1876.] the Expansion of Sea-water by Heat. 161 



calculated and observed results, and also (after the necessary corrections 

 and reductions have been made) between the volumes calculated from the 

 formulae from different series of observations on the same solutions. 

 Finally, a general formula of the form 



was found, giving the relation between the volume (v), temperature (£), 

 and specific gravity at 0° C. (s) of any solution of the same composition 

 of sea-water the specific gravity of which at 0° C. lies between 1*020 and 

 1*033, the volume at the same temperature being taken as unity • in 

 which expression 



<j,(t) = 1 + -00008097*+ -0000049036^- -000000012289* 3 , 



,£(*) = _10- 5 (-5509^--020198* 2 --00033276* 3 ), 

 and /(V)=ll-95-940(s-l-02)*. 



In the original paper we show that if c be the specific gravity at any 

 temperature t of a solution the specific gravity of which at 0° C. is s, 



we may without sensible error assume -^ to be constant • whence, by 



means of the above formula, we are able to give in the following Table 

 all the data necessary for calculating the specific gravity of sea-water of 

 any degree of salinity at any temperature between 0° and 36°. Column 

 IT. contains the specific gravities at the temperatures given in Column I. 

 of a solution the specific gravity of which at 0° C. is 1*02000 j Column III. 

 contains the numbers which must be subtracted from those in Column I. 

 for each increase of 0°*1 over the temperatures opposite to which they 

 are placed • and Column IV. the numbers which must be added for each 

 increase of *00001 of the specific gravity of the solutions at zero. At the 

 heads of Columns III. and IV. are the numbers of ciphers which must 

 be prefixed to the figures written in them in the unit place. 



In order to facilitate the use of the Table, we subjoin directions for its 

 application in the form of rules, and give a couple of examples. 



I. Given the specific gravity of a sample of sea-water at any tempera- 

 ture t, to find it at 0° C. : — Look out in Column I. the figure giving the 

 number of entire degrees of the temperature ; multiply the corresponding 

 number in III. by the fraction by which the observed temperature exceeds 

 that number, and subtract the result from the corresponding number in 

 Column II. Subtract the difference from the observed specific gravity, 

 and divide the number so obtained by that corresponding to the observed 

 temperature in Column IV. (without prefixing the ciphers at the top of 

 the column) ; add the quotient to 1-02000, and the sum will be the specific 

 gravity required. 



Example I. Specific gravity observed at 18°-5 C. =1-02475. Number 



* The numerical constants involved in the above formula are given in the forms in 

 which they were, for facility of calculation, determined. The expression can of course 

 be easily transformed to the simpler form, 0J=S , 1 (tf)*f sF 2 (tf). 



N 2 



