1889.] Lagrange’s equations to certain physical problems. dol 
dF. dF 
Pe ae, 
dq, 44, 
It should seem that Lagrange’s equations can be applied to non- 
mechanical systems only when they can be shown to possess this 
reciprocal property. The system of two circuits was shown by 
Felici to possess it, Maxwell § 536 (2). 
If a system does not possess this property, for instance, the 
system of circuit and shell, then instead of deducing the forces 
from the energy, we must proceed in the reverse direction, de- 
ducing the energy from the forces. If 7 be the current and ¢ the 
strength of the shell, it is found by experiment that the force 
di dd 
dit a? 
, and therefore the energy T is given by 
and therefore 
required to increase 2 is L 
: eed du 
increase @ is K ree M oF 
27 =1(li+ Md) +o (Kh —-M) 
Sh Kg 
and the force tending to 
February 11, 1889. 
Mr J. W. CLARK, PRESIDENT, IN THE CHAIR. 
The following Communications were made: 
1) On Systems of Quaternariants that are algebraically com- 
y : g Y 
plete. By A. R. Forsyts, M.A., F.R.S., Trinity College. 
[ Abstract. ] 
THE aim of the memoir is to obtain for certain systems of 
quaternary quantics the respective systems of concomitants that 
are algebraically complete, that is, are such that every concomitant 
of a quantic can be expressed as an algebraical (but not neces- 
sarily nor generally an integral) function of the members of the 
system appertaining to that quantic. The method and the course 
of development are similar to those in corresponding investigations 
relating to ternariants; in the present case they are complicated 
by the presence of six (non-independent) line-variables. 
It is shown that the characteristic equations satisfied by quater- 
nariants can be reduced to twelve linear partial differential 
equations of the first order, which are independent of one another 
in form; and that these twelve can be reduced to six of them, 
