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XVI. A Consideration of some of the Objections raised by 

 Mr. Lupton* to Mr. Pickering's Methods of reducing 

 Experimental Results. By Edwaed Harold Hayes, 

 M.A.j Fellow of New College, Oxford f . 



I FEAR that it may appear very presumptuous in an in- 

 dividual whose work in a chemical laboratory has been 

 confined to the simplest cases of qualitative analysis, and 

 who has had no practice in dealing with any important series 

 of experimental results, to attempt to question the validity of 

 the arguments advanced by an expert like Mr. Lupton. It 

 chances, however, that I have studied with considerable care 

 Mr. Pickering's paper on the Nature of Solutions % ; and have 

 gradually become convinced of the very great value of the 

 methods of dealing with experimental data there described, 

 especially as regards the use of a bent lath in drawing the 

 curves. Mr. Pickering would be the first to admit that 

 mathematics are not a subject in which he is deeply versed, 

 so that there would appear to be a danger lest, on some of 

 the points raised by Mr. Lupton, judgment may be allowed 

 to go by default, and an impression be thereby created that 

 there is something essentially unsound from a mathematical 

 point of view in Mr. Pickering's methods. 



When a uniform naturally straight lath is acted upon by 

 a system of coplanar forces, the form of the curve assumed 

 by a portion of it throughout which none of the applied 

 forces act is such that the product of the radius of curva- 

 ture at any point and the distance of the point from some 

 fixed straight line is constant, provided that the radius of 

 curvature is very great compared with the thickness of the 

 lath § . It immediately follows that the general differential 

 equation of the curve is 



which contains three arbitrary constants. Since this is a 



* Phil. Mag. May 1891. 



t Communicated by the Author. 



\ Journ. Chem. Soc. March 1890. 



§ I believe that Mr. Pickering held the lath near its ends, and only 

 used the intermediate portion for drawing his curves. Hence the curves 

 obtained by him fulfil the above condition. 



|| For a discussion of this curve see Minchin's l Statics,' vol. ii. pp. 203- 

 209, Mr. Pickering is not justified, mathematically speaking, in saying 

 that the bent lath " does not form a curve of any particular nature." This 

 statement, however, is practically equivalent to a recognition of the high 

 degree of generality which the curve possesses. 



H2 



