On the Manufacture and Theory of Diffraction-gratings. 193 



trolytic motion to our electrical v, e has been found, according 

 to Weber*, to be about 3 . 10 13 for 1 cubic millim. of water, 

 even this value will perhaps be sufficiently great. 



For Siemens^ mercury unit, according to Kohlrauschf the 

 resistance is, in electromagnetic measure, 9717 . 10 6 ; according 



to Weber J, therefore, it is about = H in mechanical mea- 



sure. Consequently for 1 cubic millim. of mercury, U=- I4 . 



Accordingly, in this volume of mercury we should have 



or M < 2. 10 82 nearly §. 



If the number above admitted for the density of the free 

 aether be divided by this value, we get a lower limit for the 

 weight (in milligr.) of each molecule of aether. It would thus 



amount to considerably more than 10Q » 



These values have of course only a widely approximate signi- 

 fication, since we have no very exact knowledge of the numerical 

 values of e ; nevertheless it would be of high importance to have, 

 only so far, at least an idea of the relations of the aether. 



Aachen, October 26, 1873. 



XXV. On the Manufacture and Theory of Diffraction-gratings, 



By Lord Rayleigh, M.A., F.R.S. 



[Concluded from p. 93.] 



^T^HE remainder of this paper is principally occupied with 

 J- theoretical considerations relating to the performance of 

 gratings considered as light-analyzing apparatus. The more 

 popular works on the theory of light give only the main outlines 

 of the subject, and pass over almost in silence the important 

 questions of illumination and definition. On the other hand, 

 the mathematical treatises, such as Airy's ' Tracts ' and Verdet's 

 Leqons y though they give analytical results involving most of 

 the required information, are occupied rather with explaining 

 the production of spectra as a diffraction-phenomenon than with 

 investigating on what conditions their perfection depends. On 



* Electrodynamische Maassbestimmungen, 1856, p. 281. 



+ Pogg. Ann. Ergdnz. vol. vi. p. 1. 



% Elektrodynamische Maassbestimmungen, p. 260. 



§ Compare W. Thomson's calculation (Liebig's Ann. vol. clvii. p. 54), 

 from which the number of physical molecules in the same volume would 

 be, at most, 10 23 . 



Phil. Mag. S. 4. Vol. 47. No. 311. March 1874. 



