AT THE PHYSICO-TECHNICAL INSTITUTE 435 



' We know of other quantities of a similar kind, such as the 

 energy-supply of a mechanical system protected from external 

 influences, but otherwise arbitrarily constituted. You will have 

 heard of this in popular lectures on astronomy, in connexion with 

 the planetary system, since this is actually so far removed from 

 even the nearest fixed stars, that their action has been unable 

 to produce any perceptible effect during the whole course of 

 the history of astronomical observations. In a closed system 

 of this kind, the centre of gravity may have a motion which 

 proceeds, undisturbed by all reciprocal actions of the system, 

 at constant velocity, in an eternally unaltered direction. The 

 corresponding velocity may also have zero value, i. e. the 

 centre of gravity may be at rest; then it will never set up 

 motion. 



' We do not as yet know with any degree of certainty 

 whether the centre of gravity of the planetary system is at 

 rest or in motion. So far, the assertion of the constancy of its 

 velocity and its direction is only based on theoretical grounds. 



' But there is another similar quantity, the amount of which 

 can actually be controlled by observation ; that is the so-called 

 momentum of the rotary motion of the planetary system, 

 which embraces the mechanical total of all the individual 

 revolutions of the planets round the sun, and of the satellites 

 round the planets, and of the planets round their own axes of 

 rotation. The sum of these magnitudes can be calculated by 

 suitable means, the rotations being referred to any required 

 direction in space as the axis. 



' For every such axis of constant direction, which passes 

 through the centre of gravity of the system, and moves with it 

 through space, remaining parallel with itself, the entire 

 rotational momentum is constant. It is greatest for one of 

 these axes ; the " invariable plane " of the system is conceived 

 as being perpendicular to this, occupying a mean position 

 between all the planes of rotation of the system and the 

 equatorial planes of the several planets. The direction of this 

 plane, and the amount of the rotational momentum of the system 

 taken round the normal to it, cannot be modified by any 

 reciprocal interaction whatsoever between the bodies of the 

 system. 



'This inertia of rotation may be demonstrated on a small 



