444 Dr. Booth on a Theorem in Analytical Geometry, 



1. Does Professor Kelland admit that I have satisfactorily 

 proved that the quantity n used in his memoir on dispersion 

 is equal to zero? 



2. Does he admit that the evanescence of that quantity 

 destroys his equations of motion ? 



3. Does he admit that the evanescence of his equations of 

 motion destroys his proof of the transversality of vibrations ? 



4. Does he admit that the disappearance of his equations of 

 motion in a medium of perfect symmetry whenever Newton's 

 law is introduced, is a sufficient proof that that cannot be the 

 law of molecular action ? 



If he does admit these points our discussion is at an end ; 

 but if he does not, I shall with great willingness answer any 

 objections against these which he may think it necessary to 

 bring forward. The introduction of collateral questions (such 

 as, " whether the force acts by attraction or repulsion," 

 " whether a cubical arrangement is or is not one of geometric 

 symmetry," " whether the aether has boundaries," " how vi- 

 brations are generated," " whether it is probable that a vio- 

 lent effort would be requisite to move a particle of aether out 

 of its position of equilibrium," and others of a similarly dis- 

 cursive nature which the Professor has mooted in his letters) 

 tends unnecessarily to distract attention from the main ques- 

 tion ; they may therefore safely be allowed by both parties to 

 stand over as unimportant till all objections which are of the 

 first magnitude have been refuted or allowed. 



Cambridge, Oct. 7, 1842. 



H 



LXXVIII. On a Theorem in Analytical Geometry. 

 By the Rev. James Booth, LL.D., M.R.I. A. 

 [Continued from p. 179.] 

 AVING shown that if three fixed points assumed on a 

 ri«*ht line are always retained in three fixed planes, any 

 fourth point P will describe an ellipsoid, whose centre is the 

 common intersection of the three planes, we proceed to 

 establish the following remarkable property, that the volume 

 of this ellipsoid is independent of the angles between the co- 

 ordinate axes ; a singular result, to which an analogous pro- 

 perty may be found in the ellipse. 



Resuming the equation found at page 1 78, 



x 2 Iv 2 z 2 2 cos \ 2 cos u. 2 cos v 



When the equation of the ellipsoid is in this form, having all 

 its terms positive, the point P is supposed to be external to 



