632 



TRANSACTIONS OF SECTION A. 



or representing q^ q.^ by coordinates of a point XdS, YdS, ZdS, dS being the 



area of elementary closed circuit. Now A.r, Ay, AiS represents an indefinitely 



small displacement : — 



, dA.v , d^u , dAs n 



• ' ^^ + -T" + -J- = ^• 

 d.v dy dz 



Again, by the nature of the process considered any point in contact with 

 a solid remains in contact with it. AVheu then y„ q.^ have returned to their 

 original values the displacement repi-esented by A.r, Ay, A;? is tangential to the 

 solid, Now 



d.d^^d^^ d.dj. , fff(^x. . .)d.dyd, 

 dt dx dt dy dt du Hi \dt J 



= \[^{Xdydz+Y dz dx + Z dx dy) 



dy dz 



Both these terms vanish from considerations above. Hence our theorem is 

 established. 



7. On the Analysis of Projection. By Professor R. W. Genese, M.A. 



The importance of projection in the study of the points at infinity of a graph 

 makes a simpler treatment than that which appears in the usual texts desirable. 



p in the plane ABoy is projected from V into P in the plane ABOY ; VoBO 

 is a plane perpendicular to AB ; VOY, Yoy planes parallel to ABo, ABO respec- 

 tively, so that oy, OY are the so-called vanishing lines of the planes. 



ON = X, NP = Y being the coordinates of P, the plane VPN is parallel to 

 AB and meets the plane ABo in np parallel to AB or oy. Taking on-x, 

 np = y we have 



and also 



where Z, z are the shortest distances of V from each plane measured parallel to 

 the other plane. 



Now we may agree to take Z, z as diflPerent units of length for the two planes, 

 and the equations of transformation become 



.V 



t 



1 



