292 On the Elastic Force of the Vapor of Mercury. 



a, Z>, c, fyc. coefficients to be determined by experiment, is of the 

 form, log. e=log. A+at+bt 2 +ct*+&c. 



Taking the terms containing the first three powers of t to deter- 

 mine the value of log. e, I have deduced a formula for the tension of 

 mercurial vapor, which gives results in accordance with the experi- 

 ments of Faraday. 



I assume as before, an atmosphere of 29.94 inches of mercury, 

 as unity of tension, and 100° Fah. reckoned from the boiling point 

 of mercury, as unity of temperature, t representing the number of 

 these units; but in order to avoid the changes of sign for the different 

 powers of tf, I consider t positive below the boiling point of mercu- 

 ry. The formula just given, neglecting the terms containing powers 

 of t above the third, and observing that log. 1=0, becomes, log. e 



at-\-bt 2 -\-ct 2 . The seven observations already given, between 

 446° F. and 554° F.* would furnish seven equations of this form, 

 which combined by the method of least squares would give the most 

 probable values of the coefficients determined from all the experi- 

 ments. I have not considered such a proceeding to be necessary, 

 but have taken the two extreme observations, and an intermediate 

 one, viz. that at 500° F.f to give three equations by which to de- 

 termine the coefficients. By the aid of logarithmic tables, I find 

 a = — 0.35909, 6 =+0.023443, c= -0.031644 The formula, 

 therefore, is, log. e = — 0.35909^+0.023443 t 2 -0.03164* 3 . 



The tensions calculated by this formula agree within one or two 

 twenty filths of an inch (.04 to .08 in.) of those observed ; the differ- 

 ences being within the limits of errors of observation. The value 

 of e given by this formula does not become zero at any temperature; 

 neither does the formula show any minimum of tension, for the equation 

 corresponding to that supposition would be— 0.35909 -f-0.023443.2i 



0.03164. 3^ 2 =0, which has none but imaginary roots. The ten- 

 sions according to this formula, should decrease with the diminu- 

 tion of temperature, and, become insensible, though never mathe- 

 matically nothing. If, for example, we determine from the formu- 

 la the tension of mercurial vapor at the melting point of ice, we find 

 e=0.00000000011208 atmospheres, or 0.00000000335 inches, a 

 quantity altogether inappreciable. Faraday's observation that mercury 

 is not vaporized at temperatures below 32° Fah. cannot be consider- 



♦ 230* and 290° C. t 260° C. 



t In the Centigrade thermometer, a = — 0.64637, &=+0.075956, c= — 0.18452 



