TRANSACTIONS OF THE SECTIONS. 25 



4thly, by M. Cauchy, in the ' Nouv. Exerc.,' livr. 3 — 6, by a most exact and elaborate 

 process. The 2nd series has been computed only by the author, by the same ap- 

 proximative method as the 1st, in the Phil. Trans. 1836, whence it was reprinted in 

 Poggendorff's ' Annalen.' Some of the first results belonging to the 3rd series were 

 computed by the author, by Sir W. R. Hamilton's method, in the Phil. Trans. 1837 ; 

 and three of the higher cases, in which discrepancies appeared, were recomputed by 

 Mr. Kelland's method in the Phil. Trans. 1838. Thus it was desirable to recompute 

 series 2. by an exact method, and necessary to calculate all the new and improved re- 

 sults of series 3. This the author has now done, by means of Sir W. R. Hamilton's 

 formula, and for the sake of uniformity has included series 1. The results agree 

 perfectly with observation, except in the most highly dispersive cases. But here it is 

 found, that if an empirical change be allowed in one of the constants for each medium, 

 a sufficiently close accordance is obtained. 



On the Refraction of Heat. By Prof. Powell. 



In a short communication to the Physical Section of the British Association, 

 1840, the author alluded to that singular result of the undulatory view of dispersion 

 — the existence of a limit to all refraction in each medium, at no very great interval 

 below the least refrangible end of the visible spectrum ; and suggested the com- 

 parison of observations on the refraction of heat with this conclusion. He has 

 since followed up that suggestion, in reference to the only medium as yet examined 

 in which it is practicable to compare the refractions of light and of heat, viz. rock- 

 salt. In his Report on Radiant Heat, he has stated Prof. Forbes's indices for 

 the different kinds of heat, corrected according to the Professor's own suggestion 

 from the approximate form in which they were at first given. The proposed cor- 

 rection, however, allows of some latitude ; and, on reconsideration of the subject, 

 as before stated, it appears to the author most fair to take Prof. Forbes's result for 

 light as obtained with the Locatelli lamp. This corrected by — "04, gives for 

 the mean light /^ =: 1'558, which agrees sufficiently with the author's own obser- 

 vations conducted by a totally different method (see Report on Refractive Indices, 

 1839). With the same correction, the extreme index for the least refrangible kind of 

 heat is /n = 1 "528. By theory the author has computed the value of the limiting index 

 above mentioned, and finds it to be ft ^ 1"5277 ; also the index for a mean ray of heat 

 whose wave-length is "000079 inch, is found to be /i = 1'529. Considering that Prof. 

 Forbes allows some uncertainty in his results, this affords a very satisfactory confir- 

 mation. 



On certain Points of the Wave-Theory of Light. By Prof. Powell. 



At the Birmingham meeting of the British Association the author offered a short 

 communication relative to certain difficulties connected with the equations of mo- 

 tion on which the wave-theory is now founded, which had given rise to some con- 

 troversy. Since that time, however, he conceives the main difficulties have been 

 completely cleared up ; it was his endeavour to put the chief part of the subject, 

 in this elucidated point of view, in a paper in the Philosophical Mag., March 1841, 

 and he has since been engaged in embodying these and other points in a separate 

 work. The whole theory of the dispersion is referred to the primary equations 

 of motion, originally suggested by M. Navier, agreeably to the principles of M. 

 Cauchy, since improved upon by others. The forms assumed by these equations, in 

 connexion with the symmetrical or unsymmetrical arrangement of the etherial mole- 

 cules, have a direct relation to the occurrence of rectilinear or elliptic vibrations, a 

 distinction first pointed out by Mr. Tovey. When the arrangement is symmetrical, 

 the existence of axes of elasticity (discovered by Fresnel), as well as the general in- 

 vestigation of the wave-surface, has been shown by Sir J. Lubbock to be deducible 

 from the same primary equations ; and the difference in form between the wave- 

 surface equations of Fresnel and of Cauchy is traceable to differences in the forms of 

 the same equations. (A synopsis of the principal formulae referred to accompanied 

 the paper.) 



