FORM OF A SPONGE . 305 



in a cellular or intracellular world where distances may be even 

 smaller than those about a flagellate cell. Hence, always, their 

 rapidity has been noted as of a different order to that of common 

 external events.) 



There is also a purely physical point deserving attention 

 in the conditions of the world under an immersion lens. When 

 we watch flagella working under a high power, the water seems 

 to have lost its fluidity : a particle moved with apparent 

 swiftness by a flagellum loses its motion at once. The general 

 appearance is as if the flagella were labouring in thick gum, 

 or treacle ; and to understand microscopic physics it is a 

 serviceable short-cut to think of the water as treacle. The 

 energy of a projectile to overcome the resistance of the medium 

 through which it is thrown is as its mass multiplied by the 

 square of its velocity ; loss of energy from the resistance is as 

 its surface multiplied by the velocity and by the distance 

 traversed. We magnify its apparent mass as the cube of the 

 magnification, and the square of its apparent velocity as the 

 square of the magnification ; so that the apparent energy of 

 the projectile is magnified as the fifth power ; but the energy 

 lost, measured by surface multiplied by velocity and distance 

 traversed, is only magnified as the fourth power. Consequently, 

 with 1,000 diameters, the water offers a thousand times the 

 retarding effect which we expect, on the projectile which we 

 think we see ; and the ratio is even higher with the small 

 projectiles which concern us.^ With velocities among which 

 25 ft. an hour is the swiftest, at distances among which to^oo 

 of an inch is very great, the viscosity of water is the pre- 

 dominant phenomenon ; and this world at which we are looking 

 is a world of pushing, not of throwing. 



When the flagellum pushes in with its stroke a minute drop- 

 let of water into the flagellate chamber (Text-fig. 8), it creates 



^ Sir J. J. Thomson kindly informed me that, according to Stokes's law, 

 the resistance of water to the movement of a minute sphere is j)roportionaI 

 to the diameter, not to the square of the diameter. This would make the 

 apparent retardation under the microscope a million instead of a thousand 

 times the expected retardation. 



