" Regula Tertia Philosophandi" 31 



two heads ; so that I can do no more than direct the reader's 

 attention to the investigations contained in my ' Principles of 

 Pure and Applied Mathematics,' published in 1869, and in 

 two smaller works, one entitled ' Essay on the Mathematical 

 Principles of Physics,' and. the other l Remarks on the Cam- 

 bridge Mathematical Studies and their Relation to Modern 

 Physical Science,' published respectively in 1873 and 1875. 

 These investigations are founded, for the most part, on nume- 

 rous communications made to the Philosophical Magazine. 

 I am well aware that, as was likely to happen in so extensive 

 an undertaking, there are many imperfections and errors in 

 these productions (some of which I have rectified in later 

 communications to the Phil. Mag); but since the course which 

 they follow rests on Newton's authority, and, as 1 think I have 

 shown in this communication, is pointed out by the antecedents 

 of physical philosophy, I cannot but be of opinion that these 

 works, or one embodying like views, will eventually have to 

 be regarded as holding the same place relative to general 

 physics as Newton's Principia holds with respect to physical 

 astronomy. 



I shall here introduce a few results obtained under Parts 

 (II.) and (III.), selecting such as may serve to justify the 

 opinion above expressed as to the necessity of the course of 

 philosophy I have been advocating. 



(1) The distinction between common light and polarized 

 light is indicated by means of the function / already defined, 

 which for common Jight is a function of the distance r from the 

 axis of propagation independently of any special mode of dis- 

 turbing the sether, and for polarized light a function of x and 

 y depending on arbitrary disturbance. These results agree 

 with experimental facts. 



(2) The dynamical action of setherial vibrations on a small 

 sphere, when terms of the second order are taken into account, 

 is capable of producing, according to differences of circum- 

 stances, attraction or repulsion of the sphere, and thus of ac- 

 counting for atomic repulsion, molecular attraction, and the 

 attraction of gravity. 



(3) It may be demonstrated that no particle of the sether, 

 supposed to be of unlimited dimensions, can be transferred 

 across a plane fixed in space so as permanently to alter the 

 quantities of fluid on the two sides of the plane. Conse- 

 quently the motions are either vibratory or in re-entering 

 currents. To the former motions the phenomena of light, 

 heat, molecular adhesion, and gravitation are referable, and to 

 the latter the phenomena of electricity, galvanism, and mag- 

 netism. 



