66 Royal Society. 



The difference between /* at 50° in the two tables being 1*733, a 

 straight line is drawn from the point corresponding to 100°, making 

 an angle of 17°'33, with the chord for 50° in the uncorrected tem- 

 peratures ; and lines are drawn from the same point making angles 

 l°-38, 1°-15, 0°-68, &c. with this line, the intersections of which 

 with the distances or chords corresponding to the temperatures, 

 give the points which represent on the same magnified scale, the 

 observations with the temperatures corrected. The author remarks 

 that the line joining these points represents the empirical law of 

 density, and that its relation to the standard right line for the tem- 

 perature 50° is precisely what might be expected to subsist between 

 the empirical and true curve of tension. It intersects that line — and 

 intersection, not contact, is the character of empirical formulae — at 

 50°, 75°, and 100°, and at intermediate temperatures diverges from 

 it to the extent of about ^^^th of a degree at the maximum. 



Thus, he states, M. Regnault's observations between 50° and 100° 

 afford a distinct answer to the inquiry in the affirmative, and it seems 

 no longer possible to doubt that there is a difference between the 

 mercurial and air- thermometers below 100°; and that its amount 

 does not sensibly differ from the formulae that embrace MM. Dulong 

 and Pe tit's standard observations. He annexes these formulae in a 

 combined form adapted to the Centigrade scale. 



t^=^^-'l-'^ (1) 



^«= temperature by air- thermometer .... log B =3*7145723 

 /^= temperature by mercurial thermometer A =4539°*617 



log C3 = 6-43303 

 logD =0-78587 



It would be more convenient if we could express t„ in terms of t^ , 

 but this can only be done approximatively, as in the following : 



t^ 



/-=-.5 hl^D (2) 



A-/« o ^ r 



If greater accuracy is required, the rule is to find t^ from t^ by 

 (2), then substitute it in (1), and compute t^; this compared with 

 the 'true value shows the alteration to be made in t^ to obtain its 

 true value. 



In conclusion the author observes, it might be expected, without 

 reference to theory, that the curve deduced from the uncorrected 

 temperatures should not show, in its continuation above 100, any 

 abrupt divergence from its regular course; nevertheless from 100° to 

 111-74 the direction of the chord shows such a break in the law of 

 continuity, and which there appears no way of accounting for, unless 

 by a fault in the observations above 100°. Tiieir divergence from 

 the law of density is shown in the Chart. 



