FORM OF A SPONGE 321 



Note 6. Arithmetical Tests, Data, and Coxclusions. 



From camera lucida drawings of the canals and their aper- 

 tures in the Leucandra asperaof Figs. 1 and 7 ('A. 11 ' 

 of ray records) F is computed in the table below to be 

 180 + 30, the relative velocities being confirmed by the times 

 taken by litmus to pass through the walls of the sponge and 

 through its cloaca (p. 293). Using this value in (11), with 

 p = 1-025, V = 8-5 + 1'5, we find for A. 11 the equation 



P = 37.0±14 + (1200±420X (13) 



so that, if a; = -20, the diameter of the osculum measured in 

 spirit, then 



P = 85 + 30 = -9 mm. + 3 mm. of water ; 



and by equation (10), the optimum diameter of the osculum 

 X = -235 + -025. 



Note 2 shows the need of a probable correction in the 

 value of X. The Leucandra' A. 11' was 4 hrs. under ex- 

 periment before being preserved, and its velocity had sunk to 

 less than half its original value. If we may reason from the 

 observations on Leucaltis we should expect the diameter 

 of the osculum to have been reduced by 30 per cent., and 

 therefore that for a velocity of 8-5 cm. it had been -28 cm. 

 wide, instead of the -20 cm. measured after preservation. 



With X = -28, 



P = 131+45 = 1-33 mm. + -46 mm. of water, 



X = -26 + -03. 



The conditions under which the diameter of the osculum is 

 equal to the theoretically best diameter are found by sub- 

 stituting the value of A'^ in (10) for x in (11), giving the 



relations 



P= 1-55 v^ 



