1823.] the Barometer t6 the Measurement of Heights, 99 



air to be in a state of absolute dryness ; for the introduction of 

 moisture sensibly changes this ratio. In fact aqueous vapour at 

 the same temperature weighs less than air: and the stratum 

 (which we took as an example) will again have its weight dimi- 

 nished without changing its temperature in proportion as it is 

 mixed with a larger dose of moisture. Now as the atmosphere 

 is never perfectly dry, we must add a correction for humidity to 

 that which we employ for the temperature ; and the hygrometer 

 will serve to regulate this correction if we have for that purpose 

 a sufficient number of observations which can be relied on; but 

 considering that this correction will be in itself but very small, 

 and that if we suppose the quantity of vapour constant, its varia- 

 tions will influence but little the exactness of the measurements, 

 we may be satisfied to take the air at its usual state of a mean 

 humidity, and to combine the two corrections by raising that for 

 the temperature to l-250th for each degree centigrade. 



But in order to apply this correction, we must further consider 

 what it is that we understand by the temperature of a column of 

 air. We find that the heat decreases from the level of the sea 

 to the highest regions we have been able to reach. A column 

 of air is, therefore, more cold at its summit than at its base, and 

 its mean temperature will be found between these extremes, at 

 a distance regulated by the law which the decrease of tempera- 

 ture follows : if this decrease be uniform, that is, in arithmetical 

 progression, we shall have the mean temperature by taking the 

 mean of the thermometers at the two stations. This is the sup- 

 position most generally adopted. However some great philoso- 

 phers think that the decrease is accelerated in proportion to the 

 elevation. This may be true ; but it is not less so, that it is 

 extremely irregular; and whatever may be the general laws to 

 which it is subject, these laws are altogether counteracted by the 

 nature and form of the earth ; by the reflection of the sun's rays, 

 the variation of winds, and the action of ascending and descend- 

 ing currents ; so that we may consider the hypothesis of an 

 uniform decrease as a mean term from which we have, for the 

 present, no reason to depart. 



Another correction, of a more limited description, but not less 

 important, is founded on the variation of gravity. It is well 

 known that this force diminishes as we recede from the centre of 

 the earth as the square of the distance. Now the earth is a 

 spheroid flattened at the poles, and protuberant at the equator; 

 the radii at the equator are longer than those at the pole ; the 

 polar, therefore, are nearer the centre than the equatorial 

 regions ; and gravity diminishes in proportion as we leave the 

 former and approach the latter, for the double reason of the 

 elongation of the radius, and the increase of the centrifugal 

 force. It diminishes also, and even more rapidly when we rise 

 above the mean level of the surface of the globe ; and from these 

 causes of the dirninution of gravity, it follows as a necessary 



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