Page:Grundgleichungen (Minkowski).djvu/52

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In consequence of this condition, the integral (7) taken over the whole range of the sickle, varies on account of the displacement as a definite function of , and we may call this function as the mass action of the virtual displacement.

If we now introduce the method of writing with indices, we shall have

(9) .

Now on the basis of the remarks already made, it is clear that the value of , when the value of the parameter is , will be: —

(10) ,

the integration extending over the whole sickle , where denotes the magnitude, which is deduced from

by means of (9) and

therefore: —

(11) .

We shall now subject the value of the differential quotient

(12)

to a transformation. Since each , as a function of vanishes for the zero-value of the paramater , so in general for .

Let us now put

(13) ,

then on the basis of (10) and (11), we have the expression (12):

.

for the system on the boundary of the sickle, shall vanish for every value of