The Principle of Relativity

by Albert Einstein; H. Minkowski

and find, since f*f = Det^½f, F*F = Det^½F, we arrive at the interesting

conclusion

(79) SS = L² - Det^½f Det^½F

i.e. the product of the matrix S into itself can be expressed as the multiple of a unit matrix—a matrix in which all the elements except those in the principal diagonal are zero, the elements in the principal diagonal are all equal and have the value given on the right-hand side of (79). Therefore the general relations

(80) S_h1 S_1k + S_h2 S_2k + S_h3 S_3k + S_h4 S_4k = 0,

h, k being unequal indices in the series 1, 2, 3, 4, and

(81) S_h1 S_1h + S_h2 S_2h + S_h3 S_3h + S{h4} S_4h = L² -

Det^½f Det^½F,

for h = 1, 2, 3, 4.

Now if instead of F, and f in the combinations (72) and (73), we introduce the electrical rest-force Φ, the magnetic rest-force ψ, and the rest-ray Ω [(55), (56) and (57)], we can pass over to the expressions,—