1825.] Baroiimtrical Measurement of Heights, 89 



rules just given;* This^ correction, properly the very last in 

 order, may be readily effected by the fractions given by.Biot, in 

 the third volume of his Traitt d' Astronomies or more promptly 

 by the annexed table, differing some little from the one by 

 Prof. Littrow, inserted in the Memoirs of the London Astrono^* 

 mical Society.f ^-,,, . 'i- 



Correction for the vertical Diminution of the Force of GYavity. 



For the Air. — The force of gravity diminishing as, ascending 

 from the surface, we recede from the centre of the earth as the 

 square of the distance, it is evident that the density of the air at 

 different altitudes will diminish, ccEleris paribus^ in the same 

 ratio. The mean radius of the earth being about 3956 miles, if 

 we call the force of gravity at the level of the sea 1, its value 

 at the several altitudes of 



1, 2, 3, 4 miles 



.„ , , , ,. 3956 3956 3956 3956 



Will be equal to 1 x square of ^957' 3958' 3^9' 3-960' 



for which we may be allowed to sub-^ 2 4 6 ^ . 



Stitute 1 minus J 3956' 3956' 3956' 3956 * 



consequently we must augment the calculated altitudes in pro- 

 portion to the mean diminution of the density of the intercepted 

 column of air, nearly equal to half the sum of the values of the 

 diminution at the extremities ; effected by applying a correction 

 additive found by multiplying the difference of level in feet by 

 the snm of the perpendicular distances of the summit and base 

 of the object from the surface of the earth, and dividing the 

 product by 20887680, the mean radius of the earth in feet. The 

 amount of the correction for an elevation of 8000 feet above the 

 sea, being only three ieet, it may be safely disregarded within 

 that limit. iVt greater elevations the value may be readily found 

 by Table IV, 



For the Mercury. — Having proceeded in our calculations on 

 the supposition of the force of gravity, as affecting the mercury 

 being constant without regard to the altitude, we must now be 

 conscious that the absolute pressure exerted by the upper strata 

 of the atmosphere on the subjacent intercepted column of air, is 

 no longer correctly exhibited by a barometer situated above the 

 lev-eliof the sea. The specific gravity of the liquid as transported 



*■> Admitting tfe verticals to have the same latitude. 



-fit The. uppe* part of that branch of the syphon barometer containing the shorter 

 column of mercury being filled at the pole with dry air of a certain temperature, and 

 hermetically closed, note the difference of level of the mercury in the two branches. 

 Then in' proceeding towards the equator, if we do not change our distance from the 

 surface of the sea, and preserve the temperature of the air and mercury unaltered, the 

 length of th9<}^hmin of air, and the difference of level of the mercury, will continue to 

 augmeiit until \ve j^rive at the equator. The irigtrument would, therefore,' serve to fii^d 

 the latitude. ' 



