FORM OF A SPONGE 317 



Therefore if E be the loss of energy per second in N similar 

 tubes, E=8i:ix']S'ii-h^ 



Let q be the quantity of water passing per second through 

 the iV tubes in parallel, the loss of energy per second is 



where a is the aggregate area of the cross-sections of the tubes. 

 In the sponge the whole of the water passes in succession 

 through 



(1) Afferent canals ; (3) Efferent canals ; 



(2) Flagellate chambers ; (4) The cloaca. 



For the whole system, therefore, the loss of energy due to 

 resistance is the sum of the losses in these four systems, which 

 may be represented 



Let 



F.b 



^.{r^)-F. (1) 



Then the energy reaching the osculum per second is 



E = Pg-Fq\ (2) 



where P is the pi'essure maintained by the action of the flagella. 

 But if V be the velocity at the osculum, the energy of the jet 

 per second is •> 



E = p,q-, (3) 



where p is the density of the water ; and if x be the diameter 

 of the osculum 



q = -X- .V. 



* It was the late Professor Su- G. G. Stokes, in 1888, who supplied me with 

 this formula, and a clearly written exposition of its meaning, which could 

 be understood by the ignorant. I cannot allow my use of it to appear in 

 print without a tribute to his kindness to a then young man, unknown to 

 him, with no recommendation but a somewhat shameless request for 

 assistance. 



