Royal Society of London. 365 
On the Reduction to a vacuum of the vibrations of an invariable 
pendulum. 
The first of these contains a set of experiments, made for the pur- 
pose of determining the change in the dip at London, between the 
date of a former set, made by the author in 1821, and the year 
1828. This change is still in diminution, but the decrease is less 
rapid than it formerly was. By comparing the most authentic obser- 
vations, made during the century preceding 1821, the annual decrease 
in the dip appears to have been between 3”.2 and 2.9, while in the 
seven years between 1821 and 1828, it does not exceed 2.5.) . 
In pursuing the investigations with the pendulum in various parts of 
the world, an account of which he has published in a separate form, 
Sabine had come to the conclusion that its vibrations are influenced, 
not merely by the general law of gravitation on the surface of a re- 
volving spheroid, but by local circumstances. .The paper before us. 
affords conclusive evidence, that this opinion was correct... The dif- 
ference of latitude between the house of Mr. Browne, in which Ka- 
ter’s experiments were made, and the Observatory at Greenwich, 
ought to cause a retardation of 0”.15 per day, and the difference of 
level, computing by the method of Dr. Young, a further retardation 
of 0”’.12 per day. Instead of this, an acceleration was found to. 
exist, by observation, of 0”.48, making a result, which differs from 
what would have been anticipated, had no anomalies been known to 
exist, of 0.75. The most important bearing of these experiments, is 
upon the subject of weights and measures. .The British 
has taken as the national standard, the Pendulum of the Latitude of: 
London ; assuming, that the experiments of Kater, in Captain 
Brown’s house, gave its length in all other places under the same 
parallel. These experiments of Sabine shew, that this is premature, 
_and that the law ought to have prescribed as the standard the pendu- 
lum of some particular place. This has been done by the revisers 
of the laws of the State of New York, who have taken as their 
standard, the length of the seconds pendulum, determined in Co- 
lumbia College, by Captain Sabine and Professor Renwick. 
Among the reductions employed in calculating the length of. the 
seconds pendulum from observation, one of the most essential is that 
which depends upon the resisianias of the air. All experiments be- 
ing made in the open tance is a retarding force, 
whose influence is important. All philosophers have hitherto been 
of opinion, that when a body falls through the atmosphere, the force 
which acts upon it may be represented, by — the excess of the. 
