58 SCIENCE (and common sense) 



I seek only, through a simple example, to display the three func- 

 tional roles of scientific theories. 



The kinetic theory. With a constant quantity of gas at constant 

 temperature the product of pressure and volume is constant. Through 

 the reasonably clear denotations of its conceptual terms, Boyle's law 

 furnishes a good account of one aspect of our experience of gases. 

 But this account is not perfect: between the law and our experience 

 of gases we find appreciable discrepancies. With these we may deal 

 in characteristic fashion— postulating an "ideal gas" to which Boyle's 

 law is to apply rigorously. Actual gases being then only more or less 

 imperfect approximations to the hypothetical ideal, we apply Boyle's 

 law successfully only as we come to associate with it certain limits 

 in range and reliability. Charles', Leduc's, Dalton's, Gay-Lussac's, and 

 Graham's laws are similar to Boyle's in all essential respects. Each, 

 by a skillful choice of concepts, condenses into a terse abstract state- 

 ment an immense descriptive and predictive capacity. Each is to a 

 degree both general and reliable, but each carries limits in both range 

 and reliability, and applies rigorously only to an "ideal" case. 



Consider now how a rational order is imposed on this entire group 

 of "gas laws." We begin by making some hypothesis about the na- 

 ture of gases. Here, as in many other cases, we posit the existence of 

 unobservables, thereby to reduce to order the observables described 

 by the colligative relations. Creating the kinetic theory, we postulate 

 that a gas is a space thinly populated with minute corpuscles having 

 a kinetic energy proportional to the absolute temperature of the gas. 

 These particles we suppose to move in accordance with Newton's 

 laws of motion, and to be perfectly elastic in their collisions with each 

 other and with the walls of the container. We have now a model of a 

 gas— but a model still somewhat hard to handle. Hence we make two 

 auxiliary assumptions— inessential to a kinetic theory as such— merely 

 to simplify otherwise difficult deductive operations. We postulate 

 that the corpuscles are point-masses of zero volume; and we postu- 

 late that, save in their collisions, no forces whatever are active be- 

 tween them. These assumptions cannot be perfectly sound for any 

 gas we handle in the laboratory— since all such gases condense, at 

 temperatures appreciably above absolute zero, to liquids that have 

 appreciable volumes. With the introduction of the two simplifying 

 assumptions, then, we are no longer speaking of actual gases but of 

 a more tractable ideal gas. 



