412 



PROFESSOR FORBES ON THE DETERMINATION OF HEIGHTS 



My barometer having been broken in the course of my journeys, I was glad to 

 have recourse to the boiling point as a means of estimating (only roughly as I ex- 

 pected) some remarkable elevations not before measured. In several cases I had 

 the advantage of comparing my thermometric boiling point with a barometer, and 

 lately I resolved to discuss these observations empirically, without reference to 

 any theory or tables, or previous observations. 



I first projected the barometric pressures in terms of the corresponding ther- 

 mometric observations. These were the following : 



I obtained a curve, which resembled a flattish logarithmic, the barometric 

 numbers appearing to be in geometrical progression, whilst the temperatures 

 varied uniformly. This recalled to me an idea which I had entertained some 

 years ago, that the boiling point would be found to vary simply Avith the height 

 to which I was led from knowing DELUC'S formula; but the idea had since es- 

 caped me, or been postponed to other occupations. Now, however, I projected 

 the simple elevations of the points of observation (derived from the barometric 

 pressures from the common tables for computing heights uncorrected for the tem- 

 perature), in terms of the boiling points, as in the Plate XL, Fig. 3, and I was gratified 

 to find, that a straight line passed almost quite through the whole of them, shew- 

 ing that the temperature of the boiling point varies in a simple arithmetical pro- 

 portion with the height, namely, 549 -5 feet for every degree of FAHRENHEIT; 

 so that the calculation of height becomes one of simple arithmetic, without the 

 use of logarithms, or of any table whatsoever. 



When I had ascertained this fact, I looked back to DELUC'S formula, and 

 found my old conjecture entirely confirmed. Its form is 



a log p + C = h, 

 h being the height of a thermometer plunged in boiling water under a pressure p ; 



