434 Explanation of the Theory of the [June, 



Article VII. 



Explanation of the Theory of the Barometrical Measurement of 



Heights. 



(To the Editors of the Annals of Philosophy.) 

 GENTLEMEN, 



The barometer is an economical instrument capable, even in 

 the hands of the most unscientific, of readily furnishing data 

 sufficiently exact for the computation of accessible heights. The 

 consequent calculations, in spite of repeated sacrifices of accu- 

 racy to dispatch, are however disgustingly tedious, and not a 

 little liable to erroi'. In the most approved formulae, approxi- 

 mations seriously affecting in many cases the accuracy of the 

 result are admitted, v^hilst minor corrections strictly constitut- 

 ing part of the value of the coefficients are unnecessarily kept 

 distinct, and form a notable portion of the labour of the com- 

 puter. The tables expressly constructed to facilitate and ensure 

 accuracy to the nicer calculations of the philosopher, as well as 

 those designed to abridge the labour to the geologist, the bota- 

 nist, and the general traveller, for whom the approximate height 

 maybe sufficient, are capable of valuable improvement, not only 

 in regard to accuracy, but to the attainment of the other object 

 in view. To point out these errors, to remedy the defects, and 

 to render the theory of the instrument and the various formulae 

 intelligible to general capacities, will form the principal object 

 of the present paper. The task imposed is sufficiently difficult ; 

 the execution wiU therefore require the extreme indulgence of 

 your readers. 



Having formed a correct idea of the theory, we shall be able 

 to propose some alterations in the constructionof the instruments, 

 trifling in themselves, yet enabling the observer materially to 

 reduce the number of the data requisite for the calculations 

 without affiecting; in the slightest degree the correctness of the 

 result. 



Definition of Difference of Level, Vertical Height , 8)-c. 



1. The earth being a sphere at rest, any two or other number 

 of points equally distant from its centre are termed level points, 

 — on a level, — or level with each other. 2. A level surface con- 

 sists of such points, and is every where at the same distance 

 from the centre of the earth. The level surface being of incon- 

 siderable extent will be sensibly a plane, parallel to the horizon, 

 and is consequently occasionally termed a horizontal surface or 

 plane. 3. The difference of level, or the vertical height, eleva- 

 tion, or altitude of one point, or of one level surface above 



