On the Action of various Coloured Bodies on the Spectrum. 441 



the law of descent upon this supposition being that the differ- 

 ence between n t and n i+l is 1 or r ; and if the former, n h n i+l ^= 1. 



We have seen above the convenience of shifting the system of 

 subindices so as, for instance, to be able to treat the question of 

 finding u Q when we suppose u n =l and w w+e =0, as well as that 

 of finding u n when we suppose u =l, w_ e =0. More generally 

 there is an advantage in writing u m =l and w OT _ e = when it is 

 a question of expressing u n) which may then be conveniently 

 denoted indifferently by m : n or n : m, — the law being that regu- 

 larly descending or ascending series are to be formed beginning 

 with n and ending with m in every possible manner, each of which 

 expresses a known product consisting of two parts — one made up 

 of factors denoted by the conjunction of the consecutive terms in 

 every such series, the other by the duplication of the integers 

 between n and m not appearing in the series. 



It is, moreover, convenient in some cases to express the limit 

 which the descents are not to exceed (corresponding to the order 



of the equation). Thus — ^— may be used to denote the limita- 

 tion of the differences in n : m not to exceed i. The well-known 

 theorem in continued fractions ordinarily denoted by the equa- 

 tion pq'—p'q = +1 may then be expressed in a somewhat more 

 general form in the manner following. 



[To be continued.*] 



LX. On the Action of various Coloured Bodies on the Spectrum. 

 By Sir David Brewster, K.H., D.C.L., F.R.S. tyc* 



IN various papers on light published in the Transactions of 

 the Royal Societies of London and Edinburgh f, I have had 

 occasion to mention the general results of a large number of 

 experiments made on the action of numerous solids, fluids, and 

 gases upon the solar spectrum ; but the observations themselves, 

 as recorded at the time when they were made, I have not found 

 leisure to publish. 



In order to understand these observations, and apply them in 

 the study of the spectrum, it is desirable to have a copy of Fraun- 

 hofer's spectrum ; but as many persons may not possess one, I 

 have endeavoured to supply the want of it by the following 

 nomenclature of the 354 lines observed by Fraunhofer, which in 

 many respects will be found more useful than the spectrum itself. 



N.B. When lines occur in groups, the numbers indicating 

 them are generally placed in the same line. 



* Communicated bv the Author. 



t Edinb. Trans. 1822, vol. ix. p. 433. Ibid. 1831, vol. xii. pp. 123, 

 519, 538. Phil. Trans. 1835, p. 91. Report Brit. Assoc. 1855, Trans. 

 Sect. p. 7. Life of Newton, 2nd ed. vol. i. p. 103. 



Phil. Mac/, S. 4. Vol, 24. No. 163, Dec. 1862. 2 G 



