TRANSACTIONS OF THE SECTIONS. 549 



On the Theory of the Dispersion of Light by the Hypothesis 

 of Undulations. By the Rev. Baden Powell, M.A., F.R.S., 

 Sav. Prof, of Geometry, Oxford. 



The object of this communication was principally to give 

 a brief view of the nature of the explanation afforded by 

 M. Cauchy's analysis of the dispersion, which has hitherto pre- 

 sented so formidable a difficulty, whether to the undulatory or 

 to any other theory, and of some important suggestions which 

 have been made with respect to it. An attentive examination 

 of the quantities entering the analysis points out a limitation, 

 or condition, which must be annexed to M. Cauchy's conclu- 

 sion. It is the object of his analysis to show that there exists 

 generally a relation between the length of a wave and the time 

 of its propagation. It appears from the nature of the expres- 

 sions employed, that, in order that this should hold good uni- 

 versally, we must add to his original hypothesis as to the con- 

 stitution of the aetherial medium this condition, that " the di- 

 stance between two molecules must not be very small compared 

 with the length of an undulation. 



On the Repulsion excited between Surfaces at minute Di- 

 stances by the Action of Heat. By the Rev. Baden Powell, 

 M.A., F.R.S., Sav. Prof of Geometry, Oxford. 



That bodies at very small but finite distances repel each 

 other when heated, seems probable from the analogy of expan- 

 sion by heat ; — was supposed to be proved from some very deli- 

 cate, but perhaps doubtful, experiments of Libri, Sargey, and 

 Fresnel; — and has been assumed by Professor Forbes as afford- 

 ing an explanation of the vibrations of heated metallic bars, first 

 observed by Mr. Trevelyan. 



A simple mode of trying the experiment occurred to the au- 

 thor of this communication. Two lenses of very small curva- 

 ture are laid upon one another, without pressure, and form the 

 coloured rings. These afford an accurate test of the interval 

 between the glasses. Heat being applied, the rings always 

 contract, and the colours always descend on the scale ; or the 

 glasses are separated, and consequently repel each other. 



The curvature, or warping, of the glass, owing to the heat, 

 will, upon consideration, be found to be such as ought, in the 

 first instance, to diminish the angle of contact, and conse- 

 quently to make the rings enlarge. 



It should also be observed that the curvature must be suffi- 



