QUANTITATIVE INDUCTION. 119 



Engraved sheets of paper ready prepared for the draw- 

 ing of curves may be obtained from Mr. Stanford, at 

 6 and 7 Charing Cross, or from Messrs. W. and A. K 

 Johnston, of London and Edinburgh. When we do 

 not require great accuracy, paper ruled by the common 

 machine-ruler into equal squares of about one-fifth or one- 

 sixth of an inch square will serve well enough. I have 

 found Vere Foster's Exercise Book, No. 1 2 m , which is 

 ruled in this way, very useful for statistical or other 

 numerical purposes. I have also met with engineers' and 

 surveyors' memorandum books ruled with one-twelfth inch 

 squares. When a number of complicated curves have to 

 be drawn, I have found it best to rule a good sheet of 

 drawing paper with lines carefully adjusted at the most 

 convenient distances, and then to prick the points of the 

 curve through it upon another sheet fixed underneath. 

 In this way we obtain an accurate curve upon a blank 

 sheet, and need only introduce such division lines as are 

 requisite to the understanding of the curve. 



In some cases our numerical results will correspond, 

 not to the height of single ordinates, but to the area of 

 the curve between two ordinates, or the average height of 

 ordinates between certain limits. If we measure, for 

 instance, the quantities of heat absorbed by water when 

 raised in temperature from o to 5, from 5 to 10, and so 

 on, these quantities will really be represented by areas of 

 the curve denoting the specific heat of water; and, since 

 the specific heat varies continuously between every two 

 points of temperature, we shall not get the correct curve 

 by simply laying off the quantities of heat at the mean 

 temperatures, namely 2^, 7^, and so on. Mr. J. W. 

 Strutt has shown that if we have drawn such an incorrect 

 curve, we can with little trouble correct it by a simple 



m Published by Whittaker & Co., London. 



