MR. BAILY’S DESCRIPTION OF A NEW BAROMETER. 
433 
satisfactory method to compare them together, if possible, on the same spot, more 
especially where great accuracy is required*. 
The correction for the temperature of the mercury is by far the most important, since 
it is in most cases more than ten times the amount of the correction for the expan- 
sion of the scale. The correction, for both these sources of discordance and error, 
may be reduced to one general expression by the following well-known formula : viz. 
, m (t — 32) — s (t — 62) 
^ 1 + m (t — 32) 
where h denotes the observed height, as read off from the scale, which represents En- 
glish standard inches when at the temperature of 62° Fahr., m the expansion of mer- 
cury in volume, and s the expansion of the scale in length, for 1° Fahr. : t denoting 
the temperature of the mercury and the scale, which are supposed to be the same, and 
to be ascertained by the thermometer that dips into the cistern of mercury ; the slight 
dilference which may exist in the temperature of the scale making no perceptible 
difference in the results. 
According to the accurate experiments of MM. Dulong and Petit, it appears that 
mercury expands in volume (=*000100100) for each degree of Fahrenheit’s 
thermometer : and, with respect to the linear expansion of brass (of which the present 
scale is made) we may assume it to be *000010434 for each degree of Fahrenheit. 
Consequently the above formula becomes 
, % > -0001001 ( t — 32) — -000010434 ( t — 62) 
“ h X 1 + -0001001 (t — 32) 
which, by proper reduction, becomes 
•000089566 t — -002553092 
h X -0001001 t + -9967968 
This expression may be easily formed into a table of double entry, which would be 
very convenient for correcting the observed heights of the barometer. And it is agree- 
ably to this formula that Professor Schumacher has constructed the tables which are 
printed in the first volume of his Astronomische Hiilfstqfeln, showing the correction 
for every difference of half an inch in the height of the mercury, from 27^ to 31 inches; 
and for every degree of Fahrenheit from 6° to 88°, to four places of decimals. These 
tables, having been afterwards slightly corrected, were (together with some others) 
printed on a separate sheet, and distributed with No. 114 of his Astronomische Nach- 
richten. They have been recently much enlarged by the distinguished author ; and 
* In one of my barometers, the tube of which is about a quarter of an inch in diameter, the mercury has 
generally stood about a quarter of an inch lower than that of a standard barometer placed by its side, after every 
correction made for capillarity and temperature, and after a careful examination of the scale. I satisfied myself 
that there was no air in the tube ; having had it re-filled with mercury for the express purpose of determining 
that point, and having also placed it by the side of other excellent standards, and always with the same results. 
This anomaly, I have since been informed, is by no means rare, and shows the necessity of direct comparison of 
such barometers with standard ones. Mr. Newman however conceiving that the imperfection arose from 
vapour, has remedied it by drying and wiping out the tube and filling it again with heated mercury. 
