HYGROMETRY. 



577 





Hrgnxne- itances weighs 257-776 grains. * But, according to 

 the verv accurate experiments of Biot and Arago, a 



* ~~""' litre of dry air at the boiling point, and under a pres- 

 sure of .76 metres, weighs .9454476 grammes, and 

 therefore the weight of vapour at the temperature 100 

 centigrade, is to the weight of air at the same tempera, 

 t ure, and under the some pressure, as . 58948 1 to -9454*76, 

 or as 5 to 8 nearly. Now as Gay Lussac has proved 

 by experiment, that vapour*, so long as they remain in 

 the aeriform state, expand, by increase of temperature, 

 precisely in the same manner as permanently elastic 

 fluids, and suffer corresponding changes of volume by 

 change of pressure ; and as he has also determined that 

 air expands | of its bulk from the freezing to the boil- 

 ing point of the centigrade scale, and that the expan- 

 sion is uniform between these points; if P' be the weight 

 in gramme* of a litre of vapour, at the temperature (; 

 he corresponding elastic force ; and P the weight, 

 in grammes, of a litre of vapour at the boiling point. 



.76{1+.00375/) 



76( 



35. If we substitute 

 grammes, 



1 



3t 



h ~6l)0 I 



for P its value, vi*. .589181 



,, _ 8I96P 4 



ft: i- .- 



K066495F, 

 I + .1 . i-75< ' 



\ml if the value of F,, at determined by the formula 

 jwn in f 30, be substituted for that quantity, the 

 weight of the water contained in a litre of vapour, will 

 be expressed entirely in known terras. 11 the pressure 

 of the barometer be different from .7(i metres, and ex- 

 pressed by 3, the result must be multiplied by -. 



The formula we have given is a little different from 

 that of Biot. 



86. The value of P expressed in English grains, 

 ' to cable inch of vapour at the 

 i / of Fahrenheit, requires serertlcorrection s. 

 In the first place F, mast be determined by the fanra- 

 b in f 31. for Fahrenheit's scale, or taken from the 

 Table constructed from that formula ; and. in the next 

 place, the oo- efficients 1375, and .00375, must be adapt, 

 ed, net only to the general graduation of that scale, 

 bat to the barometrical pressure at which the boiling 

 point of it is fixed. In the centigrade scale, the boil- 

 ing point is taken at a barometrical pressure of .76 

 metres, or 2&92I96 English inches, whereas the boil- 

 ing point of Fahrenheit's scale is fixed under a pres- 

 sure of 30 inches ; but 27 millimetre* of increase in the 

 pressure raise the boiling point 1* centigrade, and SO 

 inches being equal to .76199 metres, the boiling point 

 of Fahrenheit's scale must be ,VH- or about t ' T of a 

 Malign Ji decree above the boiling point of the centi- 

 grade scale. Consequently the co-efficient 1.375 will 

 be increased, by this correction, to 1.37528; and the 

 co-eftcieirt .00375, after being reduced in like manner 



to .0037528, must, to make it applicable to the degrees Hygrorce- 



100 * tr '* 



of Fahrenheit, be multiplied by , which makes *- ^\-^^ 



180 



it .00208(5. 



37- By these corrections, our formula becomes 

 .37528 GF, 



S = 30( 1 +.002086. <H32) 



G being the weight in grains of a cubic inch of vapour 

 at the tailing point, and g the weight expressed in the 

 same denomination of an equal volume of vapour at 

 the temperature t . Since G has a reference to the boil- 

 ing point of Fahrenheit's scale, its value, as formerly 

 determined, must undergo a slight correction, to adapt 

 it to the pressure and difference of temperature at 

 which the two scales are fixed. Under a pressure of 

 29.92196 inches, it was found to be .149176 grains, at 

 the boiling point of the centigrade scale ; but the boil- 

 ing point ot Fahrenheit having been shewn to corre- 

 spond to IDOjV of the same scale, .149176 must be mul- 



30 



tiplied by -= to correct it for pressure, and then 



* 39.92196 



by to correct it for expansion, by the 



1 + iV X .00375 



increase of temperature. These corrections reduce it 

 to .1495204 grains. Therefore 



1.3752$ GF, 1.37528 X .1495204F, 



g = 30( 1 + .002086.' 33) = 30(1 +. 002086. 5Jl) = 



.0068544 F, 



= 1 +.002086.1^.52 



38. This expression will give the weight, in grains, 

 of the water contained in a cubic inch of vapour, at the 

 temperature I, and under the pressure of 30 inches of 

 mercury. For the purposes of calculation, it may be re- 

 duced to the form, 



3.2859 F f 3.2859 F, 



* = 479-4 +/ 32 = 447.4 +/' 

 To illustrate this formula, let it be required to find 

 the weight of a cubic inch of vapour at 6b of Fahren- 

 heit, under a pressure of 30 inches of mercury. 

 S.2859 F, 3.2859 F M 



g = 44774~+T = 447.4+66 '' 



And if we introduce the value of Fan, which will be 

 found by the Table of the elastic force of vapour to be 

 EM 



_ 3.8859 X. 63795 _ A^". 

 513.4 



Hence a cubic foot of vapour, under the same circum. 

 stances, would contain 7.055 grains of moisture, t 



39. The following Table, calculated from the for. 





mulag = 



.00685+4 F. 



exhibit* the quantity of 



.002086. I 33 

 moisture contained in a cubic inch of vapour, from ze- 

 ro to 100 of Fahrenheit, under a pressure of 30". 



Al S cubic inch of wttn at the temperature of 60 weight 252.176 grains, cubic foot of vapour, and a cubic Inch of water, in 

 Ik* circumstance* Mated, weigh erv nearly the ume. 



f Amarnr* found, in one of hit eipeHmmU, that a cubic foot French of vapour contained, at the temjwrature of 15.1 Heau- 

 wmr. or M.*ll Pabrabrit, a quantity of noiMon equal la weigfct to 1 1.049 grains French. Thii reult, reduced to F.nglith mea- 

 tt. would be T.4M grain* to a cubic foot, differing ery little from tb* quantity determined bj our formula. Tbe difference 

 woold hate been Mill less, if UM temperature bad been uacllj tf. 



OU XI. PART II. 4 D 



