1865.] Pendulum Base Observations for India. 427 



the only change introduced was a very slight one, with the view of obtaining 

 a more correct arc of vibration. 



It is usual to observe the arc a little after the coincidence, which does not 

 give the true arc corresponding to it. To obviate this, the arc was read in 

 our series about 30 seconds before, and again 30 seconds after each observed 

 coincidence, marking first the right edge of the tailpiece and then the left 

 one. If we call these four readings of the scale a, b, c, d, we may consider 



as a very exact representation of the reading for the arc at the instant of 

 the coincidence. 



The adjustment of the diaphragm, disk, and tailpiece was made very 

 carefully at the commencement of the experiments. Nevertheless it was 

 found slightly deranged when the pendulum was reversed. In this case, 

 as is well known, the disappearance and reappearance of the disk are not 

 each instantaneous ; but we see first one side of the disk, then the other 

 disappear, and in the same order reappear, so that we have four events, 

 of which, calling the time of their happening respectively a, /3, y, c>, either 



)> lastly> r 



will give us the time of coincidence. In a few sets of our series the first 

 formula was used ; but it was soon found that the correct registration in 

 such a case is a matter of the greatest difficulty, and it was therefore thought 

 in one instance preferable to stop the clock and repeat the adjustment, and 

 afterwards a similar derangement was rectified by a lateral motion of the 

 observing telescope. With a few trials, using a few successive coincidences 

 for the purpose, it is quite possible to adjust the whole to the greatest 

 nicety without stopping the clock. 



The reduction of the observations was made entirely after the manner of 

 former experimenters. It comprises the following corrections : 



A. Correction of the observed arc-readings and reduction of the vibra- 

 tions to infinitely small arcs. In the first place, the scale for reading the arc 

 being behind the tailpiece of the pendulum, the registered readings are too 

 large. 



Let D be the distance of the scale from the object glass of the telescope, 

 d its distance from the tail of the pendulum, O the observed reading of the 

 whole arc on the scale graduated from end to end, S the distance of 

 the indicating- point of the tailpiece from the knife-edge, then the true arc, 

 or more correctly semiarc observed (=a), through which the pendulum 

 moved from the vertical, is given by the formula 



expressing all distances in inches, into which the scale was divided. 



2 K2 



