SECTION 23. GENERALISATION. 327 



law to law until we reach the pinnacle. Frequently, however, 

 the facts are represented by a heterogeneous mass which can 

 only be slowly reduced to order and understood. In such in- 

 stances we pursue our researches until some slight semblance 

 of order is created in part of the mass, and we finally resolve 

 on exploring as exhaustively as practicable one or another 

 direction suggested by the preliminary conclusions reached. 

 Here, obviously, there can be no rising from law to law, since 

 the value, or even the correctness, of the conclusions reached 

 is undetermined, since our most heroic endeavours will probably 

 yield only modest fruits, and since the discovery of a com- 

 prehensive law is, in the circumstances, a counsel of perfection. 

 For this reason we relegate the grading of generalisations to 

 the conclusion of the enquiry, and are content that our most 

 comprehensive generalisation should be a comparatively restricted 

 one. Accordingly, the scientific pioneer must toilsomely wrest 

 truths from nature wherever he can, without being truly cognisant 

 of their value, whereas, with the advance of science, it becomes 

 gradually easier to take advantage of established classifications 

 and proceed at a perceptible pace in a forward or upward 

 direction. To rise from law to law is therefore only practicable 

 when we are already familiar with many verified generalisations. 



It will be well to define as precisely as possible the process 

 of graded generalising. Finding, for example, that consequent 

 on the application of pressure some hydrogen gas occupies less 

 space, I carefully ascertain the relation of pressure to density 

 in the sample at different times, and think I perceive that its 

 density is directly proportional to the pressure to which it is 

 subjected, that is, if the pressure be doubled, its volume is 

 halved, and when the pressure is halved, its volume is doubled. 

 I formulate then, after sundry experiments, the hypothesis that 

 hydrogen always behaves in this manner; but ascertain, on 

 closer investigation, that allowance needs to be made for tem- 

 perature, very high pressure, and so forth. This we might 

 term a simple generalisation : reasoning from a given fact at a 

 given time to the class to which it appertains. 



I advance now a step further. I experiment whether the 

 gas nearest to hydrogen in specific gravity reacts in a similar 

 way to pressure and removal of pressure, and observe identity 

 of effect. I inspect then a few samples of gases of greater 

 and greater specific gravity, and tentatively conclude that the 

 volume of a sample of any gas normally varies inversely with 

 the pressure thereon. I test this conclusion repeatedly, applying 

 it perhaps to every gas I can procure, studious of including 

 the largest variety of gases, and recording the conditions under 

 which I obtain the results. I feel now warranted in converting 

 the simple generalisation into a compound generalisation, and 

 assert that the volume of any gas varies inversely with the 

 amount of pressure to which it is subjected. (Boyle's law.) 



