65 



fords a very satisfactory approximation, at least, to the expression 

 and explanation of the actual law of nature. In order, however, to 

 remove any possible discrepancy which may still exist, or hereafter 

 be found to obtain, the author considers that further examination is 

 requisite of the principles on which any extension or modification of 

 the theory might be pursued; and such is the object of the investi- 

 gation undertaken in the present paper. 



The phenomena of interference, on which the undulatory theory 

 was originally based by Dr. Young, obliged us to adopt some idea 

 of an alternating motion, as well as a motion of translation, in our 

 conception of light ; and this, with all the accessions it has received, 

 especially from the investigation of Fresnel, has, at the present day, 

 been connected by the labours of M. Cauchy and others, with gene- 

 ral dynamical principles, which regulate the propagation of vibrator)'' 

 motions through an elastic medium. From such dynamical prin- 

 ciples there have been deduced certain differential equations of mo- 

 tion, the integration of which gives the well-known expression for a 

 wave, involving the relation between the velocity and the wave- 

 length which explains the dispersion. The direct and complete in- 

 tegration of these forms, effected by M. Cauchy, and simplified by 

 Mr. Tovey and M. Kelland, involves certain conditions; namely, 

 the evanescence of certain terms, the interpretation of which implies 

 peculiar views of the constitution of the ether. Mr. Tovey shows 

 that without these conditions, a certain form of the wave-ftinction 

 is a particular solution of the equations ; and this form is precisely 

 that expressing elliptically polarized light. If the absence of the 

 condition in question be essential to the case of elliptically and cir- 

 cularly polarized light, it follows that all the preceding investiga- 

 tions, which depend on the fulfilment of those conditions, are ap- 

 plicable only to unpolarized and plane-polarized light, and conse- 

 quently the general integration is limited in a most material part of 

 its application ; a defect which is only remedied by the supplement- 

 ary investigation of Mr. Tovey, in which, for this case, a particular 

 solution is assigned. It seemed, then, necessary to show explicitl)'' 

 that the non-fulfilment of the conditions, that is, the non-evane- 

 scence of the terms in question, is essential for elliptically polarized 

 light, as their evanescence is for common light, and thus to exhibit 

 distinctly the relation between the cases of elliptically polarized, of 

 plane-polarized, and unpolarized light; and, again, to remove, if 

 possible, the obscurity and discrepancy of opinion in which the phy- 

 sical interpretation of those conditions, with regard to the supposed 

 constitution of the ethereal medium, appeared to be involved. 



The author then enters upon the analytical investigation of the 

 subject, and in conclusion remarks that when light is elliptically or 

 circularly polarized, that is, when any one of the two component 

 vibrations is retarded behind the other, then, in the differential equa- 

 tions of motion, the opposite terms do not destroy each other in the 

 summation, which they can only do in general by supposing a great 

 number taken into account ; that is, the number of terms is limited, 

 or the sphere of the influence of the force by which the vibrations 



