AND ITS APPLICATION TO MR. B. TOWER’S EXPERIMENTS. 
203 
Equation (86) is a quadratic for c in terms of sin <£ 0 , from which it is clear that as c 
increases from zero (/> 0 goes through a minimum value when 
c 2 = 
2K, 
6 1 sin 0 1 
K, „ / • /i sin 30, 
J |0i - 5 — 1 
„ sin 20, 
— 3 (sin 0 X — 0 X cos 0 X ) —^ - 
(37) 
As the load increases from zero the value of c increases from that of equation (79) 
to the positive root of (87). As the load continues to increase c further increases, but 
<j) 0 again increases, so that, as shown by equation (86), for values of <£ 0 greater than the 
minimum there are two loads, two values of c, and two values of y. 
If 6 X is nearly ^ c will be of the order \Z c’y when <f> 0 is small, and sin </> 0 will be of 
the order 4c; so that, so long as \ f — is sufficiently small, no error has been intro- 
V Z XL 
duced by the neglect of products and squares of these quantities. 
For example 
0 X = 1 '37045 (78° 31' 30" as in Tower’s experiments). . . . (88) 
By equation (86) 
sin<£ 0 =3*934c+l-9847^ . 
And by (87) at the minimum value of <£ 0 
/a "1 
C = V2R 
sin 4> 0 =5’G1 j 
Putting sin (f ) x — sin <£ 0 equation (82) becomes 
sin <bi= —’16776c-b ’5656 — . 
Kc 
or, when <£ 0 is a minimum, 
sin <^=’682 ^ 
Therefore 
X =4-928 V / |. . . 
Equations (84) and (85) give 
|=-l’1753K lC . . . 
JLw 
(89) 
(90) 
(91) 
(92) 
(93) 
(94) 
-2-74K. 
2 D 2 
( 95 ) 
