Saline Solutions at High Temperatures. 



83 



four t'onnulae which he considered requisite, and obtained the 

 following results : — 



It will thus be seen that between the limits of 30° and 100'' 

 the third difference is sometimes positive and sometimes nega- 

 tive, having a mean value of only "000001, as if the varying 

 third difference were almost or altogether due to errors of obser- 

 vation; and therefore apparently for temperatures higher than 30° 

 the empirical formula should not involve any terms having higher 

 powers of t than the second. It is evident that for tempera- 

 tures below 30° an entirely different formula would be requisite; 

 but since this paper has special reference to high temperatures, 

 I need not further dwell on those when the same cause which 

 gives rise to the expansion of water somewhat above the freezing- 

 point, has evidently begun to make itself apparent. Calculating 

 from the above data, I deduce the following general formula, 

 giving the volume at ^° C. : — 



V = -997696 + OOOllOh + -00000343^, 



The volumes at various temperatures, calculated by means of 

 this formula, are compared with those given by Kopp in the 

 following Table : — 



G2 



