QUANTITATIVE INDUCTION. 117 



and almost always desirable, to call in the aid of space- 

 representations. Every equation involving two variable 

 quantities . corresponds to some kind of plane curve, and 

 every plane curve may be represented symbolically in an 

 equation of a more or less complex character, containing 

 two unknown quantities. Now in an experimental re- 

 search we obtain a number of values of the variant cor- 

 responding to an equal number of values of the variable ; 

 but all the numbers are affected by more or less error, 

 and the values of the variable will often be * irregularly 

 disposed. Even if the numbers were absolutely correct 

 and disposed at regular intervals, there is, as we have 

 seen, no direct mode of discovering the law, but the dif- 

 ficulty of discovery is much increased by the uncertainty 

 and irregularity of the results. 



Under such circumstances, the best mode of proceeding 

 is to procure or prepare a paper divided into small equal 

 rectangular spaces, a convenient size for the spaces being 

 one-tenth of an inch square. The values of the variables 

 being marked off along the scale formed by 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 corresponds to the 

 amount of the variant. 



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

 portance, 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 

 now a curved line be drawn through all the extremities 

 of the ordinates, it will probably exhibit many irregular 

 inflections, owing to the errors which affect all the numbers. 

 But, when the results are numerous, it soon becomes ap- 

 parent which results are more divergent than others, and 

 guided by a so-caUed sense of continuity, it becomes pos- 



