[52] PROFESSOR STOKES, ON THE EFFECT OF THE INTERNAL FRICTION 



— F = 4 -Kg (<t - p) a 3 , where g is the force of gravity, and <r, which is supposed greater than 

 p, the density of the sphere. Substituting in (126) we get 



F= ^(-- 1 ) fl2 < 127 > 



9m \p J 



Let us apply this equation to determine the terminal velocity of a globule of water forming 

 part of a cloud. Putting g = 386, /a' = (.116) 8 , an inch being the unit of length, and supposing 

 ap~ l - l = 1000, in order to allow a little for the rarity of the air at the height of the cloud, 

 we get V = 6372 x 1000a 2 . Thus, for a globule the one thousandth of an inch in diameter, 

 we have V = 1.593 inch per second. For a globule the one ten thousandth of an inch in dia- 

 meter, the terminal velocity would be a hundred times smaller, so as not to amount to the one 

 sixtieth part of an inch per second. 



We may form a very good judgment of the magnitude of that part of the resistance which 

 varies as the square of the velocity, and which is the only kind of resistance that could exist 

 if the pressure were equal in all directions, by calculating the numerical value of the resistance 

 according to the common theory, imperfect though it be. It follows from this theory that if 

 h be the height due to the velocity V, the resistance is to the weight as 3ph to 8aa. For 

 V = 1.593 inch per second, the resistance is not quite the one four hundredth part of the 

 weight ; and for a sphere only the one ten thousandth of an inch in diameter, moving with the 

 velocity calculated from the formula (127), the ratio of the resistance to the weight would be 

 ten times as small. The terminal velocities of the globules calculated from the common theory 

 would be 32.07 and 10.14 inches per second, instead of only 1.593 and .01593 inch. It appears 

 then that the apparent suspension of the clouds is mainly due to the internal friction of air. 



44. The resistance to the globule has here been determined as if the globule were a solid 

 sphere. In strictness, account ought to be taken of the relative motion of the fluid particles 

 forming the globule itself. Although it may readily be imagined that no material change 

 would thus be made in the numerical result, it may be worth while to point out the mode of 

 solution of the problem. Suppose the globule preserved in a strictly spherical shape by 

 capillary attraction, which will very nearly indeed be the case. Conceive a velocity equal and 

 opposite to that of the globule impressed both on the globule and on the surrounding fluid, 

 which will reduce the problem to one of steady motion. Let fa, &c. refer to the fluid forming 

 the globule, and assume fa =/, (r) sin 2 9. Then we get on changing the constants in (119) 



/, (r) = A.r- 1 + B,r + C^ + X>,^. 



The arbitrary constants A u .Bj vanish by the condition that the velocity shall not become 

 infinite at the centre. There remain the two arbitrary constants C lf D y to be determined, in 

 addition to those which appeared in the former problem. But we have now four instead of 

 two equations of condition which have to be satisfied at the surface of the sphere, which 

 are that 



R = 0, #, = 0, e = G„ T e =T w whenr = o. . . . (128) 

 We shall thus have the same number of arbitrary constants as conditions to be satisfied. Now 

 T 19 will involve ^ as a coefficient, just as T t involves f/p or yu; and p n which refers to water, 



