xxii.] QUANTITATIVE INDUCTION. 493 



Under such circumstances, the best mode of proceeding 

 is to prepare a paper divided into equal rectangular spaces, 

 a convenient size for the spaces being one-tenth of an 

 inch square. The values of the variable being marked 

 off on the lowest horizontal line, a point is marked for 

 each corresponding value of the variant perpendicularly 

 above that of the variable, and at such a height as cor- 

 responds to the value of the variant. 



The exact scale of the drawing is not of much import- 

 ance, but it may require to be adjusted according to 

 circumstances, and different values must often be attri- 

 buted to the upright and horizontal divisions, so as to 

 make the variations conspicuous but not excessive. If 

 a curved line be drawn through all the points or ends 

 of the ordinates, it will probably exhibit irregular inflec- 

 tions, owing to the errors which affect the numbers. But, 

 when the results are numerous, it becomes apparent which 

 results are more divergent than others, and guided by a 

 so-called sense of continuity, it is possible to trace a line 

 among the points which will approximate to the true law 

 more nearly than the points themselves. The accompany- 

 ing figure sufficiently explains itself. 



VARIABLE 



Perkins employed this graphical method with much 

 care in exhibiting the results of his experiments on the 

 compression of water. 1 The numerical results were marked 



1 Philosophical Transactions, 1826, p. 544. 



