ULTRAMICROSCOPY 81 



trations n and n for heights differing by h, and the mass and 

 density, m and p, of the particle are known, the value of k, 

 the average osmotic pressure exerted by each particle, can be 

 calculated. 



We have seen how the values of n and n were determined ; 

 the method of finding m has still to be discussed. 



Determination of the Mass of a Particle. — A body falling in 

 vacuo has an acceleration of 32 feet per second, and in air 

 bodies of high density usually fall with the same acceleration. 

 Considering the case of small particles, however, certain 

 differences arise. The viscous resistance of the air becomes 

 important, and tends to prevent the increase of the velocity. 

 A raindrop as it falls has its velocity increased ; at first rapidly, 

 because the weight exceeds the resisting force, and then more 

 slowly, until a maximum value is reached, when the change 

 of potential energy is equal to the work performed against 

 viscous forces. It is this resistance, due to the viscosity of 

 the air, which accounts for the comparatively small velocity 

 of such a drop when it reaches the ground. 



Sir George Stokes has shown that in the case of a sphere 

 of radius a, moving with a small uniform velocity, V, through 

 a fluid, the coefficient of viscosity of which is p., the force 

 resisting the motion is equal to 67r p a V. Now the weight 

 of the sphere is equal to apr a 3 (p — <r) g/3, where d— a is the 

 excess of the density of the sphere over that of the fluid, and 

 g is the acceleration due to gravity ; and hence we have the 

 relation 



tr = 9/xV/2^p - a). 



The velocity is determined by observing the rate of fall in 

 a capillary tube ; in one of Perrin's experiments this was 0*97 

 mm. per day. Knowing V, and the values of /a, g and p — 0-, 

 we can calculate the radius a of the particle, and hence its 

 mass m. 



All the terms, except k, in the above expression being 

 known, the value of the latter can be determined. From his 

 experiments Perrin finds the value k = 40 x io -15 . 1 



The number of molecules N in a gram molecule of a substance. — 

 The average pressure exerted by each granule in unit volume 



1 Perrin gives two values. Duclaux has pointed out some errors in Perrin's 

 first paper, in which the value k =36xio -15 is given. Perrin, in his second 

 paper, gives the value 40 x io — a . 



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