COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 133 



tively, from the values predicted by the Bode-Titus law. In the face of 

 these setbacks, and still lacking theoretic justification, the law was 

 then dismissed as "accidental" by many astronomers, though by 

 others it was still held a genuine relation distorted by conjectural 

 "secondary eflFects." Recently the postulates of a revised nebular 

 hypothesis for the origin of the solar system seem to yield the Bode- 

 Titus law as a deduction. If this promise is borne out, the law will no 

 longer be dismissed as an "accident" and, conversely, its accommoda- 

 tion will become one of the strongest bits of evidence for the new 

 hypotliesis. Theory and law have here a powerful mutual interaction. 



CONNOTATIONS AS WELL AS DENOTATIONS 



A scientific theory may affect our appraisal of a given relation; con- 

 versely, a relation may help us to the first conception of a theory. 

 Beyond predictively efficient denotations, one then draws from the 

 relation theoretically suggestive connotations. To be sure, these con- 

 notations do not simply inhere in the colligative relation as such: 

 only one, or a very few, of many who know the relation may fully 

 grasp its implications. A Newton reads the connotation of Kepler's 

 laws to be the action on planets of a sun-directed centripetal force; 

 after more than two centuries an Einstein finds in the equivalence of 

 gravitational and inertial masses a connotation previously grasped 

 by no one. In the gifted mind even a crude or fragmentary relation 

 may suffice to spark the flash of insight. But always the connotations 

 of a relation will be most readily grasped when, beyond a discovery, 

 it is also an optimal invention, i.e., cast in an abstract form well 

 suited to theoretic consideration. 



We saw that by the time we attain even as simple a relation as 

 Boyle's law, we have already traversed a great, if not the greater, part 

 of the road from "concrete fact" to "abstract theory." With the ac- 

 quisition of Boyle's law a chaos is reduced to at least comparative 

 order. Moreover, the law provides the reference standard that first 

 permits us to recognize, and measure, the departure of real gases 

 from ideal behavior. The theoretic connotations of these systematic 

 deviations thus first become accessible only dirough the mediation of 

 the abstract law that contributes to the organization of even the 

 "imperfections" of which it renders no account. Consider now a re- 

 lation of a still more abstract sort. 



Moseleys law. Let Z represent the "atomic number" of the element 



