546 Mr. C. W. Raffety on some Investigations of 



curious conclusion that when n = 2, da r >da, as happens for 

 all values of n (exceeding unity) when the boundary con- 

 dition is w = 0, but that when n>2, da/<da. The existence 

 of the exceptional case n — 2 precludes a completely general 

 statement of the effect of a departure from the truly 

 circular form ; but if the terms for which n — 2 are absent, 

 as they would be in the case of any regular polygon with 

 an even number of sides, regarded as a deformed circle, we 

 may say that da <da. In the physical problems the effect 

 of a departure from the circular form is then to depress the 

 pitch when the area is maintained constant (da' = 0). But 

 for an elliptic deformation the reverse is the case. 



At first sight it may appear strange that an elliptic 

 deformation should be capable of raising the pitch. But 

 we must remember that we are here dealing with a vibration 

 such that the phase at both ends of the minor axis is the 

 opposite of that at the centre. A parallel case which admits 

 of complete calculation is that of the rectangle regarded as a 

 deformed square, and vibrating in the gravest symmetrical 

 mode *. It is easily shown that a departure from the square 

 form raises the pitch. Of course, the one-dimensional vibra- 

 tion parallel to the longer side has its pitch depressed. 



LX. On some Investigations of the Spectra of Carbon and 

 Hydrocarbon. By Charles W. Raffety, F.R. A. S."\ 



[Plate XIII.] 



THE spectrum of the Bunsen flame (the " Swan " 

 spectrum) has been made the object of a vast amount 

 of experimental work directed towards the determination 

 of its chemical origin, a resume' of which is given by 

 Dr. Marshall Watts in a paper in the * Philosophical 

 Magazine ' of July 1914 J. 



The present communication gives the results of a photo- 

 graphic study of the " Swan " spectrum obtained from 

 different sources, and is intended to direct attention to 

 certain features which appear to be worthy of further 

 research — namely, the physical significance of the changes 

 produced in the spectrum by a change in the conditions 



* Theory of Sound, § 267 (p = q = 2). 



f Communicated by the Author. 



% " On the Spectra given by Carbon and some of its Compounds ; 

 and, in particular, the ' Swan ' Spectrum," W. Marshall Watts, Phil. 

 Mag. July 1914. 



