COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 121 



straight line may be reduced, but not eliminated. We look then for 

 sources of "experimental error." Perfectly typically, we find them in 

 variables originally passed over as "irrelevant." We find the points 

 very much less scattered when we control the temperature with a 

 thermostat. A brief wait ("to establish equilibrium") before each 

 reading sometimes helps; otherwise the gas may remain slightly over- 

 heated by the compression consequent to rapid addition of the 

 mercury. We find further that the gas sample must im^olve no 

 equilibrium mixture (lest the number of gaseous particles change 

 with the pressure), that it must be reasonably far from its critical 

 point and also reasonably dry (lest at high pressure part of the 

 sample be "lost" though condensation), that the two arms of the 

 J-tube must be reasonably equal in diameter (lest there be "capil- 

 larity effects" ) , and on and on. 



We find that the more we take such precautions the more we re- 

 duce the scatter of the experimental points. But always, in any large 

 set of measurements, we will have to dismiss (perhaps as "reading 

 errors") one or a few points that fall far from the line. And always, 

 as Poincare observes, the bulk of the points will still show residual 

 scattering away from the line we actually draw. 



. . . the curve that we shall trace will pass between the observed 

 points and near these points; it will not pass through these points 

 themselves. Thus one does not restrict himself to generalizing the 

 experiments, but corrects them; and the physicist who should try to 

 abstain from these corrections and really be content with the bare 

 experiment, would be forced to enunciate some very strange laws. 



If the points form an approximately rectilinear array, we draw the 

 straight line, defined perhaps by the method of least squares, that 

 goes nearest to but not through all of them. Not to take as "best" the 

 curve that is the smoothest reasonable approximation to the experi- 

 mental points— that restraint our scientific taste, long molded by a 

 conception of gradualism, would find "strange" indeed. The slightly 

 uneven line actually defined by the points is, we feel, uneven only 

 because of small but always finite experimental errors. By an act of 

 faith we then pass to the limit: we say that if there were no such 

 errors there would be no deviation from exact linearity. We then 

 write the mathematical equation: pV = constant; but this expression 

 refers rigorously only to the outcome of experiments we have not 



