relative to Stationary Motions. 243 



much further distant from each other as the time is greater. It 

 hence follows that the reciprocally corresponding* values of the 

 variables dependent on the positions of the points become con- 

 tinually more different as the time increases ; and therefore the 

 variations of these variables do not undergo merely such fluctua- 

 tions as repeat themselves in a similar manner, but much rather 

 with increasing time ever greater variations of the variables must 

 occur. 



If, instead of being supposed =0, the time -variation 57 be 

 accommodated to the changed period of one of the points, we can 

 thereby cause the variations, at any rate, of those variables which 

 depend only on the position of that point to alter only in a pe- 

 riodical manner. For the rest of the variables, however, which 

 depend on the positions of the other points, whose periods have 

 changed in different proportions, there still exists the inconve- 

 nience that with time ever greater variations occur, whereby the 

 equation becomes as unsuited to our purpose as before. 



6. I now turn to the explanation of the method employed by 

 me for the treatment of stationary motions. 



To determine more closely the corresponding values of any 

 quantity Z which varies in the course of the motion, and thereby 

 also to give a more complete definition of the variation §Z, which 

 represents the difference of the corresponding values, we will 

 select a quantity dependent on the time as the measuring quan- 

 tity, and settle that those values of the variable Z which belong to 

 equal values of the measuring quantity shall be regarded as corre- 

 sponding values. 



If we first take the time itself for the measuring quantity, we 

 obtain the already discussed species of variation, which we will 

 now more closely characterize by putting the measuring quan- 

 tity t as an index to the S and consequently writing B t Z. 



But now, instead of the time t, another quantity <£, which 

 changes with the time, may be introduced as the measuring 

 quantity, so that <£ can be represented as a function of t, or in- 

 versely t as a function of (f>. With the original motion we will 

 first put generally 



t=M); (9) 



and with the deviating motion, in which the relation between 

 the time and the quantity <f> can be somewhat different, we will 

 put, the time being for distinction denoted by t*, 



<*=/(« +«/iW, •'■;• • • .• (»«) 



in which / and /, represent two yet undetermined functions, and 

 e shall be an infinitesimal constant factor. If now in these two 

 equations the quantity <£ has the same value, the times t and t* 

 are to be regarded as corresponding times. If, further, the 



S2 



