o — 



EEDÜCTION. 



The method of calculation was similar to that used in the previous 

 expedition. The complete numerical data are arranged in tables at the end 

 of the paper. 



The correction for arc rras deduced from Captain Basevi's formula* 



Correction 



= - ^{(^+ ßy--u^- ßr-}> 



in whicli t is the observed time of oscillation, and a and /3 arc respectively 

 the initial and the final semi-arcs of the corresponding set of oscillations. 



In making the temperature correction, we assumed the value of the 

 coefficient of expansion to be 0.0000187 per degree centigrade, which is a fair 

 average of the determinations hitherto made on brass. From want of time 

 and also from other considerations the direct measurement of the coefficient of 

 expansion could not be made ; but in all probability the error arising from 

 any inaccuracy in the value of the expansion coefficient must be very small. 



The correction fur temperature was applied so as to reduce the observed 

 time of oscillation to the time of oscillation at 25° C. This temperature is a 

 convenient one as being approximately the average temperature for all the 

 experiments at Tokio, Kagoshima and Naha. 



If AT is the difference between the actual temperature and 25", and 

 f the observed time of oscillation, the necessary correction as calculated from 

 llio expression 



i t a AT 

 is very nearly 



-^ AT = 0.00000935 AT 

 as t differs very slightly from unity. 



The chronometer correction was calculated from the mean daily rate, any 

 slight error so arising being minimised over the whole series of observations 

 by a suitable distribution in time of the different sets of pendulum observations. 

 In cases of bad weathers, the determination of the average rate for two or 

 three days only was possible. This was not of course very good: but in tlio 

 long run individual errors would probab'y balance. It may be remarked tlint 

 the chronometer was carefully protected and carefully managed, and its rate 

 in any one locality tolerably uniform. 



The corrections due to the buoyancy and the resistance of air have 

 been neglected, as was the case in the reduction of results in the previous 

 expeditions. t 



• nic (iroat Trijjoiioinclriiil Siirvry of Iiidi.i, veil. V. 

 t St'o iiifiiiiiir 5 ami al.-io iU u[i|H!ii(lii(. 



