128 COLLIGATWE RELATIONS AND SCIENTIFIC LAWS 



maximum generalization of a relation is clearly the optimal policy. 

 Certainly it is the policy best designed to bring to light any inade- 

 quacies of the relation: "Gi\'e a man enough rope . . ." By generali- 

 zation a relation is put to proof and, as we come sooner or later to 

 recognize its limitations, its value to us is not impaired but very 

 much enhanced. 



We say: "Two things cannot occupy the same space at the same 

 time." At first sight this statement seems perfectly general and per- 

 fectly reliable. But a great deal depends on how we understand the 

 denotation of "things." We might eliminate some failures of the re- 

 lation by excluding gases from "things"; with increase of pressure two 

 gases can easily be crowded into the container formerly "occupied" 

 by one of them. Some other failures we might eliminate by excluding 

 liquids; still others, by excluding solids (in sodium sulfide the 

 sodium and sulfur together occupy a volume less than that initially 

 occupied by the sodium alone ) . Denying status as "things" to gases, 

 liquids, and solids, out of fear of error we reduce the relation to 

 naught. Actually, of course, we do nothing of the sort. Ordirmrilyy 

 surely, volumes are additive— even in gaseous systems if they are 

 nonreactive and held at constant temperature. Precisely as we recog- 

 nize that the relation has a proper domain of application, it becomes 

 a more reliable guide. 



Certainly an ill-founded colligative relation may be discarded, as 

 erroneous or fortuitous; and certainly a relation may be extensively 

 reformulated to acknowledge (or surpass) previously unrecognized 

 limits to its applicability. But de Broglie quite correctly stresses that 

 once a relation has been properly authenticated— 



. . . we have a definitely acquired result which no later speculation 

 is able to undo. If it were not thus, no science would be possible. But 

 it can very well be that, in the light of new experimental facts or of 

 new theoretical conceptions, we are led to consider previously verified 

 laws as being only approximate, that is to assume that, if the precision 

 of the verification were indefinitelv increased, the laws would not be 

 more exactly verified. This has happened many times in the course of 

 the history of science. Thus the laws of geometrical optics— for ex- 

 ample, the rectilinear propagation of light— although having been 

 verified with precision and at first regarded as rigorously true, were 

 seen to be only approximations that day when the phenomena of dif- 

 fraction and the wave character of light were discovered. 



