Cambridge Philosophical Society. 135 



Let 



A=-, B=:-^-, C = (Z=)-, 



then we have 



2;=A + ?B+iC; (12.) 



and, since (12.) is a virtual solution of (7.), the problem is 

 solved. A BCD is a regular tetrahedron. 



Scholium. These solutions may be readily verified. The 

 form, which imaginary geometry will finally take, may possibly 

 be very different from that exhibited here, but I have endea- 

 voured to show a j)riori that, under certain limitations,,/ indi- 

 cates perpendicularity to a plane. As to those limitations the 

 reader is referred to pp. 44, 45 of this volume. The geome- 

 trical illustration given at the latter of those pages will be more 

 correct if we suppose the small sphere to be moved, parallel 

 to itself and perpendicular to its axis, until its pole is at a di- 

 stance unity from its former position. The reader who is in- 

 terested in the subject of the impossible quantity j is referred 

 to my papers at pp. 435-439 of the last, and pp. 37-47 of the 

 present volume of this Journal. For distinctness of reference 

 I have in this paper used / andj instead of a and /3. I have 

 not thought it necessary to refer to the case where k (or y) 

 enters into a geometrical problem, as it was beyond my pre- 

 sent object. 



Nb/^. The value of Wjix.'^ + 23/1/^ {supra^ p. 47) should be 



tt) W -f y.r" + t/y" + 2/2;". 



The omission of accents has occasioned the error. 



2 Church -Yard Court, Temple, 

 January 16, 1849. 



Correction. Supra, p. 42, note*, line 6, 



for " and then n " read when the index. 



XIX. Proceedings of Learned Societies. 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 

 [Continued from vol. xxxiii. p. .394.] 



Nov. 13, QECOND Memoir on the Fundamental Antithesis of 

 1848. »^ 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- 



