202 Lord Rayleigh on the Manufacture and 



tage gained in the spectra of even order is not in dispersion, nor 

 in resolving-power, but simply in brilliancy, which is increased 

 to four times. If we now suppose half the grating to be cut away, 

 so as to leave 3000 lines in half an inch, the dispersion will 

 evidently not be altered, while the brightness and resolving- 

 power are halved. If, therefore, resolving-power be our object, 

 we should aim at covering a considerable breadth with very 

 accurately placed lines, rather than at extreme closeness of the 

 lines themselves. On the other hand, for experiment on dark 

 heat, or whenever a narrow slit is not available, resolving-power 

 is of less importance, and the best grating will be one that covers 

 the largest space with the finest lines. 



I have already mentioned that my 6000-to-the-inch Nobert 

 defines not only not better, but decidedly worse, than the one 

 with 3000 lines in the inch. This inferior definition is probably 

 an accident ; for there seems to be no theoretical reason for it. In 

 brightness the closer-ruled grating has greatly the advantage. 



The preceding investigations are founded on the principles 

 ordinarily adopted in explaining diffraction-phenomena, and not 

 on a strict dynamical theory. In the present state of our know- 

 ledge with respect to the nature of light and its relations to 

 ponderable matter, vagueness in the fundamental hypotheses is 

 rather an advantage than otherwise; a precise theory is almost 

 sure to be wrong. Nevertheless it is often instructive to ex- 

 amine optical questions from a more special point of view ; and 

 therefore I hope that an investigation of an ideal grating on 

 dynamical principles will not be out of place, though not very 

 closely connected with the preceding portion of the paper. 



In actual gratings the lines or grooves occur at the boundary 

 of two media of different refrangibilities ; but, for the sake of sim- 

 plicity, we shall here suppose the medium on both sides to be 

 the same. The grating will thus consist simply of bars (infi- 

 nitely long) whose optical properties differ from those of the rest 

 of the medium ; and we further suppose 



(1) that the variation of optical properties depends upon a 

 difference of inertia, and is small in amount ; 



(2) that the diameter of the bars is very small in relation 

 to the wave-length of light. 



The supposition that refraction depends upon a difference of 

 inertia is that of Fresnel and Green, and has been shown by the 

 latter to lead to Fresnel* s laws. In several papers in this Maga- 

 zine*, I have shown that, if the analogy with an elastic solid 

 holds good at all, no other supposition is reconcilable with the 

 facts of the reflection of light from surfaces and its diffraction 



* Phil. Mag. 1871, February, April, June, August. 



