60 sciExcE (and common sense) 



law: pV = constant. Boyle's law here emerges as a limiting law. 

 However, when the \^olume of the gas is small— i.e., at low tempera- 

 ture and/or high pressure— the correction terms become significant, 

 and the predictions of the van der W'aals relation then difiFer sub- 

 stantially from the comparatively inferior predictions furnished in 

 these conditions by Boyle's law. 



Remembering, understanding, discovering. Our first theory sug- 

 gests how Boyle's law may arise, and further suggests how it may 

 come to fail where it does fail. Our second theory ofiFers us means to 

 estimate in advance the magnitude of the failure. And Boyle's law 

 here is paradigm of all the familiar gas laws. We can then feel we 

 understand both the successes and the failures of all these laws. The 

 kinetic theory thus proves its eflFecti\'eness as an explanatory device. 



Always we remember better what we feel we understand, and in 

 any case the need for remembering is now triply reduced. First, we 

 can now derive any of the many gas laws, as it is needed, from a 

 few easily remembered theoretic axioms. E\^en making no derivation, 

 each law now reminds us of others in the group with which we have 

 come to associate it. Second, making the deri\'ations, we find the sim- 

 ple laws obtainable only with the aid of certain auxiliary assump- 

 tions and approximations. Grasping the circumstances in which these 

 are likely to fail, we simultaneously grasp the limits in range and 

 reliability attaching to the simple laws. Third, the task of memory 

 is reduced even as concerns the many alternate denotations attach- 

 ing to the concepts that figure in the derivative relations. We must 

 still learn some primary denotations, but the "equivalence" of any 

 alternate denotation is itself a colligative relation we come to grasp 

 easily as it too finds theoretic accommodation (ordinarily elsewhere 

 than in the kinetic theory ) . Scientific theories thus function superbly 

 as correlative devices. 



Good theories are more than correlative devices, more even than 

 explanatory devices. Good theories are also heuristic devices— tools 

 that assist us in winning new knowledge. From theoretic postulates 

 we arrive deductively at theorems we identify with known colliga- 

 tive relations; sometimes also at other theorems we identify with 

 colligative relations not previously known. We are then led to look 

 for certain things not before seen, or perhaps even thought of. Thus, 

 for example, the kinetic theory suggested to Maxwell the novel idea 

 that gas viscosity should be independent of gas pressure. Investigat- 



