 and P 2 , the points of maximum and minimum pressure. 
For the extreme cases 
<£.1— =b\/t#i ~) 
^=0 
6^ = 77 
From equations (73) and (47) 
2/AW 
a— 
and from (75) 
</>i=± cos J - \- 
(77) 
4 > =°i 
j 
M 
sin 6 y 
When L increases 
From (72) and (75) 
, , E /sin 29 x a 
tan 4= l K,( — r l ~6 1 
(78) 
(79) 
2 sin #. 
2 sin 2 #. . . 0/a 
#!— a— x + i sm 2#! 
■ (80) 
Hence as L increases tan (jj Q diminishes until the approximation fails. This, how¬ 
ever, does not happen so long as c is small. 
MDCCCLXXXYI. 2 T> 
