122 COLLIGATH'E RELATIONS AND SCIENTIFIC LAWS 



done and cannot do. Human invention plays here no inconsiderable 

 role. 



We are still far from Boyle's law as it is commonly concei\'ed. We 

 ha\'e made a few experiments, at a particular time and place, with a 

 particular apparatiis containing a particular gas. We aspire to far 

 greater generality. We extend Boyle's law to measurements made by 

 very different means, e.g., with pressures imposed by a solid piston. 

 To the concepts pressure and volume we thus attach additional de- 

 notations we deem "equivalent." We assign the denotations; but also 

 ice discover, applying them to experiments, that in each case the 

 product pV is gratifyingly constant. Now, with a few additional 

 trials, and further invocation of the principle of continuity, we gen- 

 eralize the law to apply in all places, at all times, and under all con- 

 ditions of constant temperature. Drawing still further on the princi- 

 ple of continuity, we suppose that in nature there are not simply 

 things but things of a species: on the basis of a few more trials we 

 generalize our results to all "gases"— including N^arieties yet unknown 

 —and so arrive at last at Boyle's law in all its lustrous majesty. The 

 luster is of course somewhat tarnished by the subsequent discovery 

 that Boyle's law applies exactly only to an "ideal gas" we must our- 

 sehes invent. 



Here is a recapitulation of the steps by which we reached Boyle's 

 law: 



1. Creation of certain conceptual and experimental tools 



2. Experiments of which "relevant" elements are reported in concep- 

 tual terms and "irrele\'ancies" are dismissed 



3. Reintroduction of variables originally concei\'ed "irrelevant," as 

 restrictions on applicability of law 



4. Rejection of deviant points, and scattering of points, as "experi- 

 mental error" 



5. Generalization of points to line: statement of law as a mathemati- 

 cal relation 



6. Generalization to other systems, and to entirely different kinds of 

 systems 



7. Generalization of law in place, time, and circumstances 



8. Generalization of law for all "gases" 



9. Gonception of ideal gas to which law applies rigorously by defi- 

 nition 



