26 



ciple was found by Mr. Russell to be so nearly exact that he could 

 not detect any deviation from it in his experiments, it is shown by 

 theory that from this circumstance there will be a rapid degradation 

 of the summit of the wave, and a consequent loss of the velocity of 

 its transmission, both which results of theory were observed to be 

 ♦rue experimentally. The memoir concludes with pointing out the 

 agreement of theory with some minor phenomena noticed by Russell. 



May 11, 1846. 



A theory of Luminous Rays on the Hypothesis of Undulations. 

 By the Rev. J. Challis, M.A., Plumian Professor of Astronomy and 

 Experimental Philosophy in the University of Cambridge. 



In this communication, the sether, which is supposed to be the 

 medium of the transmission of light, is regarded as a continuous fluid 

 substance, such that small increments of its pressure are proportional 

 to small increments of density, and is treated mathematically accord- 

 ing to hydrodynamical principles. The author shows, by means of 

 the usual hydrodynamical equations, and by an additional equation 

 of continuity, the existence and necessity of which he has considered 

 in the Cambridge Philosophical Transactions (vol. vii. part hi. pp. 

 385 and 386), that a given slender cylindrical portion of the fluid 

 may continue in motion without tendency to lateral spreading, while 

 all other parts remain at rest. It is shown, — 1, that the motion in 

 this filament of fluid may be propagated with a uniform velocity ; 

 2, that in one straight line, which may be called its axis, the motion 

 is entirely longitudinal ; 3, that at all other points the motion is 

 partly longitudinal and partly transversal ; 4, that the motion is 

 vibratory, the vibrations both longitudinal and transversal following 

 the law of sines ; 5, that the condensation (s) in any transverse plane, 

 at a point whose co-ordinates in that plane reckoned from the axis 

 are s and y, is given by the equation 



d°~s d°~s 



g being a certain constant. It follows that the condensation in any 

 transverse plane, being determined by a partial differential equation, 

 is arbitrary, and by consequence that the transverse velocity varies 

 at a given time from point to point of any transverse plane in an 

 arbitrary manner. To obtain the foregoing equation, it is assumed 

 that the condensation at any point of a transverse plane, has to the 

 condensation at the intersection of the plane with the axis, a ratio 

 not variable with the time. 



Each fluid filament in vibration is supposed in this theory to cor- 

 respond to a ray of light. The vibrations in different fluid filaments 

 may co-exist, and consequently rays be propagated in the same direc- 



) 



