970 
y= sf de, dx, de, dx, + [20 ine dre da, de, de, de, =. (i) 
Here K, denotes the p* component of the force acting on the 
system per unit of volume. V—g de, de, de, de, being a scalar (if 
g is the determinant of the gas), K/W —g and not K must be a 
covariant vector, which further will be denoted by &. For the same 
reason not L, but LA’—g must be a scalar, if the variation law 
shall be expressed invariantly. We suppose the function of LAGRANGE 
L to consist of different separate parts for the gravitational field, 
for the matter, for the electro-magnetie field and for the electric 
convection-current, 
Structure of the function of LAGRANGE. 
3. The contribution of the gravitational field to L will be denoted 
by V—g H. It will be known, that for 7 must be taken (7/2, where 
G is a scalar indicating the curvature of the field figure and x the 
gravitation constant. By means of Riemann’s symbol, G may be 
expressed as follows : 
Ei (im) gin Gis 
Gim = (kl) gk! (ik, ln), 
(ik, lm) = 5 (Gim,kl + GYklim — Yil,em — Jkm,il) + 
Stabler im kl il km | a 
rde | ol Le | IE in 4 
The quantities get (a, b= 1, 2, 3,4) are the algebraic complements 
of the gas Yim,ki is written for the second derivative of gin with 
respect to a, and z/; and Cpristorrel’s symbols mean : 
am 
| Dn | — 4 (Jia,m == Imai — Jima )- 
; b heers : 
Further the notation ie and Jed for the first, respectively second 
derivative of ge? with respect to 2, and aa will be used from time 
to time. 
4. The contribution of the matter to L will be denoted by 
V—q R. In order to find out what has to be put for V-—g hk we 
must investigate how the element — mds, which occurs in the 
variation law for the motion of a single material particle, can 
be extended to V~—g Rdu,dv,du,dx, for the matter we are consi- 
dering. Lorentz has indicated *) what V —g R becomes for a con- 
1) 1. e. XIX p. 754, XXV, p. 478. 
