432 Professor Booth on the Focal Properties 



"that light ought to bend into the shadows of bodies to an 

 indefinite extent, as sound is known to pass through all aper- 

 tures and to bend round all obstacles." Consequently, "that 

 the result Mr. Airy (Tracts, p. 270,) has obtained by an 

 approximate method is not to be depended upon, and that 

 the objection to the undulatory theory, which was believed to 

 have been removed, remains in full force." p. 246. 



I thought it possible that Mr. Airy might reply to this, but 

 as he has not yet done so, I beg to be allowed to offer a few 

 words, in order to point out the mistake which I conceive 

 Mr. Potter has made. 



The expressions, which Mr. Potter obtains for the inten- 

 sity of the light, have reference only to a certain line C B. 

 He has not shown that there ought to be any light in the 

 shadow except on this line. But a luminous line is merely 

 a geometrical conception, from which no inference can be 

 drawn as to the sensible intensity of the light in the shadow 

 where this line is found. 



It appears then that Mr. Potter has mistaken a luminous 

 line for a luminous space ; and, consequently, that his con- 

 clusions have, in reality, no foundation. 



The meaning of what I have here stated may be illustrated 

 by a fact which Mr. Potter has mentioned. The intensity 

 of the light at certain points on a line in the centre of the 

 shadow of a circular disc is, according to the theory, the 

 same as if the light passed uninterruptedly. Now, when the 

 disc is very small, and the light properly managed, a luminous 

 spot may be observed in the centre of the shadow: when the 

 disc is larger the spot vanishes; not from the diminution of 

 its brightness, but from the diminution of its magnitude. 

 I am, Gentlemen, yours, &c. 



Littlemore, Clitheroe, Nov. 5, 1840. John ToVEY. 



LXIII. On the Focal Properties of Surfaces of the Second 

 Order. By James Booth, A.M.,, of Trinity College, 

 Dublin ; Principal of and Professor of Mathematics in Bris- 

 tol College. 



\7LTH ETHER properties of surfaces of the second degree 

 " * exist, analogous to those of the foci of the conic sec- 

 tions, has long been a subject of inquiry with the most distin- 

 guished geometers ; among whom may be mentioned as pre- 

 eminent in researches of this nature M. Chasles and Professor 

 MacCullagh, who have arrived independently at a series 

 of discoveries, of which may be stated as the most im- 

 portant and fundamental, the property, " that in the prin- 





