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PROFESSOR J. H. POYNTING OX RADL\TIOX IX THE SOLAR SYSTEM : 
If we resolve this along’ the normal to the surface A and integrate over the 
hemisphere we obtain the total normal pressure. As we only want to know the 
change in pressure P we may neglect the first term which gives the pressure on A at 
rest, and we have 
p _ C N cos- 9 
~ ) ~ U 
If is tlie angle between the normal ])lanes through B and P we have 
cos X — cos d cos (f) -|- f^in 9 sin (j) cos (f). 
Putting = sin 9 d9(/(f), 
P = p I cos" 9 sin 9 (cos 9 cos \p 29 sin ifj cos (/>) d9 d(f) 
_ttN u cos xfj _ cos xjj 
- U- “ ■ 
The change in the tangential stress is evidently in the direction AC, that of the 
component of n in the plane of A. 
We may therefore resolve each element of tangential stress in the direction AC. 
Omitting the first term again, since in this case it disappears on integration, the 
element due to doj in the direction AP will coiitribute 
N cos 9 sin 9 cos 7> 2u cos y , 
u ■ U ' 
and integrating over the hemispliere we have 
h d^2u^ 
O), 
T = I “ 1 cos 9 siiP 9 cos (cos 9 cos t// + sin 9 sin v/; cos d9 dtj) 
J 0 J 0 U ~ 
_ ttN u sin i/; _ Rw sin ip 
~ 2U" ~ 2U- 
Force on a Sphere moving with Velocity “ (O’ in a Given Direction. 
If a sphere, radius «, is moving with velocity u, we may from symmetiy resolve the 
forces on each elemeiit in the dii ection of motion. The resolutes will be P cos ip and 
T sin Ip. Evidently it is suificient to integrate over the front hemisphere and then 
double the result. We have the 
-r, . T , ih/Rw cos'-ik , Rw sin-,, o • ,7, 
Ptetarding Force = 2 | (- —- + - - - j lira-' sm ip dip 
' 0 \ 
Rw 
3 ry 
U'^ 
Trar. 
