Force of the Earth's Magnetism. 19 



mall arcs. I have taken for this correction the usual formula, 



m/ m/r-, sin. (A. + a )— sin. (A — a) _ , . . . 



T^rri+ oo km /i • x i — ^T". T being the ob- 

 L 32 M. (log. sin. A.— log. sin. a) ' b 



served time of vibration, A and a the commencing and 

 concluding arcs, and T' the time of vibration corrected for the 

 arc. By comparing the corrections given by this formula with 

 the vibrations in different arcs, I have ascertained that it repre- 

 sents, with sufficient approximation, all the differences which 

 are observed to take place. It was my usu il custom to com- 

 mence the registry of the vibration when the arc was at 30°, and 

 to continue it till the arc had diminished to 10°. In such case 

 A =30° and a=10°, and the formula becomes T' a T -f- T . 

 •0065. In some of the repetitions which I have made with the 

 needles in London, I have begun and concluded with smaller 

 arcs ; which exceptions to the usual custom will be expressly 

 noticed in the cases which occur in the following pages. 



I proceed next to consider what should be regarded as the 

 time of vibration of each needle, corresponding to the periods 

 at which observations were made with it in different parts of the 

 world. The times of vibration in London, in 1821, 1823, and 

 1824, uncorrected for temperature and the arcs, are given in 

 the account of the experiments with horizontal needles (Pen- 

 dulum and other Experiments, page 481). The original re- 

 cord of the observations in 1821 and 1823, is still existing, and 

 enables me to supply the necessary corrections, by furnishing a 

 knowledge of the temperature and of the arcs. After the com- 

 pletion of the experiments in 1824, the needles were laid by in 

 pairs, each pair contained in a separate box with opposite poles 

 united, and the boxes tied up together. In this state the 

 needles remained for four years, until 1828, when they were 

 taken out to have the corrections for temperature determined. 

 By collecting in one view the several observations properly cor- 

 rected made with each needle in London, we may readily 

 examine and assign the rate of vibration corresponding to the 

 periods at which the needles were used at foreign stations. 

 Commencing with No. 3, we have in 



1821. October. In the Regent's Park. Th. 55°. Arcs 20° to 5°. Rate 

 165".9 ; + 0".14 reduction to Th. 60°; + 0".41 to infinitely small 

 arcs = 166".4. 



C 2 



