Changes of Curvature by Means of a Flexible Lath. 451 



any doubt as to the position of the break ; by using a non-wavy 

 curve for the first portion of the figure in this case the break 

 might be made to occur at the experimental point next above 

 that shown for its position in the figure. 



The particular figure which was selected for the graphic 

 and mathematical examination is, it will be noticed, the one 

 which exhibits the greatest seeming regularity, and which 

 would appear most favourable for representation by a single 

 curve. 



The instances here detailed will, I trust, be sufficient to 

 show the very strong nature of the evidence as to the reality 

 of these changes of curvature : that the recognition of them 

 is certainly not a mere matter of taste on the part of the 

 draughtsman, even in the case of feebly marked breaks, and 

 that the deduction of parabolas from the experimental results 

 themselves tends to precisely the same conclusions as the much 

 more expeditious method of examining the results with a 

 flexible lath. At the same time I trust that the present 

 communication will show that the application of the graphic 

 method requires a great amount of care and a close attention 

 to experimental and other considerations, and it is to be 

 feared that the hurried use of it by those who have not taken 

 the trouble to master the necessary details, or to acquire the 

 requisite amount of skill, may bring it into undeserved 

 disrepute. 



It must be remembered, of course, that a bent-lath curve 

 is not necessarily suited to every curvilinear figure, any more 

 than is a section of a parabola ; but as far as my experience 

 goes the application of a bent lath to a curvilinear figure 

 differing materially from a bent-lath curve (such as a large 

 portion of an hyperbola) would not lead to wrong conclusions, 

 but simply to no conclusions at all. In such a case we find 

 that the error of the drawing increases regularly with the 

 length of the figure drawn in one section, and that any supposed 

 breaks to which we may have been erroneously led by the 

 examination will be found to be false when the method of 

 plotting is altered so as to obtain a figure of a different 

 character. 



October 1891. 



