Composition of Dilute Sulphuric Acid, 205 



empirical expression of the facts unless the number of con- 

 stants involved be inordinately large. 



This brings me to the second of Mr. Pickering's arguments. 



(2) The number of constants in my equation is so great that 

 a close agreement with his results is not surprising. 



I reply that it is not disputed that my curve covers a range 

 greater than that embraced by three, and less than that 

 embraced by five of his curves. If we assume that each one 

 of these curves could be expressed with sufficient accuracy by 

 means of approximate formulaB each of which involved two 

 disposable constants only, it follows that Mr. Pickering 

 expresses by the aid of 6 and 10 constants respectively 

 ranges of which the first is somewhat less, and the second 

 somewhat greater, than that which I cover by means of 7 

 constants. As the assumptions I have made are extremely 

 favourable to Mr. Pickering, this shows that he cannot claim 

 any superiority on this head. 



(3) Mr. Pickering objects to the numbers given by those 

 terms in my equation which occurred to me first being- 

 brought into harmony with experiment by means of another 

 term. 



What would he think if, when a computer had noticed that 

 the results of certain experiments could be approximately 

 expressed by means of the circle 



x 2 -\-y <2 =r 2 , 



he was thereby debarred (though a better result could be 

 thereby obtained) from converting the circle into the ellipse 



where a is a small quantity. It is often only by first using a 

 rough approximation that a formula for the results of expe- 

 riment can be framed. 



(4) Mr. Pickering regards the last term in my equation as 

 a " hump," and the points at which it becomes and ceases to 

 become important as " marking the practical starting of a 

 fresh order of things." 



This may be answered in the same way as the last argument. 



The values of y given by the two equations y 2 = r 2 — a; 2 and 

 y 2 — r 2 — x 2 {l— a 2 ) agree when x = 0. Does Mr. Pickering- 

 think that if the results of observation are expressed more 

 accurately by the latter, that the points in which the two 

 corresponding values of y in the two curves become noticeably 

 different mark " a practical starting of a fresh order of things " 

 in the ellipse. 



The projection of the ellipse beyond the circle is an integral 



