274 Dr. R. S. Ball on tlte principal Screws of Inertia 



Thames I Lave often observed this. The waves or ripples of 

 the surface cause the sun's rays to enter the water with 

 unequal intensities at different points. At certain points the 

 beams will enter almost without loss by reflexion, and will be 

 traceable by their illuminating the particles of the turbid 

 water. These beams will be nearly parallel to one another ; 

 but as they all retreat from the observer, they will appear to 

 converge to a point exactly opposite the sun ; to a point within 

 the shadow of his head, in fact, giving the nimbus effect. 



The other analogous phenomenon requires to be explained 

 by reflexion. If you stand upon a ridge, or a high wall in 

 the sunlight, so that your shadow falls upon a field of waving 

 corn, you will notice that the corn-field appears to be illumi- 

 nated in the region all round the shadow of your head. This 

 is best seen when travelling by railway, with the sun about 

 50° above the horizon, from the top of an embankment, so 

 that the shadow of the train and observer fall upon the corn- 

 fields below. 



University College, Bristol. 

 July 31, 1878. 



XXXVII. On the principal Screivs of Inertia of a Free or Con- 

 strained Rigid Body. By Robert S. Ball, LL.D., F.R.S., 

 Royal Astronomer of Ireland* . 



IN the following paper I propose to treat of the effect of an 

 impulse upon a quiescent rigid body, so far as the initial 

 movement of the body is concerned. The analytical investiga- 

 tion of this problem is so well known, that I do not propose to 

 enter into that subject at present. I believe, however, that 

 the ordinary method of viewing the question may be supple- 

 mented by the purely geometrical or physical treatment which 

 I shall endeavour to sketch. This geometrical aspect of the 

 problem, as it has presented itself to my mind, has been de- 

 veloped in the course of certain researches in the dynamics of 

 a rigid body which I have ventured to call the Theory of 

 Screws. I shall here indicate the more salient points of this 

 theory which are necessary for the present question. 



The most important feature of the geometrical method of 

 viewing the subject is its extreme naturalness, as well as the 

 wide generality with which the problem is grasped. If the 

 rigid body were perfectly free, the questions presented are 

 comparatively simple, so much so that there is not a great deal 

 of interest attached to the investigation. But when we con- 

 sider the case of a rigid body whose movements are more or 

 * Communicated by the Author, having been read before the British 

 Association, Dublin, August 1878. 



