226 Mb POWER'S THEORY OF 



24. Let us imagine two different experiments, all circumstances, 

 as regards the materials, form and disposition of the apparatus, being 

 exactly similar, but the proportions in which the substances are mixed 

 on each side the membrane, being different in the two experiments. 

 Let us suppose also that the mixing process takes place in both experi^ 

 ments after exactly the same type, only with different velocities, that 

 is to say, that at certain times, t and t', t + T and t' + r, # + 2t and 

 #' + 2t', &c., the protruding spiculae from the lighter fluid exist in 

 exactly the same state in both experiments, as regards their number, 

 shape, size and situation. 



This supposition being made, the volume of the lighter fluid absorbed 

 by the fluid in the endosmometer in the two experiments, will be equal 

 in the intervals t and t' : also the summits of the spiculae will have 

 described the same paths in the two experiments during these same 

 corresponding intervals. Let t and t be indefinitely small, and let us 

 equate the spaces described by the summits of any two corresponding 

 spiculae between the epochs t and # + r, t' and t' + t', and also between 

 the epochs t and ^ + 2t, t' and #' + 2t'. 



Let a be the sphere of sensible attraction, and imagine a small 

 normal column 2 a at the vertex of each spicula, being half in one 

 fluid and half in the other. 



The two spiculse having by the hypothesis the same shape, the 

 moving forces upon these columns are as {p — rf and [p' — r'f, and the 

 masses moved are as ap + ar and ap' + ar', that is, as p + r and p' + r; 



the accelerating; forces will therefore be as — and '^ , / ; let 



^ p+r p +r 



(p _ rY (p — r'f 

 them be k ^ '- and ^ k . ^ f- . Then if v and v' be the velocities 



p+r p +r 



of the two summits at times t and t', equating the corresponding spaces, 

 we shall have 



and 



P + r " ■ ^' p+r' 



■^ p + r ^ p +r 



