90 Prof. Chattock, Miss Walker, and Mr. Dixon on the 



in hydrogen may be somewhat too high from this cause, and we 

 have therefore marked it doubtful in the summary of results. 



The effect of real changes in V being to alter the difference 

 P\—p 2 without altering the ratio pi/p 2 , while fluctuations in 

 the back-discharge alter the two pressures independently, 

 and on the average equally, we may apply the test of pro- 

 portionality between p l and p 2 to distinguish between the 

 two alternatives a and b. 



Take z 1 z 2 as before for the two distances from point to ring 

 used in the " double-position" method, and let p l p 2 , p/ p 2 

 be two pairs of pressures observed at these distances which 

 give different calculated values of V. In case a there will 

 be no particular connexion between these pairs of pressures; 

 but in case b we shall have 



Pi ]p% —PilPt ={ z \- *b)/(*« - *o) = constant. 

 This may be shown graphically as in fig. 3, by plotting 

 pi with p 2 and p{ with p 2 ' ; the higher pressures being ordi- 

 nates, the lower abscissae. If the above equation holds, the 

 two points thus obtained will lie on the line BB, of which 

 the tangent of the angle with the horizontal is (z 1 — z Q )l(z 2 — z ). 



Fig. 3. 



?>* 



In fig. 3 besides BB two other lines AA and CC are shown 

 at right angles to each other and at 45° to the vertical. CC 

 is obviously a line for which P\—p 2 and therefore V is con- 

 stant ; points falling above CC giving values of V below that 

 for CC, and vice versa. 



Suppose that in the case of an actual determination of V 

 the point represents the mean value of, say, n individual 

 observations. If these were plotted separately in the figure 

 they would lie symmetrically within a circle centred at for 

 case a ; but for case b they would all lie on BB. 



Arrange the n values of V with their corresponding pres- 



