COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 125 



chaos we must, Ste. -Claire Deville enjoins, rally to defend the threat- 

 ened relation: 



Every time an exceptional fact has been discovered the first task, even 

 the first duty, practically imposed on the man of science has been to 

 make every effort to cause the fact to come under the common rule 

 by means of an explanation which sometimes requires more work and 

 reflection than the discovery itself. 



For the preservation of the rule we have abundant resources, as is 

 shown in Chapter IX. Even if all these fail, we can almost always 

 find an escape hatch in the assumption that the system in question is 

 "nonideal." Thus, for example, we suppose that Kepler's laws fail of 

 perfect accuracy because the motion of any given planet is "per- 

 turbed" by its interaction with other planets. And blithely we hy- 

 pothesize ideal systems in which no such complications exist, and to 

 which the ideal law applies perfectly. How then can we ever bring 

 ourselves to recognize as genuine the failure ( s ) of a colligative rela- 

 tion in which we have confidence? If the colligative relation is made 

 true, regardless of what the data indicate, is it not simply a conven- 

 tion? Consider a relation that, at least superficially, well lends itself 

 to such interpretation. 



Galileo's law of free fall. We express this law mathematically as: 

 5 ^ i gt'^. Here g is a proportionality constant that measurably de- 

 pends only on the locale of the experiment, and t is the "elapsed time" 

 during which a "freely falling body," starting from rest, traverses the 

 "vertical distance" s. The denotations of s, g, and t seem adequately 

 clear; but on many occasions the law may seem to fail, and fail badly. 

 A sheet of paper or a feather do not fall in accordance with the law. 

 A dead pigeon or a steel ball bearing, falling a short distance in air, 

 conform to the law; but a live pigeon in air, or a steel ball bearing in 

 oil, do not. Stipulate that a "freely falling body" can only be one 

 falling in a vacuum, unopposed by viscous resistance? So doing we at 

 once eliminate the discrepant cases just noted, but not all discrepant 

 cases: even in vacuum charged objects moving in electromagnetic 

 fields may not behave as "freely falling bodies." 



How then do we treat the law? Quite simply. We assert that it is 

 invariably valid in the absence of "extraneous forces." When the re- 

 lation is found to apply satisfactorily we declare that we have dealt 

 with a "freely falling body." When it does not so apply we declare 



