On the Graphical Treatment of Experimental Curves. 403 



on the assumption of Boyle's law, in terms of the degree of 

 dissociation of the salt as found from the electrical conduc- 

 tivity ; afterwards, without that assumption, in more general 

 terms. According to this expression the E.M.F. of a cell 

 depends on the total osmotic pressure of the salt, not on that 

 of the metallic ion only. 



Experiments are then described, hoth old ones recalculated, 

 and new ones made for the occasion, in which the E.M.F. of 

 concentration-cells of ZnCl 2 and ZnS0 4 are measured; the 

 results being expressed by curves and tables. 



Finally, from the data thus provided the osmotic pressures 

 of those salts in solutions nearly up to the point of saturation 

 are calculated, and the analogy between those pressures and 

 the pressures of highly compressed gases pointed out. 



East London Technical College, 

 June 1900. 



w 



XXXV. Note on the Graphical Treatment of Experimental 

 Curves. By R. A. Lehfeldt*. 



HEN as the result of experiments a relation between 

 two quantities 



has been found, it is sometimes desirable to calculate from it 

 some other function of x of a kind that involves differen- 

 tiating y. The form of the function /being unknown, it is 

 necessary to deal directly with the numerical observations, 

 or with the curve expressing them. This is often done by 

 finding an empirical equation for y — f{x) and differentiating 

 it, but to find a satisfactory empirical equation is not always 

 possible; and if the subsequent treatment involves integration, 

 the choice of forms is closely limited by the possibilities of 

 the integration. There remains of course the method of 

 differentiating the experimental curve graphically, by drawing 

 tangents ; but this should be avoided if it is in any way 

 possible to do so, because the errors of the experimental curve 

 are greatly exaggerated in taking its tangents ; and no sub- 

 sequent process of integration can smooth out the errors thus 

 introduced. 



In certain cases the difficulty can be avoided, and a process 

 of graphical integration, which can be satisfactorily per- 

 formed, substituted for the graphical differentiation, Thus 



* Communicated by the Physical Society : read Nov. 20, 1900. 



