44 



THE VOYAGE OF H.M.S. CHALLENGER. 



value of their own as showing the connection between the strength of a salt-solution 

 and its expansibility : — 



From Dr. Gibson's numbers, with the help of a table of reciprocals, we have the 

 following data as to volume instead of density : — 



Next, to find the maximum density for each solution, and the corresponding 

 temperature, we must represent these volumes by parabolic functions of t. Thus the 

 first three numbers are closely represented by 



y = 0-97083 + °'°^ 11 (9 + 2 , 



so that the first solution has its maximum density (l - 030) at —9° C, and its coefficient 



of expansion is 



0-0000093 (9 + t). 



Such formulae, of course, must be taken for no more than embodiments of the data, 

 and any application of them considerably beyond the temperature limits 0° — 1 2° C. is 

 purely hypothetical. 



For the second solution — 



y = 0-93306 + O " 00 °0 951 ( 37 . 2 + tf, , 



so that (under the reservation just made) the maximum density is T0717, at — 37°'2, 

 and the coefficient of expansion is 



0-0000056 (37-2 + 0- 



For the third — 



y = 0-89884 + 0-0000018 (72 + tf 



The maximum density is 1-1125, at —72° C. ; and the expansibility 



0-000004 (72 + 0- 



