486 
ME. A. COHEN ON THE DIEEEEENTIAL COEEEICIENTS 
R, it follows at once from the formulae of the preceding section, that 
dec 
dy , 
These formulae simply express the fact, that the absolute velocity is equivalent to the 
relative velocity together with det(0, R). 
38. Let us next apply the formulae to the acceleration of a particle. Let, as before, 
v^, Vy, be the components of the particle’s velocity V, and let/^,^,/^ be the components 
of the particle’s acceleration. Then, since the acceleration is the complete differential 
coefficient of the velocity, of which v^, Vy, are the components, it follows at once from 
section 36, that 
/. dvx 
p dVy 
A = — 'Vz'^x, 
P dv^ , 
jz=~^+Vym^~V^7ffy. 
If we substitute in the last equations the values obtained for Vy, in the preceding 
section, we obtain 
,. d'^ic , d-sT,, dsfz . ^ /dz dy \ . , , 
and similar formulae for and/^. 
These are the ordinary formulae. It would not be difficult to deduce their real 
meaning from their analytical form ; but it will be better first to prove the result of 
such interpretation in a different and more direct manner. 
39. We have already seen that, if V denote the particle’s absolute velocity, and R the 
dec dxj dz 
radius vector, and if Vj denote the relative velocity which has ^ for its compo- 
nents, then 
V=Vi + det (O, R). 
Let then F denote the particle’s absolute acceleration, and let F, denote the particle’s 
• d^oc d^y d^z 
relative acceleration which has for its components ; then 
F=:D,(V)=.D,(V0+A det (Q, R) (1.) 
Now it follows from the fundamental proposition in section 35, that 
D,(VJ=:F,-fdet(Q, VO. 
