1863.] 565 



resultant of a lineo-linear system of equations in its most perfect 

 form. It is easy to obtain two different solutions, each of them 

 unsymmetrical in respect of the data of the question ; the conversion 

 and fusion of each of these into one and the same determinant, sym- 

 metrical in all its relations to the data, is effected instantaneously 

 by a process derived from the above theorem. In that particular 

 application of it, the umbrae involved each represent columns of 

 actual quantities in number equal to the number of places in the 

 width and length of the umbral matrix to which they belong, 

 so that each coefficient in the product of a lateral by a longi- 

 tudinal factorial represents an ordinary determinant made up of 

 these columns, from which it is evident that the polar law of sign 

 and nullity necessary for the truth of the theorem are satisfied in 

 the case supposed. 



V. "Notes, principally on Thermo-electric Currents of the 

 Bitterian Species." By C. K. AKIN, Esq. Communi- 

 cated by Professor STOKES, Sec. R.S. Received March 26, 



1863. 



(Abstract.) 



The electromotive force of a thermo-electric couple is a function of 

 the nature of the metals of which it is composed, and of the tempe- 

 ratures of the junctions. It is expressed in this paper by 



[*. yJT. 



where x and y are names of metals, and T and t are temperatures. 

 In this notation Becquerel's two laws become 



la, S$=[a, 4]f-[>, 4]f; .... (I.) 

 and 



(a, e )7=[, i]7+[4, e ...... (II.) 



From (I.) we learn that the electromotive force of a couple may be 

 expressed as the difference of two quantities which are functions of 

 the temperature and of the nature of the circuit, or 



[*,y]7-[:,y] T -[.y] ( ..... (in.) 



VOL, XII. 2 S 



