208 M. Soret on Ozone. 



power of the nilf actum of the equation ; and observing that 



canont. U is of the form (a, . . .)" +1 (^ y) n+ \ *• e - tnat ^ ^ s °f tne 

 degree w+1 as well in regard to the coefficients as in regard to 

 the variables (x, y), it is easy to see that the resultant is of the 

 degree 2w(w + l) as well in regard to the coefficients as in regard 

 to (X, Y) ; that is, we have 2n as the index of the power in 

 question. 



3. In particular, if Y = 0, the theorem is that the resultant of 

 the functions canont. U, canont. ^ 2 \J is equal to the 2/ith power 

 of the first coefficient of canont. U. 



Thus for n= 1, that is, for the cubic function (a, b, c } d^jc, y) 3 , 

 we have 



canont. U = 





y 2 , —%y, ^ 



a , b , c 



b, c , d 



= (ac — b 2 , ad— be, bd—c^Jx 9 y)% 



canont. ^^U = 





y, -x 

 a, b 



= ax + by. 



And the resultant of the two functions is 



= (ac-b*, ad -be, bd-c^Jb, -df 



= -{ac-b 2 f, 



which verifies the theorem. 



The theorems were, in fact, given to me in relation to the 

 quantic U and the second differential coefficient B*U ; but the 

 in troductioninstead thereof of the second emanant (XB^ + YB ) 2 U 

 presented no difficulty. 



2 Stone Buildings, W.C., 

 February 16, 1863. 



XXIX. Experiments on Ozone. By M. Soret. 

 In a Letter to Professor Tyndall *. 



YOU have perhaps remarked that I have made a note of one 

 or two observations relative to ozone. This leads me to 

 say a few words to you on some experiments which I have since 

 then made on this subject in M. Bunsen's laboratory. I had 

 formerly ascertained [Archive, 1854, vol. xxv. p. 263) that the 

 quantity of ozone is greatly increased when the voltameter is 

 cooled, as you have also found. I had made some analyses by 

 arsenious acid, but the method was not perfect. I resumed 

 experiments of the same kind, using M. Bunsen's method with 

 sulphurous acid and a standard solution of iodide of potassium. 



* Communicated by Professor Tyndall. 



