388 RESEARCHES ON FUNGI 



of hymenial surface, and (2) a tendency to economise gill-substance. 

 Now these tendencies are antagonistic, and the gills, as they exist 

 to-day, embody within them a compromise between the two. If 

 the gills were four times as deep as they actually are, more than 

 four times as much substance would need to be put into each of 

 these deeper gills than was present in the shallower gills which each 

 deeper one would replace, while the actual increase of hymenial 

 surface would be very slight. The absolute amount of increase of 

 fruit-body substance with this increased depth of the gills would 

 be relatively considerable, for the volume and weight of the whole 

 gill-system would be increased by about four times. If the gills 

 were only one-quarter as deep as they actually are, somewhat less 

 than one-quarter of the substance present in one of the original 

 gills would be put into the shallower gills which would replace it, 

 but at the same time the decrease in the area of the hymenial surface 

 would be considerable. The absolute diminution of fruit-body 

 substance would be relatively inconsiderable and it would be pur- 

 chased at the cost of a marked decrease in hymenial area. Owing 

 to the fact that in the course of evolution a certain percentage of 

 fruit-body substance in Psalliota campestris has been converted into 

 deep and narrow gills, the hymenial surface has been increased 

 about twenty times. 1 It seems to me, however, very probable 

 that a further increase in the percentage of fruit-body substance 

 put into gills would not be advantageous, owing to the fact, suffi- 

 ciently indicated above, that the deeper the gills become the less 

 the gain in surface relatively to the expenditure of gill substance. 2 



The Thickness of the Gills. The amount of hymenial surface 

 on the under side of a pileus is decided not merely by the depth of 

 the gills but also by their thickness. With a constant depth, the 

 thinner the gills, the more numerous can they be and the greater 

 will be the hymenial area on their exterior collectively. As if with 

 the object of producing as extended an hymenium as possible, the 



1 Vol. i, 1909, pp. 30-31. 



1 The geometrical principles relating to hymenial surface and gill-depth, which 

 have been dealt with above, have been illustrated mathematically in an interesting 

 manner by my colleague, Dr. C. D. Miller ; but the mathematics involved would 

 be considered by most mycologists as very abstruse. I believe that Dr. Miller 

 intends to send his paper to one of the mathematical periodicals. 



