MEASUREMENT OF HEIGHTS. 



data, to comprehend which it would be necessary to have reference 

 to some principles drawn from the physics of heat and from 

 physical astronomy, which cannot be introduced here. Such a 

 formula, therefore, cannot be usefully given here. 



16. The barometer in the balloon in which the celebrated De 

 Luc made his scientific voyage, fell at the greatest altitude to 12 

 inches. Supposing the barometer at the surface to have stood at 

 that time at 30 inches, it follows from this, that he must have 

 left below him in quantity exactly three-fifths of the entire 

 atmosphere, since 12 inches would be only two-fifths of the 

 complete column sustained in the barometric tube. His elevation 

 at this moment was estimated to have been 20000 feet; but 

 it is certain that he had not attained .a point amounting to more 

 than a small fraction of the entire altitude of the atmosphere. 



Since the density of air is proportional to its pressure, other 

 things being the same, it would follow that the density of the 

 air in which the balloon floated on this occasion was only four- 

 tenths of the density at the surface. 



Now when the barometer is at 30 inches, air is 10400 times 

 lighter than mercury; and, consequently, the air surrounding 

 De Luc's balloon must have been 26000 times lighter, bulk for 

 bulk, than mercury. The height, therefore, of air above the 

 balloon, supposing its density to be undiminished in rising, would 

 have been 26000 feet, and in this case the entire height of the 

 atmosphere would be nearly 50000 feet. But here it is to be con- 

 sidered, as in the former case, that in rising above the level of 

 the balloon, the air would constantly diminish in density ; and, 

 consequently, a column supporting 1 2 inches of mercury would 

 have a much greater elevation than 26000 feet. 



17. The physical effect of which the barometric column is the 

 measure, is the weight of the atmosphere at the place where this 

 barometric column is situated ; and consequently, the variations, 

 whatever they may be, which are incidental to the column, indicate 

 corresponding variations in the weight of the atmosphere. Now 

 it has been found that the barometric column is subject to two 

 species of variation : one of an extremely minute amount, and 

 which takes place at regular periods ; the other of much greater 

 amount, and which may be considered as comparatively contin- 

 gent and accidental. The extreme limit of this latter variation 

 is, however, not great. The greatest height, for example, 

 which the barometer kept at the Paris Observatory has been 

 known to attain is 30'7 inches, and the lowest 28'2 inches, 

 the difference being 2-5 inches, or ^th of the average height of 

 the column. 



The mean height of the barometer at Paris, obtained from 



185 



