BY THE BOILING POINT OF WATER. 243 



This rigorously represents M. Regnault's Tabular numbers up to a height of 



20,000 feet, and probably much farther. 



The distinction between the results of this formula and the one given in this 



paper 



h = n T (B) 



(where n is 540 nearly),* is easily specified, and their practical agreement within 

 certain limits shown, as follows : — 



(A) is an equation to a parabolic arc PQ (Plate III., fig. 3), referred to a line 

 PR parallel to a tangent at the vertex ; (B) is an equation to a straight line p q, 

 not necessarily passing through P (if we assume a small correction Pp for the 

 standard boiling point), but which shall represent the parabolic arc PQ as nearly 

 as may be. It may be shown that the greatest deviation of the line p q from 

 the curve at any point need not exceed one-eighth of the value of T 2 in formula 

 (A). If we suppose the range of the boiling point to be 20°, (corresponding to an 

 elevation of 11,000 feet), T 2 is 400 feet, and the greatest error of the linear 

 formula at any height inferior to 11,000 feet is 50 feet, corresponding to one-tenth 

 of a degree of Fahrenheit, thus confirming the results previously arrived at. 



Edinburgh, 4th December 1854. 



* If we aim at representing M. Regnault's Table only, between the temperatures 212° and 192°, 

 the coefficient should be only 535. The difference in the kind of glass used in constructing thermo- 

 meters would alone account for the variation. The reason of the different coefficient in the formula? 

 (A) and (B), arises from the different inclination of the tangent line PT, and the intersecting line p q, 

 in Plate III., fig. 3, as explained in the succeeding paragraph of the text. 



VOL. XXI. PART II. 2 T 



