490 Messrs. Stewart and Loewy on the true [June 17, 



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

 tions to infinitely small arcs. 



"We have previously shown that if 



D = distance of scale from the object-glass of the telescope, 



^—distance of scale from the tailpiece of the pendulum, 



0= observed scale-reading for the whole arc of vibration, 



S= distance of indicating-point of the tailpiece from the knife-edge, 



a = true semiarc of vibration, 



. O(D-rf) 

 then tan «= , 



expressing all distances in inches into which the scale is divided. 



In our case repeated measurements gave the following mean values for 

 these quantities : — 



D= 101-86 inches ; d=0'56 inch ; S=47'55 inches. 



Hencewehave to add log(^)=log ( 2 x J* 47 . 55 ) =2-0194252 



to the logarithm of the observed scale-readings to obtain the semiarc of 

 vibration. 



For the reduction to infinitely small arcs, we have again used the well- 

 known formula number of infinitely small vibrations 



M sin (a + a) sin (a — a') 

 — n + n. 22 ^ g gm a _l g si Q a 'y 



the symbols having the same meaning as previously stated. 



We are well aware that more convenient formulae, and more correct 

 methods, have been used or proposed by different observers for this cor- 

 rection ; but we thought it best to adhere to a uniform method in the 

 reductions, in order to facilitate any future rediscussion of our original 

 observations (which are preserved at the Kew Observatory), should such 

 appear desirable when the results of the Indian pendulum observations 

 will be published. 



B. The precise determination of the rate of the clock might have been of 

 minor importance in our experiments, an approximate uniformity of rate 

 being the chief desideratum. We expected, however, that very small dif- 

 ferences in the number of vibrations would result in those experiments 

 where the pressure differed only by an inch or even less. We considered 

 it hence of the utmost value to have a precise record of the behaviour of 

 the clock during these experiments, so as to discover at once changes in 

 the rate, and to make our reductions depending on it for each experiment. 

 A great number of transit-observations were accordingly made, and during 

 these not only the pendulum-clock, but also the behaviour of a chronometer 

 by Dent and a meantime-clock by Shelton was accurately determined. 

 These two latter served during those days when no transits could be ob- 

 tained for deducing the rate of the pendulum-clock by intercomparison. 

 From the whole of these observations the following Table of the number 

 of vibrations during a mean solar day has been calculated for every day of 



