LIQUIDS AND ALUED EXPERIMENTS. 5 



right section is equal to the area of the annular space between the outer wall 

 of the swimmer and the inner wall of the vessel A, if the column of water 

 above the swimmer is removed during the prolonged intervals of time 

 between observations, the section a through which capillary transpiration 

 takes place is definitely given. It is obvious that the swimmer must be 

 suspended, for instance by fine cross-wires, above the bottom of the tank A . 

 Reference is finally to be made to convection and to temperature. The 

 manipulation during observation necessarily stirs up the water and distorts 

 the regular pressure gradient. Hence observations are to be made rarely. 

 Again, to obviate convection in general the vessel must be kept in a room 

 of nearly constant temperature. 



8. Values of the Coefficients. — If the data of table i be inserted in the 

 equations for k P and k p , 



k = mRr = 5.35Xio~ 12 X2.87Xio 6 X2 9 8 =0 oX - 6 

 " adp/dl 10314X23470/40 



k p = kjRT^o.2c,Xio~ n 



Hence for a gradient of 1 dyne per centimeter, 2.9X10 -13 grams of air 

 flow between opposed faces of a cubic centimeter of water per second. 

 This may be put roughly as about 2.4X10 -10 c.c. of air per second. The 

 speed of migration of individual air molecules intermolecularly through a 

 wall of water is thus 2.4 X io -10 cm. /sec. for a dyne/cm. gradient. 



Since the gradient is the energy expended when the cubic centimeter is 

 transferred 1 cm. along the channel, and if the number of air molecules per 

 cubic centimeter be taken as A T = 6oXio 18 , the force acting per molecule to 

 give it the velocity just specified is i/(6oXio 18 ) dynes. Hence the force 

 or drag per molecule, if its speed is to be 1 cm. per second, is 



/= — — rio ~T~T / — Ts = w — s dynes /= 6.9 X io -11 dynes if v = cm./sec. 



2.4X10 60X10 144X10 J J J ' 



This may be compared with the force necessary to move a small sphere 

 through a very viscous liquid of viscosity 77. This force is 



f—6-Krirv 



If v= 1 cm./sec, 2r = io~ 8 X2 cm. the diameter of the sphere of influence of 

 the molecule, and/=6.9Xio _u dynes, the value just found, 



6.9X10- 11 _ 8 



V= 6rXio- =366Xio 



In other words, the molecule moves through a liquid about twice as viscous 

 as the air itself. 



It is not improbable that from results of this kind some light will be 

 thrown on the molecular interspaces of a liquid ; for the problem in hand is 

 ultimately that of a single molecule transferring through the intermolecular 

 channels. The relations here obtained will, however, be considerably modi- 



