§15 OF ARTS AND SCIENCES. 41:^ 



formula derived from the fundamental equation and from 

 equations (3) and (5) of § 13, namely, 



^ K =5-9-^(4 -^-3) V. 



For curiosity's sake, Table XV. was also constructed 

 to show the surface tension at intervals of 10" correspond- 

 ing to a given ratio of /' to /. It was assumed that the 

 density varied as the quotient of the absolute molecular 

 weight b}' the cube of the absolute molecular distance; 

 and having determined the value of / for water (about 

 .000,000,01), we have from § 13, IV. and (4), approxi- 

 mately. 



^JS=--('-T^-~ 



T 



■^ "' • V" I J To 



by which the value of S may be calculated roughly from 

 that of/' -T- /, and conversely. 



In the construction of the last three tables it was neces- 

 sary to calculate the ratio, /' -^ /, at various temperatures, 

 in terms of its value at o", which might have been done 

 indirectl}^ by means of Table X. and Table III. — the ratio 

 var3'ing inversel}' as the cube root of the volume. To 

 facilitate this calculation, however, an auxiliary table 

 was constructed (XVI.), by means of which, if the ratio 

 of /' to / is known at any one temperature, it may be 

 found at anv other. 



It is easy by means of these tables to find the values of 

 all of the six specific constants of this section, when a?iy 

 one is given. By reference to the proper table, the ratio 

 of /' to 4 can be found, already reduced to the tem- 

 perature zero; then with this as an argument, the val- 

 ues of the other constants can be derived, each from its 

 own table. It is assumed tliat the density and molecular 



