Principles of Energetics. 279 
and opposite differences of polar pressures on two rigidly con- 
nected points; the condition of compound Translation and Ro- 
tation is unequal and opposite differences of polar pressures on 
two rigidly connected points; and the relation between the 
former and the latter depends on the distance between the centre 
of gravity of the body and the point of application of the result- 
ant of such unequal opposite forces. 
12. In explanation of this principle, it will be sufficient to 
remark that it is merely an expression of the ideas of a single 
force at the centre of gravity, a couple, and a single force not at 
the centre of gravity, in terms of the above general physical con- 
ception of a Force. 
13. The latter paragraph suggests the following general pro- 
blem :—Given a force which, acting instantaneously at the centre 
of gravity of a body of a given mass in a vacuum, gives it a cer- 
tain velocity: what are the different relations between the velo- 
city of revolution and that of rotation when the same body is 
struck at certain different distances from the centre of gravity, 
and on any axis, by the same force ? 
The interest of this abstract problem is in the generality of 
its application to bodies which, while trans- 
lated along 2, rotate about y from a resultant z 
of unequal pressures and resistances, having 
its point of application in or parallel to z (a oe 
wheel) ; and to bodies which, while trans- f 
tive impulse” applied at some point in y (a 
planet). For “le double mouvement de y, 
translation et de rotation des planétes, qui 
parait au premier abord si compliqué, a pu résulter d’une seule 
impulsion primitive qui ne passait pas par leur centre de 
gravité*.” From what previously existing conditions such a 
primitive impulse originated, whether from the rotation of a 
genetic ring, as in the Nebular Theory of Laplace, or other- 
wise, we have not here to inquire. But towards a mechanical 
explanation of the planetary elements, or a hydrodynamical 
theory of the formation of the solar system, the experimental + 
and analytical investigation of the above general problem seems 
to open the way. 
14. In reference to the application of general or particular 
solutions of such a problem to the planets, it may be remarked 
that, as we are not of course here given the primitive impulse, 
lated along 2, rotate about z from “a primi- at 
* Pontécoulant, Théorie Analytique du Systéme du Monde, vol. i. p. 144. 
f~ Extend Plicker’s experiments, for stance. See Taylor’s ‘ Scientific 
Memoirs,’ vol. iv. p. 16, and vol. v. pp. 584 and 621. : 
