494 THE PRINCIPLES OF SCIENCE. [chap. 



upon a sheet of paper very exactly ruled at intervals of 

 one-tenth of an inch, and the original marks were left 

 in order that the reader might judge of the correctness of 

 the curve drawn, or choose another for himself. Eegnault 

 carried the method to perfection by laying off the points 

 with a screw dividing engine ; ^ and he then formed a 

 table of results by drawing a continuous curve, and 

 measuring its height for equidistant values of the variable. 

 Not only does a curve drawn in this manner enable us to 

 infer numerical results more free Irom accidental errors 

 than any of the numbers obtained directly from experiment, 

 but the form of the curve sometimes indicates the class of 

 functions to which our results belong. 



Engraved sheets of paper prepared for the drawing of 

 curves may be obtained from Mr. Stanford at Charing 

 Cross, Messrs. W. and A. K. Johnston, of London and 

 Edinburgh, Waterlow and Sons, Letts and Co., and probably 

 other publishers. 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 met with engineers' and 

 surveyors' memorandum books ruled with one-twelfth inch 

 squares. When a number of 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 in- 

 stance, 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 s])(^ciHc heat varies continuously between every two 

 points of temperature, we shall not g<^t the correct curve 



1 Jtimin, Cours de Physique, vol. fu p. 24, «&c. 



