86 Mr. C. Chree on the Theory of 



Then we easily find 



^ ^ (yyo- 1 + x ""^ff" - Wi -V ) + *V (i -V) 1 



v 2n =MyyoH^w(i-y)+«''(i-/)H j> (58 } 



^ = * T, + (* 2n _ 2 - ^/("i + 26,V) , 



s 2n ^v"T 2 +(v 2n _ 1 -vJ/(a 1 +2b 2 Y"). 



Let S be the whole space travelled by the centres of the 

 cups in n double intervals T x + T 2 . Then we find 



= n(U / T l + « / 'T 2 )+ {v -v 2n )/{a 1 + 2b 2 V t ) 

 It is easy to prove 



*-tw= ( i - W) > { »• - s ' + (* - s ") ^£77 } ' 



»l+«3+---+» 2 »_ 1 -(»2+»4+---+V) 



..(fi'-c")(i-y')(i-y") 



= n 



and, after some reductions, we find 



«» «T 4. r.»T ^ + 2^(V'-V")(f'-f")(l-y)(l-y) 



S = „(r'T 1 + t - T,) + » (ai + 2ft 2 V')(aH-2i 2 V'')(l-yy') 



2^(v-v")y(i-y') j 



i + 



We may regard S as composed of three terms. The first 

 term, nfv'T, + r-"T 2 ), would alone exist if the equilibrium 

 theory were true ; it is proportional of course to n. The 



