18 Dr. Arnott oh the Measurements of Heights. 



Ex. 4. Humboldt observed the barometer on Quindiu to stand at 

 0.509818 metres, or 20'072 English inches, and the detached thermometer 

 to be at 18"75 Cent. The boiling point of a thermometer, by my formula, 

 would thus be SO^^S. In formula U, t = 18°-75, B — 6 = 10-57; 

 whence the height is 11,708 feet ; the height obtained, by the most refined 

 barometrical methods, is about 1 1,500, so that there is here an error of 

 about 200 feet. But this example is an unfair one, for there was only a 

 difference of 6°*55 Cent, observed between the temperature of the atmos- 

 phere on the mountain, and that at the level of the sea, whereas by my 

 general formula, it is supposed to be 21°. In other words, while Fahren- 

 heit's thermometer stood at 77°"54 at the level of the sea, it was as high 

 as 65''*75 at the great elevation of upwards of 11,000 feet: such must 

 have arisen from accidental or local causes, and it has always appeared 

 to me that in such cases, some new correction must be applied before we 

 can make use of that element in the calculation of heights by the 

 barometer. 



Ex. 5. The last example I shall give, is taken from Professor Forbes' 

 Observations, (p. 415 of his paper on this subject :) he states, that the 

 thermometer having been corrected to show the boUing point at 212° 

 Fahr., or 100° Cent., at a pressure of 30 inches, indicated the boiling 

 point to be 191°-93 or 88'''85 Cent, on the Col d'Erin in the Vallais, the 

 temperature of the external air being 34° Fahr., or 1°-11 Cent. At 

 Geneva, the boiling point was not observed, but the barometer stood at 

 28*73 inches. Now 2873 corresponds, by my formula, to the boiling 

 point of 98'86; whence in formula U, t = I'll, B — b = 1001, and 

 the height above Geneva is 20-02 (495 + 2-22 + 20-02) = 10,355. 

 According to Professor Forbes, the height was 10,377, partly by the 

 ordinary barometric calculation, and partly by his own constant multi- 

 plier : this makes the height of the Col d'Erin, above the level of the sea, 

 according to him, 11,720 feet; by the formula U, 11,698, or almost 11,700 

 feet. If we suppose that the boiling point was 100° at the level of the 

 sea, then t = 1°-11 Cent., B — 6 =^ 11'15, and the altitude is 11,585 ; 

 on the same supposition, Mr. Forbes makes it 11,586. But water by 

 that thermometer must actually have boiled at the level of the sea at 

 that time, at 212°-225, or 100°i Cent. 



In giving these formulas, I do not intend them for the man of science, 

 for I suppose there are few such who have not had recourse to similar 

 methods of correcting the approximate heights given by their barometer, 

 in default of actual simultaneous observations on the temperature of the 

 atmosphere at both stations ; but because they may prove useful to those 

 who work only by the formulas of others. Whenever a barometer is at 

 hand, it is a much more trustworthy instrument than the best thermometer 

 adapted to take the boiling points, for as justly observed upon the latter, 

 by Professor Forbes, " in no circumstances, even the most favourable, is 

 the observation true to less than ^l of a degree." But there are few 

 who have travelled in mountainous districts who cannot tell of barometers 



