448 Mr. S. U. Pickering on the Recognition of 



In Table VII. I have given the results obtained by the 

 Graphic method when sections of different length, starting 

 from the lower end, are drawn as one cnrve. Thus when only 

 ^9 of the whole figure are drawn in one section (column 

 vin.) the average error is only very slightly too small ; it 

 becomes practically identical with the experimental error 

 when -f-Q of the figure are taken (column vn.), and the length 

 of the section taken may be increased to \^, ■}-§, and even 

 •]-§■ of the whole (columns vi., v., and n.) without any 

 appreciable increase in this error ; whereas as soon as a par- 

 ticular point is passed, an increase in the length of the section 

 taken involves a rapid increase in the apparent error, so that 

 the remaining -^ of the figure cannot be included in the 

 drawing without giving an average apparent error 2*6 times 

 greater than it should be. The average error, e l9 has alone, 

 as will be seen, been considered in this case, and the numbers 

 would have been far more striking if the total errors had been 

 taken *, but, even without taking these, the results afford a 

 striking illustration that the breaking up of a figure into 

 separate sections, when examined by the lath, is by no means 

 analogous to the splitting up of a figure into separate sections 

 of any unsuitable form, which necessarily shows a gradually 

 decreasing concordance with the experimental points as the 

 lengths of the separate sections are increased : here we find 

 practically no decrease till a certain length is reached, and 

 then there is a rapid decrease. The break in the case of these 

 results is, moreover, one which I should by no means term very 

 well marked. 



Case IV. 



This is an instance of a break between two curves of which 

 the curvature (in the form of plotting used) is in the same 

 direction. The experimental results (Table VIII.) refer to the 

 depression of the freezing-point of benzene by ethyl alcohol. 

 Two entirely different samples of alcohol (one of which was 

 prepared in Prof, van t'Hoff's laboratory) were used, the 

 determination with this latter sample being marked by an 

 asterisk in the table. The two series agree very closely 

 together, although the solutions in the case of one of them 

 were not made up with very great exactness. The mean 



* For the two-curve drawing, with a break at 2 niols., the total error 

 is 1*27 times the experimental error ; for the one-curve drawing 

 (column in.) it is 425 times, and for a one-curve drawing from 1 mole- 

 cule downwards (column iv.) it is 4-3 times the experimental error. 



