MR. BAILY’S DESCRIPTION OF A NEW BAROMETER. 
437 
wholly imperceptible ; or at all events now inappreciable, since we are not informed 
at what temperature the relative measures were ascertained. The true formula for 
the correction of the expansion of the mercury alone is 
, m (t — 3C) 
A y — 
A 1 + m (t - 32) 
where m denotes, as in page 433, the absolute expansion of mercury for 1° Fahr. 
(= -0001001), and not the apparent expansion (= -0000857339) as assumed in the 
table above mentioned*. 
Besides this correction, there is another, which is peculiar to Mr. Daniel’s mode of 
constructing this barometer, and which is called the correction for the capacity of the 
cistern. As the height of the mercury in the cistern is constantly varying with the 
variation in the height of the mercury in the tube, it is necessary that the relative 
capacity, or contents, of the volume of the cistern and the tube should be determined ; 
as also some fixed point on the scale, as the zero of comparison. This has been done 
with great care by Mr. Daniel ; and the capacity of the cistern has been determined 
to be exactly --^th part of the capacity of the tube, and the neutral point fixed at 
30-576 inches-f-. So that the correction for capacity is 
30-576 — h 
“• Too 
The diameter of the tube is -530 inch : the correction for capillary attraction is 
therefore, by Laplace’s formula, + ‘006 ; and this is the value that is engraved on 
the front of the barometer case. 
The whole of the corrections therefore for Mr. Daniel’s barometer will be as fol- 
lows^: 
. _ -000100 1 {t — 32) 30-576 - h 
— h X i _j_ *0001001 (t - 32) ' fed •" ’ 006 
There is a short brass scale, of about 4 or 5 inches, on which the divisions are cut : 
but the expansion of this would, in no possible case, cause an error of more than an 
unit in the third place of decimals : and as it is screwed to the wooden frame, which is 
* The absolute expansion of a liquid is that which is independent of the form, or expansion, of the vessel 
that contains it : the apparent expansion is obtained by deducting 3 times the linear expansion of the contain- 
ing vessel. Thus, the absolute expansion of mercury being ‘0001001, and the linear expansion of glass being 
•0000047887, we have ‘0001001 — ‘0000143661 = ‘0000857339 for the apparent expansion of the mercury. 
See my Paper on this subject in the Memoirs of the Astron. Soc. vol. i. page 383. 
f Fifty inches, measured in the upper part of the tube before it was sealed, raised the float in the cistern 
exactly half an inch. 
X Amongst the tables, separately printed and distributed with No. 114 of the Astron. Nach. by Professor 
Schumacher (as already mentioned in page 433), there is one showing the value of that part of the expression 
in the text which is denoted by — h x 
•0001001 (t — 32) 
-, for every ^ inch from 27| to 31 inches; and 
1 + -0001001 (t - 32) 
for every degree of Fahrenheit from 6° to 88°. And this is the table that should be used for barometers of 
the ordinary construction, not furnished with a brass scale extending the whole length of the tube. But I am 
not aware that any such table has been published in this country. 
3 l 2 
