428 Pendulum Base Observations for India. [1865. 



The values of t ~- were determined for each pendulum from accurate 



measurements, and are 



9874 



For pendulum No. 4 in position, face on =- 

 face off = 



No. 1821 face on = 



face off = 



2 X 100-22 x 49-89 



99-67 

 2x100-22x49-89 



99-47 

 2x100-22x49-3 



98-95 



2x100-22x49-3 



The logarithms of these expressions were added to those of the observed 

 readings for the logarithm of the tangent of a. 



In the next place, the reduction to infinitely small arcs was deduced from 

 the well-known formula, 



Number of infinitely small vibrations =n + n x M S '" (a + a>) sm (*."*? *, 



32 (log sm a log sin ) 



where M denotes the logarithmic modulus =0-4342945 ; * the initial, and 

 ' the final semiarc of vibration, expressed in degrees, minutes, and seconds, 

 n being the number of observed vibrations ; and to obtain a more correct 

 result from this formula, the calculation was made/or each interval between 

 two successive observations. 



B. The rate of the clock was determined from a series of observations 

 of star-transits, the results of which are given in Table I. The rate was 

 somewhat unequal during the experiments, the range being equal to T %ths 

 of a second ; and besides, the unfavourable state of the weather occasioned 

 longer intervals between the observations than was desirable. To free the 

 results as far as possible from any errors arising from this source, the rates 

 were represented in a series, as shown in Table II., which also gives the 

 actual number of vibrations made by the sidereal clock in a mean solar 

 day, as deduced from the following formula : 



Number of vibrations in a mean solar day =N r =86636-5554( 1 r \ 



\ b0400/ 



where r is the observed rate, which in our case was a losing one throughout 

 the whole of the observations. 



If we now call V the number of observed vibrations of the clock -pen- 

 dulum from beginning to the end of one experiment, V the number of 

 observed vibrations of the detached pendulum during the same time, cor- 

 rected for the amplitude of the arc, and finally N' the number of actual 

 vibrations of the clock in a mean solar day at the date of the experiment, 

 found as above, we have for the number of infinitely small vibrations of 



* See Memoirs of the Royal Astronomical Society, yol. vii. p. 22. 



