212 PHILOSOPHICAL TRANSACTIONS. [aNNO]777. 



inch, for the effect of the expansion of the glass for 1° on a column of 30 

 inches; this added to the quantity before found, which was only tlie excess of 

 the greater expansion above the less, gives for the true ecjuation for each degree 

 0.00304 inch when the barometer stands at 30 inches.* Mr. De Luc's correc- 

 tion in this case was 0.003 12; a difference so small that I shall take no notice of 

 it as to its influence on our observations. It may deserve a remark here, that this 

 equation, rigorously taken, is variable according to the height of the thermo- 

 meter; for J°, which at freezing is = Trrg- ^^ the whole volume, at the tem- 

 perature 82° becomes -g-gVrj ^ difference indeed that may fairly be neglected^ 

 and which I neglect myself; yet I cannot help observing, in justice to Mr. De 

 Luc, that his method of reducing his barometers always to the same standard 

 temperature was free from the error I am speaking of. 



To conclude, the defect of Mr. De Luc's rules being supposed -j-«-|4^-, or 

 which comes to the same thing, the correction being -f- t-H-bt-o > when the tem- 

 perature of the air is 6l°.4, and the true expansion of the air for each degree 

 being , ^''/ J'^ ^. when the heat is 39°.7 ; required to find the temperature in which 

 the difference of the logarithms shall give the true height in English fathoms, 

 that temperature, according to Mr. De Luc, being 39°.74, and the expansion 



1 0* 



Let T be the temperature 6l°.4; s Mr. De Luc's standard temperature; e the 

 expansion for 1°; e the same, according to Mr. De Luc; a the supposed cor 

 rection of the rules, and x the temperature sought. We have then the following 

 formula, v^ — sj x (e — e)t— * ;_ g — ^ . hence, proceeding with the above 



E 



numbers, s — x comes out 8°.50, and consequently x = 31°.24:}: the tempera- 

 ture required; which, if it should be thought convenient, may be considered 

 as the freezing point. 



In the whole of the above inquiry I have taken no notice of the effect of 



* It has been suspected, and I believe will appear from very good obser\'ations, which however 

 I never made myself, that tlie expansion of quicksilver in the barometer is not directly as the heat 

 shown by die thermometer, but in a ratio something different, owing to some of the quicksilver being 

 converted into an elastic vapour in tlie vacuum that takes place at the top of tlie Torricellian tube, 

 which presses on the columns of quicksilver, and thus counteracts in a small degree the expansion 

 from heat. It does not however appear to be a considerable quantity, not amounting to above a l6'th 

 of the whole expansion in a range of 4(1" of temperature ; I shall tlieiefore venmre to consider this 

 equation as truly uniform, since the error on 1000 feet would not amount to 5. — Orig. 



•J- This sign is negative, because the assumed expansion e is less than the true one e, and con- 

 sequently tended to increase the apparent error of the rules ; had it been greater, a would have 

 been + . — Orig. 



J Very nearly the same conclusion has been since found, in a very easy and simple manner, by 

 one observation only, viz. of the whole pressure of the atmosphere at the surface of die eardi. See 

 Dr. Hutton's Dictionary published in IZp/i, art. atmosphere 5 ;dso his course of mathematics, vol. 2, 

 p. 235, first published in 17y8. 



