768 On the Specific Gravity of Sea Water. [No. 153. 



The numbers in the last column suggest the probability, that those 

 in the adjoining column whose differences they are, increase by arith- 

 metical progression. The differences between the former numbers them- 

 selves, sometimes in excess, sometimes in defect, with respect to such 

 as have nearly the same situation in the scale, are attributable to errors 

 of observation. With respect to numbers having remote situations on the 

 scale, their differences obviously decrease with increase of temperature, a 

 fact which would have been still more obvious, had I introduced more of the 

 table than I have deemed it necessary to do. This, however, was to have 

 been expected from the increased capacity of the bottle by augmentation 

 of temperature, if the process for ascertainment of the specific gravities 

 quoted were weighing, or the greater buoyancy from the same cause, were 

 a floating hydrometer used. I am inclined, therefore, to disregard this 

 decrease, and doing so, I take the average of the differences, which I find 

 to be 1 1 1 . Resuming the preceding table and adopting this ratio, we have 

 Temperature. 



16 



0.9991260 



= A 







17 



0.9984852 



= A— d. 



(d-0001508) 



= B 



18 



0.9988133 



= B— 



(d -j- v) when v. 



= 0000111 = c 



19 



0.9986403 



= C— 



(d -I- 2v) 



= D 



20 

 2L 

 30 



0.9984562 



= D— 



(d -f 3v) 



= E 



0.9960037* 



= D— 



(d + Hv) 





This gives the nth term, commencing with any one A in the scale, 

 as follows : — 



N. A— n— 1. rf— (17 + 2t; + 3t>+ w— 2 v.) 



It will be understood that I have preferred examining the part of the 

 table above quoted on account of the analogy in point of temperature 

 to conditions of my own experiments. I have stated above, that the 

 law of variation of density with change of temperature in sea water, 

 seems to differ from that in distilled water. As has been shown, the 

 latter involves a function of a constant difference and a difference by 

 progression, while so far as my experiments go, the former consists of 

 the constant difference alone. Those experiments were made on water 

 varying in temperature from 60° to 70° of Fahrenheit, and indicated a 

 decrease of sp. gr. of 1880 for each additional degree of temperature. 

 Hence the general term, commencing as before would be 



A— w— 1 d. 

 According to this the corrections given in the fourth column of the fol- 

 lowing table have been made. 



* The observed quantity is .9959917 ; the difference is -f- .0000120, a quantity 

 too small, I apprehend, to cast a doubt upon this general law. 



