Perkins employed this graphical method with much care in exhibiting the results of his experiments on the compression of water.10 The numerical results were marked 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. Regnault carried the method to perfection by laying off the points with a screw dividing engine;11 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 from 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 instance, the quantities of heat absorbed by water when raised in temperature from 0° to 5°, from 5° to 10°, and so on, these quantities will