xo8 CAUSES -which afefi the ACCURACY 



to the difference of the tabular logarithms, to give the true 

 height of the one barometer above the other. In other cafes, 

 the proportional part, to be added or fubtracled, will be greater 

 as becomes lefs, or as the height becomes greater : It will be 

 = o, when b@ = y 2 ; affirmative, when ij3 is greater than y 2 ; 

 and negative when it is lefs. 



24. THERE remain to be confidered the two corrections that 

 depend, one, on the relation between the denfity of the air and 

 the force comprefling it > the other, on the diminution of gra- 

 vity as we afcend from the furface of the earth. It was ob- 

 ferved ( 9.), that, if D denote the denfity of the air, and F 



l+n 



the compreffing force, D F . But the force, compreffing 

 a ftratum of the atmofphere at the height x above the furface 

 of the earth, and of the denfity j', which, on the fuppofition 

 of uniform gravity, is denoted by fyx, on that of gravity 

 decreafing as the v power of the diftance from the centre of the 



- 9 



earth, is denoted by '( yx ; where s is the femidiame- 



J (-T+*) ' 



ter of the earth. This is evident, becaufe the weight of each 

 ftratum of air is proportional to its denfity, multiplied into the 

 accelerating force which draws the particles of it toward the 

 earth. Now, let q be the length of fuch a column of mercury, 

 that air, compreflfed by it, would be of the fame denfity with 

 the mercury itfelf, which denfity, in all the preceding invefti- 

 gations, is underflood to be conftant, and to be = i * j 



r 



then, 



* THE mercury in the barometers is fuppofed to be reduced to a fixed temperature, by 

 the application of a correction on account of the thermometers attached to them, after the 

 manner of M. DE Luc, or of General ROY ; the latter reduces the mercury always to the 

 temperature of 32. When the difference of temperature is not very great in the two 

 barometers, the correction of their heights may be made according to the very ingenious 

 remark of the aftronomer royal. Phil. Tranf. vol. 64. part i. f. 164. 



