14 Mr Taylor, On the history of geometrical continuity. [Oct. 25, 



ax + hy + gz, 

 hx + fiy+fz, 

 gx + fy+yz; 



and by the dynamical equations, the rates of change of angular 

 momentum about the co-ordinate axes are zero, and therefore 



1m {(gx +fy + yz)y- {hx + 0y +fz) z) = 0, 



or . ftm(y i -z*) = 0, 



or /(& 2 _ c 2 ) = 0. 



Therefore f= 0, and similarly g and h vanish. 



Therefore the hydrodynamical equations reduce to 



1 dp . n 



- - 7 - + Ax + ax = 0, 

 p ax 



l^ + Cz + yz=Q. 



p 0,2 



For experimental illustrations see a paper in Xature, Nov. 18, 

 1 880, by Sir W. Thomson, " On an experimental illustration of 

 Minimum Energy." 



(2) On the history of geometrical continuity. By C.Taylor, 

 M.A., Fellow of St John's College. 



The foci of the ellipse and the hyperbola were known to 

 Apollonius of Perga in the third century B.C., and in all proba- 

 bility to none before him ; since in the first place there is no 

 earlier trace of them, and in the next place they are introduced 

 in the third book of his Conica, of which he remarks that it con- 

 tains many wonderful theorems, for the most part new. He 

 determined the foci by a process of " application " (irapa/doXt]) of 

 areas, which amounted to dividing the transverse axis into pairs 

 of segments whose product is equal to the square of the conjugate 

 semi-axis. 



It is a fundamental fact in the history of continuity that 

 Apollonius failed to discover any focus of the parabola, the area 

 to be " applied " and the axis to which it was to be applied being 



