of the Rate of Diffusion of Solids dissolved in Liquids. 537 



increase in volume of 0'35 c.c. ; and with T = 0'12, the error 

 would be 2*1 per cent. 



It may be noted that when a small quantity of copper 

 sulphate is added to water, the resultant volume is about the 

 same as the original volume of the water. Hence if the lower 

 compartment were left open to the atmosphere instead of the 

 upper one, there would be no error from the cause under 

 consideration. 



As before errors are produced when the taps are opened 

 intermittently. 



Section VI. — Errors due to Circulations produced when the 

 Liquids of the Upper and Lower Compartments are renewed. 



When the water in the upper compartment is renewed the 

 pressure at the inlet is greater than the pressures at the outlet, 

 and in consequence the pressures at the upper extremities of 

 the tubes are not constant. Hence flows take place up certain 

 tubes and down others. 



Let there be n tubes ; and let p 1? p 2 , &c. be the respective 

 excesses of the pressures at the tops of the tubes above the 

 average pressure. Assuming the attainment of the steady 

 state, and making the usual approximations, it can readily be 

 shown that the correcting factor equals 



12 ( p?+...pr? \ 



~VT 2 L 2 \ n )' 



Let p r be the greatest of the p's ; then the fractional error is 

 less than 12 pf/y^T^U*. Neglecting inertia effects, the value 

 of p r must be less than the difference of pressure between 

 the inlet and outlet, an estimate of which could be made 

 practically. The author has not made any practical measure- 

 ments, but has made a guess as to the order of magnitude of 

 the difference of pressure by making a crude analogy between 

 the upper compartment and a cylindrical tube. Thus, if 

 100 c.c. of water pass along a tube 3 cm. in diameter in an 

 hour, the difference of pressure (assuming the formula for a 

 capillary to hold) between two points on the axis 3 centim. 

 apart, if we take the coefficient of viscosity equal to O'Ol, is 

 0-004 dyne. Let p r = 0'01, T = 01, L = 4,then the fractional 

 error equals 



12 X (-01) 2 /(j)81) 2 (0-l) 2 x 4 2 , or 7-8 x 10" 9 . 



It is clear that the error from this cause is appreciable. 



