1862.] 205 



evident from several facts. The spectra of air do not in every case 

 show all the lines of oxygen and nitrogen, and occasionally have some 

 not visible in either of them : the spectrum of graphite in oxygen is 

 quite different from those of carbonic oxide. There is even reason to 

 believe that for certain lines the actions of bodies may be antagonistic. 

 The spectrum of mercury electrodes and mercury vapour showed 

 48 lines, and the author expected that the spectra for any gas with 

 mercury electrodes would add to those of mercury the peculiar lines of 

 that gas, which could thus be certainly determined. In the nitrogen 

 spectrum, however, 20 of the mercurial lines had disappeared, in the 

 hydrogen 18, and in the carbonic oxide 13. 



4. The brilliancy or visibility of the lines is very little increased by 

 greatly augmenting the heating power of the discharge. The two 

 halves of the induction machine can be made to act either consecu- 

 tively for tension, or collaterally for quantity. In the latter case the 

 quantity is doubled, and therefore the heating power quadrupled. 

 When the apparatus is so used, the violet bands are something brighter, 

 but not so much so as to be noticed by an unpractised observer. The 

 red and green show no appreciable difference ; but the author is in- 

 clined to think the change may be greater in the ultra-violet part. He 

 proposes, however, to repeat the experiment with coils of much greater 

 power as to quantity. If electricity can produce thermic vibrations by 

 its transmission, there seems no a priori reason why it cannot produce 

 luminous ones ; and no evidence that it cannot is known to him. 



It seems to follow from these observations that the tendency to 

 show such lines belongs to matter in general, but that different forms 

 of it have different powers of manifesting that tendency, and that 

 those powers may sometimes interfere. If this be confirmed by 

 further research, the result will be that, though the electric spectrum 

 may give useful indications to the analyst, it should never be his sole 

 dependence, or be trusted without full cognizance of the conditions 

 which may affect its indications. 



XXV. " On Fermat's Theorem of the Polygonal Numbers." 

 Second Communication. By the Right Hon. Sir FREDERICK 

 POLLOCK, F.R.S., Lord Chief Baron. Received June 19, 1862. 



(Abstract.) 



The object of this paper is to show the result of combining the 

 three series (which have been the subject of previous communica- 



