Cambridge Philosophical Society. 63 



unless we make the startling supposition that the " sether passes 

 freely through the earth as the earth moves round the sun. The 

 ohject of this paper is to show that if we make the following suppo- 

 sitions, that the earth in its motion pushes the sether out of its way, 

 that the aether close to the surface of the earth is at rest relatively 

 to the earth, and that light is propagated through the disturbed 

 sether as we suppose sound to be propagated air in motion, the ob- 

 served law of aberration will still result, provided the motion of the 

 sether be such that udx + v dy + w dz is an exact differential, where 

 u, v, w are the resolved parts of the velocity of any particle of the 

 sether along the rectangular axes of x, y, z. 



On the Pure Science of Magnitude and Direction. By the Rev. 

 H. Goodwin, Fellow of Caius College, and of the Cambridge Philo- 

 sophical Society. 



This memoir may be considered in some degree supplementary to 

 the preceding one by the same author, " On the Connexion of the 

 Sciences of Mechanics and Geometry." In that memoir it was 

 argued, that if the views there advanced were sound, there must be 

 such a science as that of pure direction, or rather a pure science of 

 magnitude and direction which should include within itself the sciences 

 of geometry, of kinematics, and of mechanics ; in this the attempt is 

 made to establish mathematically the fundamental proposition of 

 such a science. 



By making use of De Moivre's formula, the author conceives him- 

 self to have established this proposition, that if P represents the 

 magnitude of any cause which varies uniformly and continuously 

 into its exact opposite, i. e. into — P while its direction varies uni- 

 formly from a given direction to the exactly opposite direction ; and 

 if be the angle which the direction of P makes with a given direc- 

 tion, then P is equivalent to two causes, P cos Q in that given direc- 

 tion, and Psinfl in the direction perpendicular to it. 



The author is aware of the improbability which may appear to 

 exist, that so general a proposition should be susceptible of proof 

 without reference to particular instances, and has therefore endea- 

 voured to obviate some objections, which will be more or less 

 strongly felt, according to the nature of the philosophy of knowledge 

 adopted by the mind which makes them, and which in some cases 

 will probably be invincible. 



The memoir concludes with some remarks on the general question 

 of the transition of a quantity from the + to the — affection, which 

 the author conceives to be illustrative of his general design. 



December 8. — On the Heights of the Aurora Borealis of Septem- 

 ber 17 and October 12, 1833. By Professor Potter, A.M., of 

 Queen's College. 



The data for the calculations are almost entirely taken from the 

 conspectuses of the observations printed and distributed in 1833 by 

 the British Association ; and although so long time has elapsed, no 

 calculations of the heights of the phsenomena, which are the first 

 steps to be taken in finding the nature of the meteor, have, to the 

 author's knowledge, been hitherto published; the only imperfect 



