BAROMETRIC MEASUREMENT OF HEIGHTS. 369 



been found, depending on the values assumed for m and a. Arago 



and Biot found = 10,467. This makes the " barometric coeffi- 

 a 



cient" 60,122"4 feet. Raymond's value, namely G0,158'6 feet, was 

 found by comparing the values given by the formulae with the 

 results of actual leveling with a spirit level. His observations 

 were, however, few in number, and, although his coefficient is 

 frequently used, it is probably the least accurate of all the'deter- 

 minations. In Laplace's formula, Raymond's constant is used. 

 Babinet used the constant 60,334, and in Baily's formula the con- 

 stant is 60,346. In Williamson's formulse the constant is 60,384, 

 which is the value found by Regnault, and is probably the most 

 accurate of all. Sometimes the coefficient in the formula is given 

 as 10,000 fathoms, which is roughly correct. 



We will now consider the errors underlying the barometric 

 measurement of heights, which render the method inapplicable 

 in cases where great accuracy is required. The most important 

 of these sources of error is probably that due to what is called the 

 " barometric gradient," a term frequently used in meteorological 

 reports. Taking three points at which the barometric pressure 

 is, the same, if the atmosphere was in a state of statical equi- 

 librium these points would lie on the same level plane. But 

 usually this plane is not level, but inclined, and the inclination 

 of the plane is termed the " barometric gradient." For a number 

 of points the surface on which they lie would not be a plane at 

 all, but an undulating surface. These surfaces for diiferent 

 heights are never parallel, and frequently slope in opposite direc- 

 tions. Allowance can not be fully made for this disturbing 

 cause, but the error can, to some extent, be eliminated by making 

 a number of simultaneous observations at the two stations, and 

 taking the mean of the results. 



Another cause of error is due to variations in the temperature 

 of the air. It is generally assumed that the mean temperature of 

 the column of air between two stations, one vertically over the 

 other, is the mean of the temperatures at the upper and lower 

 stations, but this is not always the case. The error may be par- 

 tially eliminated by making observations at intermediate stations, 

 but can not be entirely overcome. High winds also cause a vari- 

 ation in the height of the barometer. 



In addition to the errors mentioned, there are, of course, errors 

 of observation, and instrumental errors. The former may be 

 caused by imperfect adjustment of the zero point, and erroneous 

 reading of the mercury on the scale. These errors are, however, 

 usually small, and may with care be neglected. The instrumental 

 errors are due chiefly to imperfect graduation of the scales of the 

 barometer and attached thermometer, the impurity of the mer- 



VOL. XLVI. 27 



