of Air- and Mercury-Thermometers. 217 



Sn intersects NB in NS which is the point corresponding to 

 M. Regnault's observations at 60°, and So intersects CO in 0, 

 which is the point of the same for 70°, &c. 



§ 6. Thus M N P Q R S represent M. Rcgnault's observa- 

 tions with temperatures uncorrected, and A B C D E F S the 

 same with temperatures corrected by the formula. If this latter 

 coincided with the straight line AS, we should have the desired 

 proof at once of the tbermometric formula, of the law of density, 

 and of the extreme accuracy of M. Reguault's observations. 



With reference to the shght apparent deviation, we must keep 

 in view that the tensions employed are, strictly speaking, not 

 those actually observed, but those given in the Table at the end 

 of M. Regnault's memoir computed from the empirical formula, 

 log e= a 4- hoL^—c^\ the constants of which were determined from 

 the graphically equalized observations at 0°, 25°, 50°, 75°, and 

 100°. There is abundant evidence in the memoir of the remark- 

 able efficiency of this formula to represent the observations within 

 their limits of error. It does not profess to represent the true 

 line, but it must coincide with it at the five points, and at inter- 

 mediate temperatures cannot be more than a small fraction of a 

 degree removed from it. 



The line A B C D E P S thus represents the formula of inter- 

 polation, and its relation to the straight line A S, it will be re- 

 marked, is precisely what might be expected to subsist between 

 an empirical and a true curve of tension. It intersects, and 

 intersection, not contact, is the character of such formulag, as 

 proved by the differences between the computed and observed 

 quantities being alternately of different signs. 



If we suppose the point B shifted to k, C to I, &c., and the 

 points N, 0, P shifted the same respective amounts, these points, 

 N, 0, P, &c., trace out the curved line i\I w w w, which conforms 

 nearly to a circular arc. There is little doubt that this curve 

 represents the true equalized densities observed by M. Regnault, 

 while M, N, 0, &c. represents the densities by the empirical 

 formula. We have thus a semi-arch and semi-chord defining 

 the graduated difference between the air- and mercury-thermo- 

 meters below 100°. 



§ 7. The only evidence of real discrepancy is to be found at 



D, which ought to coincide with j. If we take Aa = y-r AM 



and DS = TT ^^> ^^^^^ "^^ ^^ ^ straight line. Thus the diflfer- 



cnce JD, which does not amount to more than y^n*^ ^^ ^ degree, 

 may indicate that the formula gives the correction j'jjth in 

 excess throughout. Otherwise it may be caused by it not jjcr- 

 fectly represcuting the curve of expansion of mercury in glass 



