154 



ME J. Y. BUCHANAN ON THE 



The variations are more strongly marked in the values of —. — , which, in an 



am 



exaggerated manner, indicate the nature of the changes from high to low values. 



The values of v/m show an undulatory variation in consecutive values as contrasted 

 dA 



with the values of 



dm' 



§ 78. In the following diagram the values of v/m are represented by the ordinates, 

 and those of m by the abscissae : — 



m 













V 

















17 00 

 16-50 

 16 00 











/^ 



\ 













/ 







"- 









N 



\ 





/ 







/ 



















\ 



/ 





































I5S0 

 15-00 

























' 



























- 





64 



3 



2 



5 



3 



7 



4 



6 



6 



7 



8 























128 



64 



128 



64 



128 



64 



64 



64 



64 



64 



The changes in the value of v\m with change of m, as shown by the contour of the 

 curve, indicate marked phases at concentrations where m = 3/128, 7/128, 4/64, and 7/64 

 gram-molecules, and a very characteristic sequence of changes takes place between 

 m = 4/128 and m = 8/128. 



The advantage of introducing the arithmetical series is that these remarkable varia- 

 tions of displacement are clearly displayed, whereas they would be apt to be masked if 

 we had only the geometric series. 



The reality of the remarkable features of solutions of low concentration ivhich have 

 for the first time been demonstrated in this research is firmly established by the care 

 ■with which the experiments have been made, and by the agreement between the results 

 of independent series of observations. 



