COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 135 



Hon and the position of one identifiable mark on the photographic 

 plate. Were we to decide that matter is non-atomic, and light non- 

 undulatory, presumably our formulation of this relation would no 

 longer be given in terms of "atomic number" and "wavelength." But 

 even such a drastic upheaval could not alter the substance of this re- 

 lation: between the position of the element in the periodic classifica- 

 tion and the position of the mark on the photographic plate there is 

 an indissoluble connection. 



A physicist might rightly object that this is a preposterous way to 

 put Moseley's law— not wrong but grotesquely insufficient. Dwelling 

 on its denotations, we have wholly ignored the law's weighty theo- 

 retical connotations. Reading the abstract law in the light of the 

 Rutherford-Bohr theory of the atom, we discover the basis for a pro- 

 found rationalization of Mendeleev's "purely empirical" classifica- 

 tion. Z we identify as both the "number of protons" in the "atomic 

 nucleus" and the "number of electrons" attendant thereto. One ap- 

 parent failure of Moseley's law was then taken to connote the prob- 

 able occurrence of an undiscovered element. That element (haf- 

 nium) was indeed discovered some years later, when excitation of a 

 sample in which its presence was suspected did yield a spectro- 

 graphic plate with a spot corresponding to the expected atomic num- 

 ber. This pretty piece of work oflFers a vivid illustration of the inter- 

 play of the connotation and denotation of an abstract law. 



The Mendelian laws. The following will serve us as a particular 

 example: "In monohybridization experiments conducted on a large 

 scale, in which dissimilar parents are crossed and the first filial gen- 

 eration is intercrossed, three-fourths of the members of the second 

 filial generation will exhibit the dominant forms of the diflFerentiating 

 characteristic." Let us assume what is not at once evident: that the 

 denotations of the many conceptual terms here involved can be 

 made adequately clear. The need for the qualification "conducted 

 on a large scale" at once signifies that we have here to do with a 

 new ( statistical ) kind of relation unlike any so far discussed. 



No relation furnishes absolutely reliable prediction of a particular 

 event in a particular system. However, when dealing with relations of 

 the kind considered earlier, we find that predictive reliability can be 

 increased without apparent limit— by improving the accuracy with 

 which we determine the conditions defining the state of the system, 

 and/or by broadening our definition of state to take account of a 



