Mechanical Equation to the Motion of Material Points. 327 



in which k and n are constants, and the latter is different from 

 — 1. From this, through integration, results 



and by employing these forms of the functions the above four 

 equations are transformed into : — 



^ l =~ x P n+1 > • • • • (25) 



P n+l , (26) 



n+l re+1 



m — t k 



\-n 



I 2 . 



(27) 



Eliminating p from the first three equations by means of the 

 last, we obtain : — 



4i^=^3 B > < 29 > 



P-Si* ^ 



i.ft^r^pj^l]*** • (31) 



In order, finally, still further to specialize, we will put for n 

 two definite values which most frequently occur. 



First, we will assume n to be equal to 1. This case corre- 

 sponds to the most simple elastic vibratory motions, in which 

 the force with which a point that has left its position of equili- 

 brium is drawn back toward it is proportional to the distance. 

 For this case the preceding equations are transformed into : — 



§-^=|p 2 = *E, ..... (32) 

 f-^=*p 2 = P, (88) 



j = 27ta/ 



I (34) 



The last equation expresses that the time of revolution is inde- 

 pendent of the elongation of the vibrations, and consequently 

 that these are isochronous. 



