Theory of Diffraction-gratings. 201 



but the distinction is not fundamental. The limit to definition 

 arises in both cases from the impossibility of representing a line 

 of light otherwise than by a band of finite though narrow width, 

 the width in both cases depending only on the horizontal aper- 

 ture (for a given X). If a grating and a prism have the same 

 horizontal aperture and dispersion, they will have equal resolving- 

 powers on the spectrum ; the greater dispersion is the only 

 cause of the superiority of the diffraction-spectra of high order. 



In estimating the value of light-analyzing apparatus, there 

 are three things to be considered — the brightness, the purity, 

 and the apparent magnitude of the resulting spectrum. In the 

 case of a prism, where the loss of light by reflection and ab- 

 sorption may in a rough approximation be neglected, the first 

 two characteristics are inseparably connected, whether a tele- 

 scope be used or not, so long as the pupil of the eye is filled with 

 light. In whatever degree the purity be enhanced, w r hether by 

 increasing the dispersion or narrowing the slit, in the same de- 

 gree must the brightness suffer. The angular magnitude of the 

 spectrum is merely a question of magnifying- power. No matter 

 how small the dispersion may be, the spectrum may yet be made 

 to appear as long as we please by sufficiently increasing the 

 focal length of the object-glass and the power of the eyepiece. 

 But if the brilliancy is not to suffer, the size of the prism and 

 the aperture of the telescope must be proportionally increased; 

 for otherwise the condition will be violated of keeping the pupil 

 filled with light. There are thus two ways of obtaining a pow- 

 erful spectroscope. The first is to procure a great dispersion 

 by multiplication of prisms ; the second is to be satisfied with a 

 small dispersion, and attain the necessary length of spectrum by 

 a high-power telescope, which may involve a larger aperture. It 

 may be questioned whether the second method has received as 

 much attention as it deserves. When there is light to spare, a 

 higher power than usual may often be employed advantageously 

 without an augmentation of aperture. 



In the case of gratings the question is complicated by the 

 choice of spectra; but some remarks may perhaps be useful. 

 Much misapprehension appears to exist as to the nature of the 

 advantage derived from ciose ruling. It is generally supposed 

 that the closer the ruling the greater the resolving-power of the 

 instrument ; but this is for the most part a mistake. When there 

 is no limitation on the order of the spectrum to be observed, re- 

 solving-power depends not on the closeness but on the accuracy of 

 the ruling. Let us take the case of a grating with 3000 lines in an 

 inch, and consider the effeet of interpolating an additional 3000 

 lines. The effect of the addition will be to destroy by interference 

 the first, third, and the odd spectra generally ; while the advan- 



