92 Mr Lachlan, On Bicircular Quartics. [May 26. 



and consequently must pass through all the points in which the 

 three surfaces U n , U n _JI 2l V n ^V 2 intersect. Hence any surface 

 of the nth degree which passes through the 4n — 1 points of 

 intersection of the surfaces U. 2 , V 2 , U n must pass through the 

 remaining point of intersection. 



12. Exactly as in § 4 we may deduce the theorem : if of the 

 4 (m + n) intersections of a surface of the (m + n)ih order with the 

 curve of intersection of two quadrics, 4m lie on a surface of the 

 mth degree, then the remaining 4<n must lie on a surface of the 

 nth degree. 



Also the definitions of residual and coresidual systems of points 

 require such slight modification that it is needless to recite them. 

 And in applying the principles of residuation we see that we have 

 merely to substitute planes for circles, and thus we obtain what 

 might be called ' planar ' constructions for finding the residual or 

 coresidual point of any system of points on a twisted quartic. 



June 2, 1890. 



At a meeting of the Council of the Society, it was decided, in 

 accordance with the Reports of the adjudicators, Sir W. Thomson, 

 Lord Rayleigh, and Prof. G. H. Darwin, to award the Hopkins 

 Prize for the period 1883—5 to W. M. Hicks, M.A., F.R.S., for 

 his memoir upon the Theory of Vortex Rings (Phil. Trans. 1885) 

 and for his earlier memoirs upon related subjects — also to award 

 the Hopkins Prize for the period 1886—8 to Horace Lamb, 

 M.A., F.R.S., for his paper on Ellipsoidal Current-Sheets (Phil. 

 Trans. 1887) and for his numerous other papers on Mathematical 

 Physics. 



