2 EIGHTH REPORT — 18.38. 



other point in it was constant ; and this follows immediately from a 

 theorem announced by Mr. Graves, viz., that '^Uhe enlmrmonic relation 

 of four diameters of a central conic section, is the same as that of their 

 four conjugates." In order to connect this mode of investigation with 

 the ordinary algebraic method, Mr. Graves formed the equation of a 

 conic section passing through the four points (x\ o), {—x", o), {o,y'), 

 (o,— y"), (the axes of the co-ordinates being made to pass through the . 

 points,) and finding only the co-efficient of xy to remain indeterminate, 

 he establishes the following equation between this co-efficient B, and (r) 

 the enharmonic relation of four lines drawn from any point in the locus 



to the four given points, r = —^, — . From this Mr. Graves 



yy -^x y' -\- B 



deduced some elegant consequences, and pointed out the readiness with 

 which M. Chasles's theorem serves to group together, and to prove 

 other very general ones ; such, for instance, as that of Pascal, relating 

 to irregular hexagons, inscribed in conic sections, of which it furnishes 

 by far the shortest and most elegant proof yet obtained. He concluded 

 with the expression of a wish, that mathematicians would not disdain 

 to employ the resources of geometry combined with analytic methods 

 in the treatment of conic sections, many valuable properties of which 

 have been lost sight of by those who seem to consider the study use- 

 ful only as an exercise in the application of algebra to geometry. 



A paper was read by Charles Ball, Esq., of Christ's College, Cam- 

 bridge, "On the meaning of the Arithmetical Symbols for Zero and 

 Unity, when used in General Symbolical Algebra." 



On the Propagation of Light in vacuo. By Professor Sir W. R. 

 Hamilton, F.R.S. 



The object of this communication was to advance the state of our 

 knowledge respecting the law which regulates the attractions or repul- 

 sions of the particles of the ether on each other. The general differential 

 equations of motion of any system of attracting or repelling points 

 being reducible to the form 



£jE = S. «i A x/(r), (1.) 



the equations of minute vibration are of the form 



^ = S. m, {Mx.fir) + ^x. Sf(r)), (2.) 



in which 



lf(r)=f'(r)W, (3.) 



and 



Zr= ^A2.r + ^ A^y + ^ A oz. (4.) 



