74 



munications in which the undulatory theory is treated on hydrody- 

 namical principles, and to elucidate or confirm results previously 

 arrived at. In particular the author enters more at length into the 

 mathematical theory of ray-vibrations, which, according to his views, 

 correspond to rays of light. The principal theoretical deductions 

 are, — (1.) that the longitudinal vibrations o f a ray ar e defined by a 



function of the form sin - — Iz—a t*/\-\-t — V \ being the 

 breadth of the undulation, and a, e certain constants ; (2.) that light 

 from any source is in general composed of rays for which a and — - 



are the same and A different ; (3.) that light coming immediately 

 from its origin is common light, whatever be the nature of the cause 

 producing it, and that to become polarized light, it must be acted 

 upon by reflexion, refraction, &c. ; (4.) that light coming imme- 

 diately from its origin is seen in all directions. 



November 13, 1848. 



Second Memoir on the Fundamental Antithesis of Philosophy. 

 By W. Whewell, D.D. 



This memoir is a continuation of a former one in which the anti- 

 thesis of thoughts and things, of ideas and facts, of subjective and 

 objective, were shown to be at bottom the same antithesis, and to be 

 a fundamental antithesis, the union of the two elements entering 

 into all knowledge, and their separation being the test of all philo- 

 sophy. The present memoir is employed in illustrating the proposi- 

 tion that the progress of science consists in the transfer of some truth 

 from the factorial to the ideal side of the antithesis, or as it may be 

 termed, in the idealization of facts. This is exemplified in mecha- 

 nics, astronomy, botany and chemistry. 



In a note, the author remarks on certain German systems of phi- 

 losophy with reference to this antithesis. The Sensatorial school 

 having reduced all knowledge to facts, Kant re-established the neces- 

 sity of Ideas, which Fichte made almost the exclusive element. Schel- 

 ling founded his philosophy upon the absolute, from which he derives 

 both facts and ideas, but which a wiser philosophy shows us that we 

 can never reach ; and Hegel took the same foundation, but in a cer- 

 tain degree rightly pointed out that the progress towards the identity 

 of fact and idea is to be traced in the history of science ; which view, 

 however, he has carried into detail by rash and blind conjecture. 



On the Elements of Plane Geometrical Trigonometry, applicable 

 to Trigonometrical Formulas. By the Rev. F. Calvert. 



The object of this paper is to define as distinctly as possible the 

 elementary terms of trigonometry, and to explain the conventional 

 use of the negative sign in expressing such simple functions of 

 angles as the sine, cosine, tangent, &c. 



