978 
In the same way we find by a virtual displacement of the electro- 
magnetic field 
OPm OdrP 
dn = — = (p) KET en eS 
These variations dga; and dy, are really covariant tensors. Tensors 
formed in an analogous way are mentioned without commentary 
in a paper by HILBerv.’*) 
14. For the case of a virtual displacement of the electric field 
we have 
ae OdrP ddr?) 
Sfnn = — 2 ( Pp) ide ior oe an ® be (13) 
We can now easily Satine the variation of Hamiiton’s integral. 
We find 
0 
ada, dar dar dr, > (mmp)| = VW op, dr? Vg F fan Br) + 
fi 0 ò, m 
= ria ky ae ase ee Bep) ie 
+ dre 
p 
EW Pin) +4 —9 Fm ie |. 
Em dx, 
Using the equation of continuity of the electric current 
0 
and transforming with 
gh! Jam 
eae ka gin 
Ee (am) g ir 
0 mn oF te 0 am 
= (mn)4 “ia wee Z — i= (almn) mn Ting al > 
we find, eae the symbol H%, for the variation 
fan de, da,dx dp iY —9(— AW” gg—)dg M—Ez dr} + 
Hor Vg ky + avon) 
den Oy 
Ògam m 
2 = —gaal > re Wd 14 
EW gE; ) —4V—99 a, Ei | (14) 
For a virtual displacement which is zero at the boundaries of the 
1) Davin Hivpert. Die Grundlagen der Physik, I. K. Ges. Wiss. Göttingen, 
Math. Phys. 1915. 
