436 
MR. BAILY ON THE CORRECTION OF 
ascertained only by actual experiment. I fear therefore that, in deducing the 
true figure of the earth from pendulum experiments hitherto made, we can 
compare together only those experiments which are made with precisely the 
same hind of pendulums. 
If we examine the new correction for the Mercurial clock pendulum, which 
is the pendulum now generally adopted for astronomical purposes, we shall 
find that a difference of one inch pressure of the atmosphere should produce 
an alteration, in the daily rate of the clock, equal to 0 S ,414; which is more 
than double the quantity hitherto assumed as depending on the change of the 
barometer; and which therefore can no longer be overlooked by the astro¬ 
nomer. In order to obviate this effect of a variation in the atmospheric pres¬ 
sure on the rate of the clock at the Observatory at Armagh, Dr. Robinson has 
recently attached a syphon barometer to the rod of the mercurial pendulum, 
so placed that the variations in the height of the column of mercury in the 
barometer may exactly compensate the effect produced by the change of 
atmospheric pressure. Mr. Davies Gilbert, in the Supplement to a paper 
inserted in the Quarterly Journal, vol. xv. has shown that the same compen¬ 
sating effect may be produced by a proper selection of the arc of vibration: 
since the effect produced by the difference of density in the atmosphere will, 
in such case, be exactly counterbalanced by the effect arising from the differ¬ 
ence in the arc of vibration caused by such difference of density. And pro¬ 
ceeding agreeably to the formula which he has there given for finding the 
value of such arc, and on the assumption of the accuracy of the new cor¬ 
rection above mentioned, I find that the value of the required arc should be 
2° 45' on each side of the vertical line, or a total arc of 5^ degrees. I believe 
that the semi arc of vibration, in astronomical clocks, is seldom more than 
2 degrees; which produces only one half of the compensating effect above 
alluded to: so that (assuming Mr. Gilbert’s theory to be correct,) there still 
remains an effect on the daily rate of the mercurial clock, by a difference of 
one inch pressure of the atmosphere, of more than T e oths of a second; which 
corresponds with the recent determinations of Dr. Robinson from observations 
made expressly for that purpose *. The attention of astronomers will probably 
in future be more particularly directed to this subject. 
The values in the last column of the Table, denoting the weight of air 
* See the Memoirs of the Royal Astronomical Society, vol. v. p. 125. 
