426 An Account of Experiments for determining the Length of 
The length then of the pendulum vibrating seconds in vacuo at 
the level of the sea, measured at the temperature of 62° of Fah- 
renheit, appears to be Inches. 
By Sir G. Shuckburgh’s standard ..  39:13860 
By General.Roy’s scale oy icc/sielyienls o BINS. 
By Bird’s Parliamentary standard -. 39°13842 
the latitude of the place of observation being 
51° 31’ 8-4 north*. 
An objection might be urged against the use of the knife edge, 
on the ground that being an elastic substance it may possibly 
suffer temporary compression, and thus perhaps introduce a . 
source of error. In order to meet any doubt that might arise on 
this important part of the subject, it is my intention to com- 
mence &# series of experiments with a pendulum of the same 
construction as that which has been described, but vibrating on 
cylinders instead of knife edges, and I trust soon to have the ho- 
nour of laying the result before the Royal Society. 
London, July, 1817. 
APPENDIX. 
Since the preceding paper was written, a very curious and im- 
portant theorem has been discovered by M. Laplace, of which 
Dr. Young has favoured me with a concise demonstration, to- 
gether with some other investigations, which I shall subjoin in 
his own words. 
‘¢ My dear sir, — I cannot forbear to congratulate you on the 
discovery of the singular property of your pendulum, which has 
lately been demonstrated by M. Laplace, since it appears to re- 
move the only doubt, that could reasonably be entertained, of 
the extreme accuracy of the results of your experiments. The 
correction for the curvature of the rolling surfaces, in the case of 
a simple pendulum, is very easily obtained from the geometrical 
determination of the curve described, although M. Laplace’s train 
of reasoning, from mechanical principles, is somewhat too ela- 
borate to be readily followed through all the symbols in which it 
is enveloped : and the same geometrical considerations appear, at 
first sight, to be equally applicable to the case of compound pen- 
dulums in general, since the motions of all their effective parts 
are concentric with those of a simple one similarly suspended. 
* The latitude was deduced from the data contained in the trigonome- 
trical survey; Mr. Browne’s house bearing from Portland Chapel 74° 38° 50’ 
west from the north, the distance being 283 feet. This differs only 0/"} 
from the latitude determined by Mr. Browne froma great number of obser- 
vations, 
But 
