320 G. t\ BIDDER 



With twice the number of flagellate chambers, ^2 will be approximately 

 equal to 2q, therefore F.^q2 = Fq. The pressure in the flagellate chamber 

 depends solely on the structure and vigour of the flagellate cells, velocity 

 there being so slow that kinetic energy is always negligible, therefoi'e 

 Pj = P, whatever the number of chambers. 



But, from (4) , F = '^ +Fq. (11) 



-'2 — 2~ ^2^12- 



Therefore v^ = v, and the velocity from the osculum is the same in 

 sponges of similar canal systems, irrespective of size ; that is, of the 

 number of similar units which are grouped to expel water by one 

 osculum ; and for Leucandra as per a gigantea in health, from 

 Note 1, L = 12x8-55 = 100 £. (12) 



Now by (10) .Y = 1-03 a/j^ . 



^ F 

 Therefore for the twin sponge 



X, = 1.03 ^VP, ^ 1 03 ^2^ ^^^-^ 



Similarly, if m similar units, for each of which the optimum oscular 

 diameter is A", be united to one osculum, and X^ be the optimum 

 diameter of this, then 



Xm = X »Jm. 



With similai sponges the external volume may be taken as the 

 approximate measure of the number of similar units aggregated into 

 one individual ; or, more conveniently, the product of length, breadth, 

 and thickness may be taken as the measure. Calling this product M, its 

 value for A. 11 is 4-1 c.c, and we shall find in Note 6 that for A. 11 

 X=.25 + .03. 



Therefore, for Leucandra as per a gigantea of similar canal- 

 system, the optimum, diameter of the osculum in centimetres is numeri- 

 cally 



A',„ = -25 ^/^ = .12 ^M, 

 and generally for any one species and metamp 



the area of the osculum varying as the volume of the sponge. 



For a sponge like the bath-sponge, with N oscula, the sum of whose 



diameters is "^ A', approximately, 



