252 Joty—On the Origin of the Canals of Mars. 
The equation determining the stress at any point is found as follows :— 
The force at any point on the elementary ring assumed one ec. m. deep (fig. 1), 
is =) the horizontal component per elementary volume is 
dh = p. 5 . pda. dp 
1 — cos’0) 
= Soy eee) 
ER ease 
(= pda(\- 5 - | cos ad) 
= pda (tog tan( 7 - 5) + sin 6,) s 
h ] ot so XO. Si 
stress = Uy sh By Se an G 3) + sin 0 aa (1) 
poa a tan 6 
This is a maximum when 
: sin 36 ene 
q sin 6 - gree log, tan ( = 3) =I 
From this the maximum value of the stress is found to correspond to a value 
ait () =, Tl Gye 
To construct the curve of 
stress, the values of that part 
of (1) enclosed in brackets for 
different values of @ are cal 
culated :— 
oy log tan (7 — ®) + sin 8 
tan 0 ie 
10° 5 0 ; 0-011 
20° : 9 C 0°088 
80° 0 < : 0-088 
40° : : c 07144 
502 S 5 0:206 
60° F 0 : 0-261 
70° 5 & : 0:290 
80° c 5 : 0°256 
85° 0 : : 0:186 
It remains to assign a value to 
Fic. 1. 
p and to a. 
If, looking forward to the time when Phobos, according to lunar theory, will 
have drawn nearer to the surface of Mars, and be about to share the fate of many 
predecessors, we assume Phobos to be the satellite responsible for the stresses 
under consideration, we must still assign at a guess a density to the satellite. 
