ITS EFFECT ON TEMPERATURE AND ITS PRESSURE ON SMALL BODIES. 547 
It is noteworthy that one half of this is due to the normal, the other half to the 
tangential stresses. 
If the sphere has density p the acceleration is obtained by dividing by imi^p, then 
dll/(it = — 2 Ru/U-p'c 
J/fft'Ct 0)1 I^OtotlOK. 
If the sphere radius a is rotating with angular velocity w, then any element of the 
surface X from the equator is moving with linear velocity at w cos X in its own plane. 
This does not affect the nf)rmal })ressure, but it introduces a tangential stress 
opposing the motion 
Itw/2U~ = Rcto) cos X/2U^. 
Taking moments round the axes and integrating over the sphere, we obtain 
couple 
a 
4 .-,3 ■'> ■’ d(x> Rnw 
%TTCr . a~ = 
whence 
" dt 2U- 
2 
dojidt = — I Rw/2UV«. 
cos® XdX, 
I he rate of dhniiiution of w is therefore of the same order as that of v_. 
To obtain an idea of tlie magnitude of the retardation of a moving sphere, let us 
suppose that one is moving tlirough a stationary medium. Let its radius be 
a = 1 centim., its density p = 5-5, its temperature 300'" A. 
Then 
1 du _ ^ 2 X 5-32 X 10“® X 30tA 
u dt ~ 9 X~1o2o^^.5 
= 1-75 X 10-1®. 
This will begin to affect the velocity by the order of 1 in 10,000 in, say, lO’^ seconds, 
or taking the year as 3T5 X 10^ seconds, in about 30,000 years. 
The effect is inversely as the radius, so tliat a dust |)ai'ticle O'OOl centim. radius 
will be equally affected in 30 years. 
Ihe effect is as the fourth })ower of the teiuperature, so that with rising tempera¬ 
ture it becomes rapidly more serious. 
Aquation to the Orbit oj a Small Spherical Ahsoi'bing Particle Moving in 
a Stationai'i/ Medium Round the Sun. 
It is evident from the above result, that the effect of motion on radiation pressure 
may be very considerable in the case of a small absorbing particle moving round the sun. 
XX'e shall take the particle as spherical, of radius a and distance r from the sun. We 
shall suppose the radius so small that the particle is of one temperature throughout, the 
4 A 2 
