404 
MR. BAILY ON THE CORRECTION OF 
I ought however here to mention that the agate planes are not, as in Cap¬ 
tain Sabine’s experiments, screwed to the iron frame, blit are attached to an¬ 
other solid frame (of brass) three quarters of an inch thick, and having three 
foot-screws, for the purpose of levelling the planes. These screws merely rest 
on the iron frame : one of them in a conical hole, another in a groove, and the 
third on the flat surface of the iron frame ; by which means, the same position 
is always preserved, without any strain on the screws. I believe that this 
method (which was suggested by Mr. Troughton,) is as secure as where the 
agate planes are screwed to the frame: and the application of Mr. Hardy’s 
inverted pendulum does not detect the least motion. But this is a question 
that need not here be discussed; since, as I have just stated, the experiments, 
about to be adduced, are only comparative. The weight of this brass frame 
is upwards of seventeen pounds and a quarter troy. 
The usual correction of the number of vibrations for the reduction to a 
vacuum has hitherto been deduced from the relative weights of the air and of 
the pendulum, by means of the following formula*: viz. 
l 13 ' „ l 
S _ i) X /3 [1 +/*(t'-0] X 1 +«(*'-*) 
where N denotes the number of vibrations made by the pendulum in a mean 
solar day, S the specific gravity of the pendulum, <r the specific gravity of air, 
(jj the expansion of mercury, and a the expansion of air for one degree of the 
thermometer, j3' the height of the barometer, t' the temperature of the mer¬ 
cury, i the temperature of the air during the experiments, (3 the height of the 
barometer, and t the temperature of the air, assumed as standards for the spe¬ 
cific gravity. 
If we suppose that the temperature of the mercury in the barometer is the 
same as that of the air surrounding the pendulum, which may generally be 
assumed as the case, in experiments of this kind, without the risk of any per¬ 
ceptible error, the above formula may be rendered more convenient as fol¬ 
lows: viz. 
, XT _ 1 _ £ _1_ 
^ X p X i + (« + p,) (£' — /) 
* See M. Mathieu’s paper on this subject, in the Con. des Terns for 1 826, page 288. 
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