32 Arthur B. Lamb 



impossible to decide this by calculation, in the present state of our 

 knowledge, but if we assume that the centrosomes are smooth, 

 hard spheres and that the cell fluid is homogeneous and as mobile 

 as water, it is not difficult to calculate how vigorously they must 

 oscillate or pulsate in order that they shall move apart with the 

 observed velocity.^ Taking the radius as 0.0002 cm., the dis- 

 tance apart as 0.003 ^'^•' ^^^ time required for this maximum 

 separation of the centrosomes as fifteen minutes; if the amplitude 

 of oscillation equaled two diameters, the frequency required would 

 be 2000 oscillations per second; if the amplitude were eight diame- 

 ters, the required frequency w^ould be 100 oscillations per second. 

 With similar dimensions, if the centrosome pulsated so that its 

 greatest volume were three times its least volume, a frequency of 

 some T30 pulsations per second would be required.* 



These frequencies are greater than one would expect. They 

 do not, however, involve any great linear velocities, for the dimen- 

 sions of the particles are very small. Thus the frequency of 2000 

 oscillations to the second only means a linear velocity of the centro- 



^ The formula of Stokes 



F = 6 TZ I'v r 



(Brit. Assoc. Report, p. 445, 1887) applying to the motion of spheres though viscous media was used 

 to determine the force needed to give the centrosomes the observed velocity. To find the needful fre- 

 quency of oscillation this was equated to the expression 



± 6 



(.f.) 



derived by Bierknes for the attraction or repulsion between oscillating spheres. 



Similarly, to find the needful frequency of puhativn it was equated to the expression 



d- 



also based on a formula derived by Bjerknes. In all of these expressions r represents the radius, d the 

 distance between the centrosomes, /ithe coefficient of viscosity of the medium (water), p the frequency, 

 5 the "action moment," v the velocity, and a the ratio between the mean and the maximum radius of 

 the pulsating sphere. 



* It might also be pointed out here that similar calculations on the hypothesis of electrostatic action 

 show that, if the capacity of the centrosomes is simply that of conducting spheres in an isolating medium, 

 a potential difference of nearly two volts would be required; if the capacity is that of spheres surrounded 

 by a "Helmholtz double layer,'' a potential difference of only a few thousandths of a volt would be 

 necessary. 



