120 COLLIGATWE RELATIOXS AND SCIENTIFIC LAWS 



that, as more mercury is poured into the open end of the longer 

 Hmb, the mercury levels ascend in both tubes. Paying no attention to 

 the complicated (and irreproducible ) oscillations of the mercury 

 columns, we note their positions only after they have become quies- 

 cent. This is our choice, but to it corresponds something that is our 

 discovery: the final positions of the mercury columns are reproducible 

 and apparently independent of the antecedent oscillations. 



That the two columns ascend together tells us essentially nothing. 

 Indeed, we must not be bothered with the increasing length of the 

 mercury column in the short limb: we note instead the decreasing 

 length of the column of air therein. This length we concei\^e a meas- 

 ure of the "volume" of the entrapped air. And, similarly, we must not 

 measure the length of the mercury column in the long limb but 

 rather the difference in the heights of the columns in the two tubes. 

 To this difference we add the height of the mercury column, meas- 

 ured from the mercury level in the reservoir, in an entirely separate 

 device— a Torricellian barometer. This complex procedure is directed 

 by the subtle concept "pressure." Thus we translate certain ob- 

 serv^ables into conceptual terms we invent, and this is no simple mat- 

 ter. Having made his experiments, Boyle did not himself arrive at 

 the law that bears his name; his friend Townley had to point out to 

 him that the product of pressures and volumes is very nearly a con- 

 stant. And here, after all the many inventions, we reach a discovery 

 —though not yet a discovery of Boyle's law as such. 



Experiment furnishes a finite series of points on, say, a plot of 

 pV versus p; but Boyle's law represents a line on that plot. Relying on 

 the principle of continuity, we link up the points with a smooth line- 

 assuming nonexistent any discontinuities that may happen to fall be- 

 tween even close-spaced points. We close the gaps by a veritable 

 generalization: we interpolate, on the strength of Newton's faith, and 

 ours, that Natura non saltus facit. And, from the line thus in part in- 

 vented, we read off any of an infinitely large set of values interpolated, 

 with a confidence not much inferior to that we have in the compara- 

 tively small set of values measured. But still we have not attained to 

 Boyle's law which, on our plot, is the equation of a straight line. 

 Lamentably enough, no straight line does pass through all the ex- 

 perimental points. 



With a gas space more constant in bore, a meter stick more care- 

 fully graduated, and so forth, the divergence of the points from a 



