H Y G R O M E T R Y. 



575 



ne- 46. When the instrument i< intended to be portable, 

 Mr Leslie prefers the form delineated in Fig. 9. The 



ohe two baN*' b*-'> n K ' n tne san 16 perpendicular line, are 

 elt* protected from injury by a case of wood or ivory ; and 

 the instrument may thus be transported from one place 

 to another with perfect safety. We shall conclude our 

 nVncniiliiin ot'tlm simple but ingenious instrument, by 

 remarking, that an ordinary thermometer, having its 

 bulb covered with moisteiK-d paper, gives the same in- 

 dications, if its temperature be subtracted from the tern* 

 perature of the air determined by a naked thermome- 

 ter, placed in similar circumstances with the other. 



Relation betmeen the Indication* of Hygrometers, and 

 the absolute Quantities of Moisture in Vapour. 



27. Having thus described the construction of the 

 various kinds of hygrometers which have hitherto been 

 employed, we shall now proceed to investigate the re- 

 lation subsisting between the indications of these in- 

 struments, and the absolute quantities of moisture ex- 

 isting in a given volume of the medium to which they 

 are exposed. To enable us to prosecute the subject 

 with sufficient precision, it will be necessary, in the 

 first place, to take a concise view of the qu mtity of va- 

 pour contained in a vacuum at different te nperature* ; 

 and, secondly, of the quantity of it which can exist, in 

 the same circumstances, un<l< r different pressure*, in 

 mixture with air. The experiments of Mr Dalton on 

 the elasticity of steam at various temperatures, together 

 with the recent researches of Gay Luuac, will enable 

 us to solve both these problems with the most perfect 

 precision. 



28. Mr Dalton has given a table, containing the re- 

 sults of his ad > nerimrnts on the force of steam 

 for every degree of Fahrenheit's thermometer, from zero 

 to 325, from which Biot has deduced the following 

 Table, adapted to the centigrade scale. 



29. The first column of this Table contains the tem- 

 perature, in da,Ttei of the centigrade scale, at the in- 

 terval of 61 degrees ; ' the second, the elastic force of 

 vapour in English inches; and the third, the relation 

 in which each term of the elastic force stand* to the one 

 immediately above it. It is obvious, that if the same 

 relation subsisted between the terms, in successive or- 

 der, the number* in the third column would form a 

 i of quantities in geometrical progression, the first 



term of which would be .2, and the last SO. The Hrgroin*- 

 terms, however, continually decrease in a slow and re- _,"*' _. 

 gular manner, as the temperature increases, and there- 

 fore the elastic force of vapour cannot proceed in a geo- 

 metrical series. In order to obtain a general expres- 

 sion for the law of its increase, Biot assumes that the 

 ratio of the terms is constant, and equal to k ; then call- 

 ing F. the elastic force, corresponding to the tempera- 

 ture 100 n, 



F = SO, 



F,=30*', 



And, in general, F m = 30 A". 



Hence, Log.F.= Log. 30 + n Log.L 



The supposition, on which this expression is founded, 

 though not rigidly true, will lead to results sufficiently 

 conformable to experiment to justify us in adopting it. 

 The quantity n, Log. *, may be exhibited by a succes- 

 sion of terms of the form a + 6n' + cn'+ &c. and 

 the expression then becomes, 



the co-efficients a, b, c being constant, and determina- 

 ble from three equations in which F, is given, and con- 

 sequently n. It is unnecessary to tnke more than three 

 terms of the series, as the co-efficients of the powers of 

 n will be found to diminish much faster than the power* 

 themselves increase. To determine the co-efficients a, 

 6, and e, Biot employs the elastic force of vapour for 

 the temperatures 25, 50 and 75, reckoned downwards 

 from the boiling point ; thu, we have, 



= 25 F,,= 11.25, 



, = 50 F, = S..6, 



= F,,= .91. 



And, Log. F,,= Log. 30 + 25o+ 6256+ 15625,:, 

 Log. F, = Log. 30 + 50a + 25006 + l25000e, 

 Log. F,,= Log. 30 + 75a + 5625 6 + 421875c. 



Substituting the values of Log. F. and Log. 30, and 

 transposing, 



25+ 6256+ 15625c = .42596S7, 

 50a + 25006+ I25000c= .9330519. 

 75 a + 56256 + 421875 c= 1.5180799. 



The solution of these equations gives, 



a = .013741955, 

 = .000067427, 

 e = + .0000000338. 



30. The values of a, I, and r, thus determined, being 

 substituted for these quantities, in the general equation, 

 we obtain the following formula for the elastic force of 

 steam at the temperature 100 n. 



Log. F.= Log. SO .013741955 n 000067 127 ' + 



.000000033S . 



31. If n be expressed in degrees of Fahrenheit's scale. Formula 

 the elastic force of vapour for the temperature 212 n ' or lllt 



rihrciuiciu 



Log. F.= Log. 30 .00854122 00002081 '+ ed to th. 

 .0000000058 J . 



By help of this formula, we have calculated the follow- 

 ing Table of the elastic force of steam, from zero to 

 100 of Fahrenheit, which includes the ordinary range 

 of natural temperature. We have also annexed a co- 

 lumn, exhibiting the elastic force of vapour, for the 

 same range of temperature, as determined by Mr Dal- 



