THE HYDRATE THEORY OF SOLUTIONS 129 



poorer the experiments the greater was the "crop of hydrates" 

 which could be obtained by Mendeleefs process of analysis ; the 

 second differentiation, introduced by Pickering, was considered 

 to be merely a more efficient method of revealing experimental 

 errors, which if carried out sufficiently often, would infallibly 

 reveal breaks even in the smoothest experimental curves. 



As an alternative to the method of differentiation, Pickering 

 introduced in 1892 the use of a bent lath as a means of detecting 

 small changes of direction and curvature {Phil. Mag. 1892, 33, 

 436). When such changes exist there is no doubt that the use 

 of a bent lath may serve to reveal them to the eye. But the 

 method requires to be used with great caution on account of 

 the risk which exists of recognising imaginary breaks in a per- 

 fectly continuous curve. It is a matter of common experience 

 that the simple logarithmic curves which represent the course 

 of a " monomolecular action " usually have to be drawn in three 

 sections, even if curves of accurate mathematical form are used 

 to guide the pen, and similar complications must ensue when- 

 ever an attempt is made to express a curve by equations 

 other than those which correctly represent it. The bent lath, 

 when used in the ordinary way, forms a parabola similar to that 

 represented by the equation y = a + bx 4 ex 2 , and affords a 

 satisfactory method of drawing curves which differ but little 

 from straight lines. Actual parabolas are, however, of rare 

 occurrence in physical or physico-chemical measurements, and 

 the attempts that are still frequently made to refer curves of 

 all sorts to this one particular type have led so often to 

 erroneous conclusions that it may be desirable to quote from 

 actual experience one or two typical examples. 



It was found by Desguisne (Dissertation Strassburg, 1895), 

 following Kohlrausch and others, that the relationship between 

 the electrolytic conductivity of aqueous solutions and their 

 temperature could be expressed over the range from 2° to 34 

 by the parabolic formula 



*«-*. C 1 + at + bf '\ 

 the temperatures t being measured from 18 C. The constant b 

 was positive for the majority of salts, negative for acids, and in 

 a few special cases where the temperature-conductivity curves 

 were nearly straight it reached almost a zero value. The idea 

 that a parabola was the normal type of curve was so widely 

 diffused that when an inflected curve was found it was con- 



