ON THE DIFFUSION <>K LIQUIDS. 

 .1=0 



and '" = -rr. p=[0,l,2 f 3 ), 



Thus u is given by 



tt'- 4n- 



u = B -f- B x e ~ ÛT 'cos.— + B.e ^ ' cos 2 ™ + (5) 



H H 



Hence it follows that at t=o, 



u=B a + B l cos— + Bxos— + (6) 



H H 



and at any time t, // may be put as 



u = b + b l cos^l— + b.,cos ' L + (6') 



H H 



where b = B , 



b^B, e~'^ rk ^ 



471-1 



■ht 



b.,=B., e H- ' 



Thus we get 



k=EL lnn (^\ =: I 1 L 1nn (^L\ = (7) 



a. / -°i \ X1 / JD ' 2 \ 



^ h H'irri^ lorj \~b7) 



Though k may be determined by any of these relations, the first 

 relation is best suited for the purpose. In fact, when the vessel is 



TT 



filled with the salt solution nearly to the height-^- initially the coeffi- 

 cients 6 2 6 3 become within two or three days so very small that 



they are of no practical use in the calculation. 



The expansions(6)and (<>') are Fourier's series. Their coefficients 

 may I if calculated by the ordinary method of multiplyingcos-^,cos— — -, 

 &c into u and integrating them, or by using harmonic analysers ; but 

 in the present case, it is more convenient to proceed as follows. 



