dq dr OH dz dy diz 
Jon = 8, $28 attend) «© 
where 
Senn qgs— rn 
2H=(pe + gy + rz — (P+ Hr) (e+ 9 + 2"), 
with similar expressions for Ja, and Jaz 
We can also write (3) — formulae of Bour — as 
Jar = Im,x + 2(Ger,2—7 7, y) + Jr,2 (Corro.is). 
For a point fixed to 7 
Jac =In,z. 
If we understand by J the absolute acceleration of the second 
order of P(z,y,2z), ie. the vector of which the projections on the 
fixed axes are: 
eden 72) _ Dan ‚wm _ Wan 
J rd an — ’ LA — ’ 
ahs a ade al Spgs gat 
it appears in the same way that 
dJa,r 
Joe =— > + qJa,z — r Jay 
and more generally 
(n—1) 
n Ze zx n — 
EN (4) 
We call attention to is fact that for each value of » the ex- 
pressions for Jen Je zi are linear in a, y, z. 4 
Remark. The preceding formulae may be simplified by making 
the axis OZ coincide with the instantaneous screw-axis; in this case 
Enig 
§ 3. If we call the motion of 7, relative to 7 the direct motion, 
we understand by the “inverse motion” the motion of 7 relative 
to FT; here the convection-velocity is therefore the velocity relative 
to T„ of a point fixed to 7; we shall represent this velocity 
by vl. 
Let P(z, y, z) be fixed to 7;, then according to (19) 
i (i) () 
OE Vn, z + w= Um, y + Um, y = Ume + Um, z 
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