Fig. 2. 



130 Dr. C. H. Lees on the Viscosities of 



medium and v 2 of the second, then 

 I = h + x ll 



In the general case where Vi, v 2 , v$, &c. c.c. of the constituents 

 V\> V2> Vsi & c « are present in 1 c.c. of the mixture 



i •=- h + E? + ^ + 



^7 ^7l ^2 ^?3 ' ' 



This result is independent of the number of layers of each 

 constituent present. In the tables which follow it will be 

 referred to as the " mobility formula.'"' 



II. Making the same assumptions 

 as to the velocities, but taking the 

 planes separating the fluids as z=z , 

 Zi, z 2 , & c -> i£ the fluids are present 

 in equal volumes (fig. 2) we have 



v= i(vi + 12) ; 



if 1 c.c. contains i\ volumes of the 

 first and v 2 of the second 

 rj = v 1 Vi + v 2 i] 2 , 

 and in the general case 



V-v 1 v 1 + v 2 rj 2 + v d 7j 3 + .... 

 A result again independent of the number of layers of each 

 constituent present. In the following pages this will be 

 referred to as the " viscosity formula." 



III. Thirdly, let there be two systems of separating planes 

 mutually perpendicular to each other. 



Fi?. 3. 



Fig. 4. 



If there are two fluids of viscosities r) { , rj 2 present in equal 

 volumes, distributed as shown in fig. 3, or in fig. 4, the 



