1 1 4 Mr. Cockle on the Method of Vmiishing Groups. 



far too striking to be merely accidental. Moreover, it must 

 not be forgotten that the observed numbers, as determined by 

 Fraunhofer, are wholly independent of any hypothesis. 



If the relation of whole numbers was rigorously true, the 

 numbers in the foregoing table would stand as follows : 119, 

 238, 476, 714, 833,^1071, 1190. 



The wave-length of the most luminous portion of the spec- 

 trum, the centre of the yellow space, is 2060 parts. If we 

 take this as an optical centre, it will be found that the great 

 lines are situated symmetrically in relation to it. E and D 

 are equidistant above and below it ; the same observation 

 applies to G and B, and also to H and A. The only de- 

 parture from this symmetry is in the case of F, which is not 

 symmetrical with C. It will be understood that I am here 

 speaking of one of those spectra which are formed when a gra- 

 ting or ruled surface is used. In this the colours are arranged 

 side by side, according to their wave-lengths ; the centre of 

 the spectrum, which is its most luminous portion, is occupied 

 by the centre of the yellow space, and the light terminates at 

 equal distances in the violet and red. 



Do not these observations lead us to conclude, that the 

 cause, whatever it may be, that produces these fixed lines is 

 periodic in its action ? 



What that cause in reality is, we have not now facts suffi- 

 cient to determine. I would not affirm that the disengage- 

 ment of incombustible matter by a flame will always give rise 

 to dark lines. But this is very clear; that in all those cases, 

 as cyanogen, alcoholic solutions of nitrate of strontian, of bo- 

 racic acid, &c., in which these lines are developed, incombus- 

 tible matter is uniformly disengaged. 



Universit}', New York, 

 Dec. 25, 1847. 



XVII. An Account of the Method of Vanishing Groups. By 

 James Cockle, Esq., M.A., of Trinity College, Cambridge ; 

 Barrister-at-Laiv, of the Middle Temple*. 



IN a paper On certain Algebraic Functions just published 

 in the Cambridge and Dublin Mathematical Journal, I 

 have given a more detailed and connected view than I had 

 previously done of the analysis which I have, since writing 

 that paper, proposed toterm the Method of Vanishing Groups. 

 I have employed this analysis, perhaps not altogether without 

 success, in the theory of equations and in analytical geometry ; 

 and I indulge a hope that the following little account of the 

 * Communicated by Dr. Nathnniel Lister, late Physician to St. Thomas's 

 Hospital, &c. 



