TERRESTRIAL MAGNETIC INTENSITY. 5 



§ 2. Corrections applicable to the Observations. 



11. When the mean of seven values of 100 or of 300 vibrations has been 

 taken, as above explained, a variety of important corrections remain to be ap- 

 plied. 



12. I. Bate of Chronometer. — The following rule due to Professor Hansteen 

 is simple and accurate : — " The logarithm to five decimal places of the observed 

 time is taken, unity is to be added to the fifth decimal place for every two seconds 

 per diem that the watch goes slow ; and unity subtracted for every two seconds that 

 the watch goes fast." The demonstration is too simple to require notice. The 

 following is a table of corrections : — 



Table I. 



Rate -f- C" 



Log. Additive. 



0.00000 



Rate ■ 



_Qsec 



Log. Additiv 

 0.00000 



2 



0.99999 





2 



0.00001 



4 



0.99998 





4 



0.00002 



6 



0.99997 





6 



0.00003 



8 



0.99996 





8 



0.00004 



10 



0.99995 





10 



0.00005 



There is another chronometric correction worth mentioning, arising from the 

 necessarily imperfect division of the seconds' circle of an enamelled dial-plate. In 

 my watch this amounts to a sensible quantity, and has often given an apparent 

 discrepancy to the partial results of a series for which I was not prepared. Upon 

 investigation, I find, however, that the effect upon the mean will always be so in- 

 significant as to be hardly worth notice. 



13. II. Arc. — A correction due to the motion of the magnetic pendulum in cir- 

 cular arcs, cannot be considered as a constant quantity, and therefore not affect- 

 ing relative results, 1. Because the rate of diminution of arc varies considerably 

 in different experiments, and is directly deduced from the observed law of dimi- 

 nution of arc ; and 2. Because we sometimes have to compare observations of 100 

 vibrations having an initial semi-arc of 10", with 300 vibrations beginning at 20°. 

 The latter case having alone been considered by Hansteen, I re-investigated the 

 theory of the correction, and confirmed his numbers. 



14. It is assumed that the arc diminishes geometrically in consequence of re- 

 sistance, the time increasing arithmetically. The best observations I have made, 

 confirm the truth of this general admission. Again, we have to recollect, that, in 

 consequence of the degradation of the arcs, the reduction to infinitely small arcs 

 for the vibrations between the 0th and the 300th, will be greater than between 

 the 10th and 310tli, &c., and that the mean of all the corrections (taking this va- 



