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/PRINCIPLES OF GENERAL PHYSIOLOGY 



Suppose next that, on this assumption, we proceed to calculate the constant 

 of Avogadro from direct observation of the Brownian movement or of states 

 of equilibrium due to its operation. -If the values arrived at agree with those 

 obtained in other ways, the proof is practically complete that the hypothesis 

 is a valid one. This is what Perrin (1910) has done. , 



Three different methods were adopted, the exact details of which will be 

 found in his little monograph. The first method depends on the fact that, if 

 the Brownian movement of particles is really the same as the movement of 

 molecules in a gas, their vertical distribution in equilibrium must follow the 

 same law as that of the atmosphere, under the influence of gravity. In order 

 to verify this experimentally, it was necessary to prepare suspensions of particles 

 of a uniform size and sufficiently large for the observation to be made in the 

 depth of a cell on the stage of the microscope. The use of the microscope was 



Fie. 40. BROWNIAN MOVEMENT. Paths obtained by joining the con- 

 secutive positions of three particles of mastic at intervals of thirty 

 seconds. They only give a feeble idea of the complexity of the real 

 trajectories. If the positions were indicated from second to second, 

 each of the rectilinear segments of the figure would be replaced by a 

 polygonal contour of thirty sides, as complicated as the drawing 

 given here. 



(Perrin, 1910, p. 64 of Soddy's translation.) 



necessary in order to count the particles. Gamboge and mastic were the 

 substances used. By a process of fractional centrifugation, preparations con- 

 taining particles of a uniform size were made. From these experiments, a 

 value of 70 "> x 1 ()'-"-' was found for the number of molecules in 22'4 litres 

 of a gas. 



The second method was based on a formula of Einstein, giving the mean 

 displacement of a particle in a given time in terms involving N, together with 

 other values capable of experimental determination. The positions of an 

 individual particle were mapped out at intervals of thirty seconds by the 

 camera lucida on squared paper. Samples of three such tracings are given 

 in Fig. 40. This figure will serve to give some idea of the complexity of the 

 movements in question, but only a limited one, since it must lie remembered 

 that, if the position of the particle had been mapped at more frequent intervals, 

 it would have been found that between each of the positions marked, a path 

 fully as elaborate as the whole of the figure would have to be inserted. 



