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 ai 

 inch square. The values of the variable being markea 

 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. 



