at different Temperatures. 3 



no clue to guide us in our present research. But we may 

 gather in genei'al that they decrease slowly ; and hence we 

 may infer that the quotients, at least for a considerable range 

 of temperature, may be expressed with tolerable accuracy by 

 means of the first and second orders of differences. But as 

 these differences cannot be found directly, we must try to de- 

 duce them in the best way we can from the numbers in the 

 Table, Representing the first and second diffei'ences by A 

 and A', we have this general expression of the quotient cor- 

 responding to the index x, viz. 



^^?^=-011857-x. A + -^--. A^ (A) 



Two values in the Table answering to given indices, are suf- 

 ficient for finding A and A^; but, on account of the irregu- 

 larities of observation, it will be better to proceed as follows. 

 Form the expressions of the seven quotients in the Table, 

 corresponding to the indices 1, 2, 3 — 7, and take a mean of 

 the whole; then, 



•010198 = -011857 — 4 A + 8 A^ 



In like manner, form the expressions of the four last quo- 

 tients, and take a mean ; then, 



•007842 = -011857 - -^ A + 61 A^ 

 By means of these two equations we get, 

 A = -0004545 

 A"'= -00001986. 

 Having now found A and A% we must return upon our 

 steps and compute, by means of the formula (A), the several 

 values corresponding to the indices 1, 2, &c. The results of 

 these calculations are placed in the next column of the Table, 

 and it appears from inspection that they are surprisingly near 

 the real quotients. Using the computed quotients in place of 

 the real ones, the elasticities have been calculated and set down 

 in the last column of the Table. Thus, to find the elasticity 

 answering to the index 4, we have the equation, 



log. — 



= -010158; 



-82 



whence, log -^ = — 0-8329 = — 1 -f -1671; 



then, —1-1671 



log. 30, 1-4771 

 log. r, 0-6442, e = 4-408. 



In like manner have the other elasticities been calculated, 



B 2 and 



