BY THE BOILING POINT OF WATER. 243 
This rigorously represents M. Reanauur’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 
ern ae Se UG eS Se ma 
(where x 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 IIL, fig. 3), referred to a line 
PR parallel to a tangent at the vertex; (B) is an equation to a straight line pq, 
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 pg from 
the curve at any point need not exceed one-eighth of the value of T’ in formula 
(A). If we suppose the range of the boiling point to be 20°, (corresponding to an 
elevation of 11,000 feet), T? 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 FAuRENHEIT, thus confirming the results previously arrived at. 
EDINBURGH, 4th December 1854. 
5 * Tf we aim at representing M. Reenavtt’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 formule 
_ (A) and (B), arises from the different inclination of the tangent line PT, and the intersecting line p 9, 
in Plate III., fig. 3, as explained in the succeeding paragraph of the text. 
VOL. XXI. PART II. aT 
