on the Hypothesis of Undulations. 471 



results explain the characters of the different kinds of light which 

 have been named plane-polarized, elliptically-polarized } and ctr- 

 cularly -polarized. 



Another problem in the theory of light the answer to which 

 depends only on properties of the medium through which it is 

 transmitted, is the law of the variation of its intensity with the 

 distance from a centre of emanation. The investigation of the 

 law of the variation of the velocity and condensation in waves 

 propagated from a centre is given in articles 36 and 37, where, 

 it is to be understood, the waves are resultants of the compo- 

 sition of the ray-undulations whose properties we have been 

 discussing. It appears from that investigation that, at distances 

 from the centre not very small, the resulting velocity and the 

 condensation both vary inversely as the distance from the centre. 

 It is true that the rays were supposed to be so compounded as 

 to destroy transverse vibration, and that the law, being proved 

 only for direct vibrations, would seem not to be established for 

 the case of light. But it should be observed that the action of 

 the eye on a bundle of rays is to bring their axes to a focus, 

 and that this concentration has the effect of making the trans- 

 verse motions reappear. The dynamical action, on the eye, of 

 the resultant transverse motion of a bundle of rays is, as I have 

 already remarked, of the same kind as that of the transverse 

 motion of a single ray, and the resultant maximum transverse 

 velocity is proportional to the maximum resultant direct velocity, 

 independently of the differences of the values of A, and c in the 

 separate components. Thus the effective transverse velocity will 

 vary inversely as the distance from the centre of emanation ; and 

 as the intensity of the luminous effect varies as the square of this 

 velocity, it follows that the intensity of light emanating from a 

 centre varies inversely as the square of the distance from the centre. 



This law seems also to admit of the following demonstration, 

 which is independent of any special consideration of the action of 

 the undulations on the eye. As the compound undulations from 

 a centre maintain the same composite character during their 

 propagation, the number of axes of individual rays included 

 within a given circular area, as the pupil of the eye, will at 

 different distances from the source of light vary inversely as 

 the square of the distance. But the aggregate luminous effect 

 must, cateris paribus, be proportional to that number. Hence, 

 as before, the intensity varies inversely as the square of the 

 distance. 



There is still another class of facts the explanation of which 

 depends exclusively on properties of the sethereal medium, viz. 

 the effect of compounding colours, it being assumed that every 

 result of such composition which the eye perceives corresponds 



