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 difr 

 ference of latitude between the house of Mr. Browne, in which Ra- 

 ter's experiments were made, and the Observatory at Greenwich, 

 ought to cause a retardation of 0'M5 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 parliament 

 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 takeu 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 resistance of the air. All experiments be- 

 ing made in the open atmosphere, this resistance is a retarding force, 

 whose influence is im.portant. 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 dividing, the excess of the 



