4.4? Rev. J. Challis on the Resistance to the Motion^ 8fc. 



of pressure which will sensibly alter their shape. An in- 

 equality of pressure very much less than the weight of a drop 

 would suffice to do this. 



Hence also we may account for the success of the common 

 method of making spherical shot, by letting them fall in a 

 melted state from a great height, so as to become solid in their 

 descent. 



It appears from our reasoning that the resistance to a small 

 spherical body descending in the air, is occasioned very little 

 by the condensation of the air it encounters, but principally 

 by its putting in motion and partly carrying with it a portion 

 of the fluid. Whatever be the law of resistance in regai'd to 

 the velocity (which it seems difficult to ascertain), we may con- 

 ceive of the nature of the resistance by supposing a variable 

 mass Mf{v) to be always attached to the descending body M, 

 and to be unaffected by gravity ; so that if F = the effiective 



accelerative force, g M = F [M+ vif[v));Y = ^^^±-j^y 



The foregoing inquiry will also assist us in ascertaining the 

 nature of the resistance of the air to the motion of a pendu- 

 lum-ball, suspended by a long slender thread. As before, the 

 resistance is not sensibly due to any change of density of the 

 air. The motion being slow and the vibrations of small ex- 

 tent, we may suppose, without chance of sensible error, that 

 the velocity of a particle of the air in the same position rela- 

 tively to the centre of the ball and the direction of its motion, 

 has always the same ratio to the velocity of the ball. Hence 

 if M be the mass of the ball, y. that of an equal volume of 

 air, 171 a certain constant, and v the velocity of the ball, we 

 have this equation of vis viva : 



Mv- + mv- = 2^ (M— ]«.) {h-x), 



h—x being the vertical descent of the centre of the ball. 



Hence the vertical accelerative force, or j~, which is 



■\i 



the only one that acts, is -7 . -^ — ~ ; and the time of vibra- 



/ M + m ^ , rj., 

 tion is to the time in a vacuum, as / t^^ — to 1 . 1 riese 



results have been obtained by M. Bessel. [Researches on the 

 Length of the Seconds Pendulum: Berlin, 1828.) 



The last application I propose to make of the preceding 

 analysis, bears upon the nature of light. The undulatory 

 hypullicbis of light requires us to give a reason why the planets 



