TRANSACTIONS OF THE SECTIONS. 19. 



prepare the way for a mechanical theory, by showing that all the 

 phsenomena may be grouped together by means of a simple geome- 

 trical hypothesis, which consists in the addition of certain terms 

 (involving only one new constant,) to the ordinary differential equa- 

 tions of vibratory motion. ITie ordinary equations contain two se- 

 cond differential coefficients of the displacements — one with respect 

 to the time, the other with respect to the coordinate z, perpendicular 

 to the wave. The additional terms may be any odd differential co- 

 efficients (with respect to z) of the alternate displacements, these 

 coefficients being multiplied by a proper function of the length of a 

 wave. The third differential coefficients are chosen for simplicity, 

 because then the midtiplier is a constant quantitj''. Setting out from 

 this hypothesis, we arrive immediately at all the known laws, and 

 obtain at the same time a law that was previously unknown, and 

 which is tecbnically called the law of ellipticity. This law is ex- 

 tremely simple, being expressed by a quadratic equation. Two 

 sets of experiments, made long ago by different observers, and re- 

 lative to two classes of phenomena, between which no connexion 

 was hitherto perceived, are now, by the law of ellipticity, connected 

 in such a way, that the one may be comj)uted solely from the data 

 furnished by the other ; the ellipticities observed by Mr. Airy in rays 

 inclined to the axis of quartz, being computed from the angles of 

 rotation obser\'ed by M. Biot in rays parallel to that axis, and a 

 strict agreement being found between calculation and experiment. 

 The discontinuous form of the wave-surface in quartz is also ex- 

 plained, and its equation for the first time determined. The parti- 

 culars of the investigation will be published in Vol. XVII. of the 

 Transactions of the Royal Irish Academy. 



On Polarization. By the Rev. Edward Craig. 



The Rev. Mr. Craig read a paper to show that the phsenomena of 

 polarization are consequences and indications of the molecular struc- 

 ture of refracting substances, and explicable by it ; illustrating his 

 views by some uniaxal crystals, and particularly the Iceland spar. 



On some Phenomena of Electrical Repulsion. By Wm. Snow Harris, 

 F.R.S. 



The only connected and extensive series of experiments in statical 

 electricity which have ever appeared are those of Coulombe, com- 

 municated to the Royal Academy of Sciences at Paris so long since 

 as the years 1782 and 1789; since which time, if we except the 

 valuable contributions of Professor Robison of Edinburgh, little 

 has been effected in this department of science. Coulombe's highly 

 important researches, however, altogether rest upon the principle of 

 electrical repulsion, employed as a quantitative measure, through the 

 agency of the proof plane and the torsion balance. The author 

 therefore considers, that some further verification of the experi- 

 mental processes resorted to by this distinguished philosopher is still a 



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