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



Addendum. 



A very important additional argument in favour of the real 

 existence of changes of curvature has been obtained by ascer- 

 taining that a set of results, which can be represented perfectly 

 by two parabolas showing a break, cannot be represented by 

 a single parabola, even if this has as many constants in it as 

 the two together had. The results with propyl alcohol in 

 water (case I.) were taken for this investigation, and the 

 calculations were simplified a little by representing the first 

 half of them by a parabola with two instead of three constants 

 (and the origin). The equation deduced for this parabola 

 was y = "58662 # + '01404 x 2 , and the values given by it were 

 almost exactly identical with those given by the three-con- 

 stant equations in Table II. column in., indeed the sum of the 

 differences was *002° less ; so that the whole results may be 

 represented by this equation together with that previously 

 deduced for the second portion of the figure (the two contain- 

 ing together six constants and the origin) with a total apparent 

 error '95 times the experimental error. A single equation 

 with six constants and the origin was then deduced from the 

 experimental results* : the values obtained were 



v = -554549^ + «0643369.r--02340953^ 3 + -004282719^ 



-•000320612037 x 5 + -000008079213 



x : 



and the differences between the values for y given by 

 equation and the experimental values were as follows : — 



this 



p = 2x. 







Diff. 



2 . . . -"002 



4 







+ •031 



6 







-•014 



8 







-•069 



10 







+ •015 



12 







-•004 



14 







+ •068 



16 



TVio or 



m 



nf \ 



+ •121 



-Up, Pi'i'nve k -4-* 



p=2x. 



Diff. 



18 . . 



. -°091 



20 . . 



-•136 



22 . . 



. --001 



24 . . 



+ •047 



26 . . 



+ •104 



28 . . 



-•038 



30 . . 



-•051 



32 . . 



+ •018 



The sum of the errors is + "404° and — "406°, the mean, e u 

 being '0506°, or two and a half times greater than the expe- 

 rimental error ; the e 2 error is 10, and the e s error is, as might 



* The deduction of this equation, in which long division and multipli- 

 cation had to be employed, occupied ten days, although the values for y 

 were the whole numbers from 1 to 16. This may give some conception 

 of the desirability of obtaining some other method of examining results. 



