Changes of Curvature by Means of a Flexible Lath. 463 



be anticipated, 1 : thus the total error is -506°, or 23*5 times 

 greater than the experimental error, and 24*5 times greater 

 than the total error of the two-curve drawing with the same 

 number of constants, representing the existence of a break 

 instead of continuity. This by itself would be an almost 

 conclusive argument in favour of the real existence of this 

 break. 



I may take this opportunity of saying a few words in 

 answer to the additional remarks which Prof. Riicker has 

 published on the densities of Sulphuric Acid (supra, p. 204). 



(1) Prof. Riicker's statements as to my opinion respecting 

 an equation of the form y = a + bx . . . gx 6 may perhaps lead 

 casual readers to the very erroneous conclusion that I used 

 such an equation in my work on Sulphuric Acid, or that I re- 

 garded it as a probable expression of experimental results. 

 The bent-lath curve may perhaps be mathematically even 

 more complex than Prof. Riicker's curve (though I doubt 

 whether Prof. Riicker can obtain such a simple definition of 

 his curve as that which can be given of the bent-lath curve 

 " the radius of curvature varies inversely as the distance from 

 some fixed straight line"), but these curves which I used 

 were, as was shown by the differentiation, practically very 

 simple, being equivalent to the parabolas y = a + bx + ca; 2 . 

 Prof. Riicker argues that if I subdivided the figures into 

 these simple curves, I might have subdivided them still 

 further into straight lines. I am certainly surprised that 

 such an argument should be used by one who studied the 

 question as closely as Prof. Riicker has done. The only legiti- 

 mate representation of a series of results is evidently that 

 which, ceteris paribus, represents fewest breaks ; the parabola 

 is just as probable a representation of physical properties as a 

 straight line (perhaps more so), and as the curvilinear nature 

 of the figure, in the present case, would evidently necessitate 

 the use of more straight lines than of parabolas for drawings 

 representing apparent errors of equal magnitude, the recti- 

 linear representation is obviously unjustifiable. 



(2) & (3) Prof. Riicker misunderstands me if he thinks 

 that I advocated my representation as being superior to his 

 as to the number of constants involved, or that I objected to 

 his having obtained his equation by first making an approxi- 

 mation, and subsequently improving it. My objections to it 

 were based solely on the grounds that it was an artificial and 

 highly improbable representation of physical facts, and this, 

 apparently, he does not refute. 



(4) It is scarcely worth while to waste words in discussing 



212 



