of the fourth order. 29 



Among such sets of four are the tangents at the points of 

 superosculation (f= 0), and the four tangents which meet the 

 curve again (H = 0). Both these are known results. As a further 

 example we may remark that the tangents at the points of super- 

 osculation are each met by one other tangent, and the points of 

 contact of these being obviously given by a rational quartic co- 

 variant, the four tangents are generators of a hyperboloid. Other 

 sets of four could be mentioned. 



II. If the curve has a stationary tangent then f has a 

 squared factor, for the point of contact of this tangent may be 

 regarded as the coalescence of two points of superosculation. 

 In this case <£ consists of the sixth power of the same factor, 

 and hence by the acquisition of a stationary tangent the curve 

 has lost six points where a linear complex contains six consecutive 

 tangents. 



This is a result depending in the end on only infinitesimal 

 properties of the curve, and hence the same is true of all space 

 curves, viz. the acquisition of a stationary tangent means the loss 

 of six points when a linear complex contains six consecutive 

 tangents. I hope to make use of this fact in a future com- 

 munication. 



Trifolium pratense var. parviflorum. By I. H. Burkill, M. A., 

 Gonville and Caius College. 



[Read 26 November 1900.] 



There are three abnormal states of the common red clover 

 in which the corolla is found unduly shortened. One of these 

 is due to an insect larva which feeds within the bud, stunts its 

 growth, causes it to remain closed and the basal parts to be 

 fleshy : the second occurs when the petals are in part sepaloid : 

 the third is a condition in which the corolla-tube is crumpled and 

 the ovary slightly foliaceous ; moreover it generally has peduncles 



