>ui. ins on si ur \i i>. 577 



body until it ceases altogether. What I am about to offer 

 therefore must be considered, like every advance which bas 

 hitherto been made, as merely a step towards the determina- 

 tion of tlu- actual phenomena. It would not he difficult to 



include in the next place the moments of the forces which 

 resist the rotation round the normal, but this must, form thi 

 subject of another dissertation. 



The fundamental equations of condition resulting from the 

 definition of the species "I' motion we are now considering 

 ire. a- we have seen | 2 



o = dg,—y,dB-h2 ,)Q. 

 o = d>;,— z, oP -+- ./• d B ■ 

 o = d£— x,dQ-hy,dP. 



Substituting these values of the variations of the position of O 

 the centre of gravity in the general dynamical equation, then 

 will result an equation of the form 



(F)dP+(Q)dQ+(M)M = o; 



in which the variations are now arbitrary, giving us therefor* 

 three equations of motion to be taken in conjunction with the 

 three above, namely. 



(P) = o. (Q) = o, (7?) = o: 



or. writing nui these equations at full length, in the case of 

 common gravity, 



V+M(*^- grc ) x - m (g - ga ) z = o, 



' r + M (?W - S* ) y - M ($ - gb') x = oj 



expressions which are true whether friction be considered or 

 not, and independently of all hypotheses of friction. 



