of Hydrogen through Palladium. 29 



would come within the range of the above formula. Schmidt*, 

 however, finds that his results agree more nearly with the view 

 that the rate of diffusion is proportional to the pressure difference 

 on the two sides. These statements are not however necessarily 

 contradictory, as the experiments were not made under the same 

 conditions. In Schmidt's case there was a high pressure on both 

 sides of the palladium tube so that the square root term would 

 not be proportional to the square root of the difference of the 

 pressures, but to the difference of the square roots of the pressures. 

 Now the differences of the square roots of a series of numbers 

 like a, a 4 b, a + c, etc., where b, c, etc. are small, are approximately 

 proportional to the differences c, b. Hence, unless the experi- 

 ments of Schmidt were very accurate we should not expect them 

 to be capable of deciding how the rate of diffusion varied with 

 the pressure. 



A closer examination of Schmidt's numbers fully substantiates 

 this conclusion. The numbers given in Tables XIV — XXVII of 

 his paper are the times necessary for the volume of hydrogen 

 inside the apparatus to increase by 1 cm. of the barometer tube. 

 If P 1 is the pressure and 6 the temperature of the gas in the 

 barometer tube it will be readily seen from the data given that 

 the number of gram molecules which correspond to this increase 

 in volume is given by 



•4005 x 5-93 x 10~ 8 x _/' * . 

 273 + v 



Now 273 + 6 is constant during the experiments within the 

 total experimental error so that the mass of gas diffusing per 

 second varies as Pjt, where t is the value given in the third 

 column of the tables cited. Hence if the rate of diffusion were 



proportional to the pressure difference (P — P x ) -^ should be con- 



P\ 



stant, if it were as the square root of the pressure (P * — P$) p- 



would be constant, whilst on the general dissociation theory this 

 constant quantity would be one of the above terms plus a constant 

 quantity into the other. 



To test the relative agreement of these formulae values of 

 (P -P 1 )t/P 1 and (P * - P 1 i)t/P 1 calculated from Schmidt's 

 numbers are given in the following table. The first column gives 

 the table in Schmidt's paper from which the numbers are taken, 

 the second the temperature in degrees centigrade of the palladium 

 tube during the experiment, the third the values of t/P 1 , whilst 

 the fourth and fifth contain values of (Po-P^t/P^ and (P *— P^)*^ 

 respectively. 



* loc. cit. p. 767. 



