1897.] amphioxus and balanoglossus. 313 



As a matter of fact, although these small cells just appear 

 at the spot which will become the dorsal lip of the blastopore, 

 where Lwoff imagines the ectodermal invagination which is to 

 give rise to the notochord to take place, it is the other lip which 

 in the later stages exhibits it most clearly. 



It is true that in those higher Vertebrates in which the process 

 of invagination can be clearly traced, the cells composing the upper 

 wall of the primitive alimentary tube are small compared to those 

 forming the under part of the wall, these being choked with yolk ; 

 and great stress is laid by Lwoff on this fact. The obvious and 

 simple explanation is, that the processes of folding, which the 

 dorsal wall has to undergo in order to give rise to the notochord 

 and the mesoderm, would be rendered impossible were the cells 

 composing it to be overcharged with yolk, and hence the yolk 

 is confined to the cells forming the ventral wall of the gut. 



(2) On the degree of the Eliminant of Two Algebraic Equations. 

 By R Lachlan, Sc.D., Trinity College. 



The object of this paper is to show how the degree of the 

 eliminant of two algebraical equations may be determined in a 

 very simple manner by geometrical considerations. So far as I 

 am aware the only method given in the ordinary text-books is 

 that given by Serret, — Gours aAlgebre superieure, 4th edit. vol. 1, 

 §§ 278 — 280, which method is due to Minding. Although not 

 difficult to apply to particular cases, it does not seem to be so 

 simple as that here given. 



1. Consider two curves G m , G n whose equations expressed in 

 homogeneous coordinates are 



f m (x,y,z) = 0, 



fn 0, y, z) = o. 



If z be eliminated from these two equations we obtain an equation 

 of degree mn, say 



Firm (#, V) = 0, 



which represents the lines connecting the point x = 0, y = to 

 the mn points of intersection of the curves G m , G n . 



Now of these mn points some will usually be found on the 

 lines x, y, z forming the triangle of reference, and some will 



