536 The Astronomer Royal on Ray-vibrations. 



scarcery scruple to admit that there is no substance. While 

 the resistance to force remains, it seems scarcely possible to 

 get rid of the idea of substance. 



Perhaps it may be said that even inertia may be represented 

 by centres of force, only supposing the development of the 

 force to be dependent in some way upon time. Such, how- 

 ever, is not the character of forces that we know best; and 

 the introduction of this idea appears to give greater complexity 

 to the force-centre-theory than is given by the idea of sub- 

 stance in the material theory. 



Now I say that, in the wave-theory of light, and in all the- 

 ories of waves where the amplitude of the vibrations does not 

 diminish transcendentally with relation to the distance passed 

 over by the wave, the supposition of inertia (or something 

 equivalent) is absolutely necessary. This will be evident to 

 any mathematician who compares the results obtained from 

 the different suppositions of inertia or no inertia. For in- 

 stance ; in the theory of the transmission of heat by conduc- 

 tion, no inertia is supposed ; the equation then has the form 



dh d?h 



-rr = A . -t-g, of which the solution (supposed to be periodic) 



'It (L it 



is, k = ]S .e~ ax .cos (fit — (3. v). But in the theory of the 



transmission of sound, where the vibrating particles are sup- 



. i . . d*X . d*X. f 



posed to possess inertia, the equation is -y-g = A . ■ , $ , 01 



which the solution (similarly restricted) is X=B.cos(»£— jSjf). 

 The former result certainly does not represent anything like 

 the law of diminution of light ; the latter does represent its 

 general constancy of intensity (the distance of the source 

 being very great). I infer therefore that the supposition of 

 inertia is absolutely necessary. 



Combining this inference with that obtained above regard- 

 ing the universality of undulations in space, I am led to the 

 conclusion that all space with which we are acquainted con- 

 tains something which exhibits the property that we call in- 

 ertia. The reasons which have led me to this conclusion 

 appear to me decisive, but I admit them to be fair subjects 

 for doubt and discussion by natural philosophers. Whether 

 we are to infer from this that there is matter through all 

 space, is, in my opinion, a metaphysical question. 



But the remarks that I have just made will enable me to 

 answer one paragraph of Dr. Faraday's paper. " Perhaps I 

 am in error in thinking the idea generally formed of the 

 aether is that its nuclei are almost infinitely small, and that 

 such force as it has, namely its elasticity, is almost infinitely 



