374 ON THE MOTION OF 



The values of the resolved partial accelerations of the centre 

 of gravity found as ahove directed are 



( (aa)d% 4- 2 (,ada)d£ 4- (dd'a)l 

 d% = ) (ab)d\ 4- 2 (adb)(h + («<r6)>7, 

 ( («c)<P£ 4- 2 (<fdc)d& 4- (arf 3 c)^, . 



- (ba)d% -+- 2 (bda)d£ 4- (&<Ta)£ 

 | (M>r->7, 4- 2 (M6>/>7, 4- (M 2 &)k 

 (bc)dt ■+■ 2 (Me>/£ 4- (bd'cfo , 



((ea)d:-z 4- 2 (cda)d£ -+- (cd*a)£ 

 d% = ] (cb)d\ 4- 2 (cdb)dyi, -+- (cd'b}^ 

 ( (cc)dt 4- 2 (cdc)dl 4- (<<c)£ , 



where the parentheses denote a sum of three quantities of 

 which the first is included between the parentheses and the 

 other two are similar and accented once and twice. These 

 abridgments, combined with analogous ones for the sum of 

 three quantities differing by a change of letters, might be used 

 with great advantage in general inquiries into the phenomena 

 of the progressive and rotatory motions of solid or fluid bodies: 

 and I should have employed them throughout this paper, had 

 I not been principally desirous of being clearly understood. 

 In case several terms were to be included in the parentheses, 

 an accent or inferior index might be annexed to the second 

 parenthesis for the sake of obviating any ambiguity. 



Substituting for the quantities in parentheses their values, 

 all of which are given (6) and (7). we shall find 



d% = d% — 2 {rdr u — qdC) — £ (<T + r) 4- r tl (pq— dr) 4- £( rp 4- dq) , 

 d% = d\ — 2 (pdS, — rd£ ) — n , (V + j»*) 4- C (qr — dp) -+- & (pq -+- dr) . 

 d% = d% — 2 {qdi —pdn, ) — 1 0=4- q') ■+- £ (rp — dq) 4- n, ( qr + * ) 



In the case of small oscillations, r at the same time being 

 small, these become, as before 



d% = fl+Sdq, d\ t = d\—ldp. 



