592 



HYGROMETRY. 



Hjrgrome- 

 "? 



Investiga- 

 tion of a 

 formula^for 



h/grometer 



tion, but by reducing the degrees of De Luc's whale- 

 bone hygrometer to the corresponding degrees of the 

 former, by means of the comparative relations of the 

 two instruments laid down in 22. In making the ob- 

 servations, two whalebone hygrometers were employed, 

 and the mean of the degrees which they indicated was 

 taken. This was the more necessary, as they frequent- 

 ly exhibited a difference of 5, though the scales of both 

 had been recently adjusted. In these- circumstances, 

 the coincidence of result is greater perhaps than might 

 have been expected ; and as the best hair hygrometers 

 often deviate several degrees from one another in the 

 same humid medium, the results deduced from the Ta- 

 ble at different temperatures, are probably within the li- 

 mits of the aberrations of different instruments. 



85. The preceding results furnish data sufficiently 

 varied, to determine a general formula for De Luc's hy- 

 grometer, the indications of which are by far too ano- 

 malous to become the subject of rigid analysis. With- 

 out attempting, therefore, any thing like precise inves- 

 tigation, we shall be satisfied with an expression for 

 this instrument, which may apply, with tolerable accu- 

 racy, to the ordinary hygroscopical state of the atmo- 

 sphere. If the degrees of this hygrometer, reckoned 

 from extreme dryness, had the same relation to the 

 whole range of the scale, as the quantity of moisture in 

 a given volume of the medium to which it was exposed, 

 had to the whole quantity of moisture that could be 

 maintained in the vaporous state at the temperature of 

 that medium : then if g were the weight in grains of the 

 moisture in a cubic inch, for the entire tension belong- 

 ing to the temperature of the medium ; g' the corre- 

 sponding weight of moisture for the actual tension : and 

 L the degrees of the instrument, we should evidently 

 have an equation of the form, 



By the solution of these equations, we obtain 'tw =1.6 

 and n = .4 nearly ; and these values of m and n being 

 substituted in the equation 



Hygrome- 



try. 



If 77^. be represented by I, this equation will assume 



1UU 



the form, 



2 / 

 or g'= --^ 



The dilatation of the whalebone, however, is influenced 

 by a law too complex and irregular to be expressed by 

 this simple formula ; and to trace it with sufficient pre- 

 cision, we must at least assume 



the coefficients m and ti being two constant quantities to 

 be determined by two equations, in which the values of 

 g', g, and L are known. 



86. If we employ in this investigation the data fur- 

 nished by the 2d and 5th observations in 84, we ob- 

 tain for the first equation, 



g'=. 00 15692 

 L=38 



and the quantity of moisture in a cubic inch for the en- 

 tire tension of the temperature, 54.4- being (by 39) 

 .0028398 grains, we have also #=.0028398. In like 

 manner, the data of the 5th observation give for the se- 

 cond equation, 



grains. grains. 



g'=,0021334, L=33.1,, and #=.0043693. 

 Hence the formula *=g(()+* ( 



becomes .0015692=.0028398 (.38 m + .38' n), 

 and .0021334-.0043693 (.331 m + .331' n) ; 



or, 



.55257 = .38 m + .1444 n, 

 and .48827 = .331 m + .10956. 



This formula being applied to the degrees of De Luc's 

 hygrometer, in the third observation, in which I was 

 .35 ; the temperature of the air 60, and consequently 

 (by ? 39.) g was .00338832, we obtain 



2 I -70 



g*= (4 I) g = y X 4 .35 X .00338832= 



grains. 



= .14 X 3.65 X .00338832 = .0017314. 

 This result differs so little from the quantity of mois- 

 ture in a cubic inch of the air, as deduced in the same 

 circumstances, both by our formula for a thermometer 

 with a moistened bulb, and by Blot's Table for Saus- 

 sure's hygrometer, that we have no hesitation in adopt- 

 ing the formula, under the restrictions which we for- 

 merly mentioned. It is proper to add, that the point of 

 extreme moisture was fixed, in the instruments with 

 which the observations were made, by immersing them 

 for six hours in pure water ; and that the point of ex- 

 treme dryness was determined by inclosing them for 

 several days in a receiver at the temperature of 50, 

 with a considerable quantity of sulphuric atid, the spe- 

 cific gravity of which was 1.84435. 



87. According to the formula which we have dedu- 

 ced for De Luc's hygrometer, the instrument ought 

 to indicate extreme humidity in the gaseous medium to 

 which it is exposed, before it reaches the point marked 

 100 on the scale; for if g, and g' be equal to each 

 other, (which will be the case at complete saturation,) 



and if, at the same time, (4 /) be represented by 







unity, we shall have 



Therefore I = .7753, and L = 77.53. 

 Hence we may infer, that the division marked 77.5 

 corresponds to the extreme range of the whale-bone 

 hygrometer, in so far as the expansions of the instru- 

 ment are effected by mere vapour. This conclusion ac- 

 cords remarkably well with the observations of Saus- 

 sure, who inferred, from numerous experiments with 

 this instrument, that the 80th or 8 1st degree of De 

 Luc's scale, corresponds to the term of saturation, or 

 extreme humidity; and that all the divisions above 

 these points measured, not the quantity of moisture in 

 the vaporous state, but the quantity of water which 

 had combined with the whale-bone, after it had been 

 condensed on its surface. 



2 I 



88. By substituting in the expression (4 I), the 



5 



value of I for every 5 from zero to 77 P .5, we obtain 

 the relative tensions of vapour for the following divi- 

 sions of De Luc's scale : 



p ; n t / 



extreme ha- 



Table for 

 De Luc's 

 hygrometer. 



