401 On the Graphical Treatment of Experimental Curves. 

 if it be required to obtain a quantity z such that 



where (/> is a known function, integrate this expression by 



Here since 4>{x) is known, <f>'{x) can be calculated: the expe- 

 rimental values of /(a?) may then be multiplied by <//(#), and 

 the products plotted with respect to x as abscissa, and the 

 curve so obtained integrated by a planimeter. 



It will, however, often happen that (f> f (x)f(x) is not suitable 

 for accurate plotting. In this case the independent variable 

 must be changed to <jy(x)=iv, say. Then 



z=[<f>(x)f(x)]-^\x)f{x)dx 



= [>«/] —§ydw. 



Two examples that may occur in practice are 



0(4=log.r (i.) 



Then 



j log x 'di dx = & log *] - J.y d (log x) . 



<£(*)=',. ...... (H.) 



Then 



J«(/«^ UJ Jr W 



The latter is the case occurring in the preceding paper " On 

 Electromotive Force and Osmotic Pressure." 



Another instance, which I did not see how to deal with at 

 the time, occurs in my paper " On the Vapour-Pressure of 

 Liquid Mixtures* (Phil. Mag. [5] xlvi. p. 61 (1898)), where 

 the relation 



dx ' ax 



was to be verified : here x is the molecular fractional com- 

 position of a binary liquid mixture, p x , p 2 the vapour-pressures 

 of the two components. It is sometimes much easier to 



