of the interval. The measurement nf these, reihieeil by tlie eliroiio5ia)ili to a 

 linear measurement, was made with a mierosi'iip'' provideil witli a nii'Viniieter 

 eye-piece. 



Having completed our experiments at Tokio, we started tor Sapporo early 

 in the month of Augnst. All the instruments liitlierto used, including tlie two 

 pendulums, the chronograph, the break circuit chronometer, and a portable transit 

 instrument, were carried witii us. The method of experiment having been the 

 same as at Tokio, it is only necessary to specify the position of the observing 

 station at Sajiporo, Through the kindness of Governor Dzusho we were allowed 

 the use of a small transit room belonging to the Geographical Bureau of the 

 Culonization Department. There were two stone pillars in the room, on one of 

 which there was already set up a small transit instrument. Upon the other two 

 additional stone lilocks were laid, from which the pendulums were swung in the 

 manner already described. The position of the pendulum was approximately us 

 follows : — 



Ulitude 43° :]' 54" N. 



Longitude 141° 22' 4" E. 



Height above sea level 21 metres. 



Everything went on smoothly, the nights being clear for transit obser\-ations. 

 Having finished our experiments in the course of a week we immt"'.iately left 

 Sapporo. On our return to Tokio the same series of observations were repeated. 



REDUCTIONS. 



The numerical data of the experiments are given in full in the accompany- 

 ing tiibles. The correction for the reduction to inhnitely small arcs has been 

 calculated from the well known fonniila which, with the usual notation, may be 

 written 



I . , A 



t -- snr ^ • 

 4 2 



A millimeter scale was placed under the pendulum and the extent to which the 



lower end of the pendulum swung was read on this scale at the beginning and at 



the end of each experiment. Tlie mean of these two readings in ni. m. is given 



in tlie 7th column under the heading " Mean Arc." Tlie semi-angle of vibration 



has been computed from this column combined with the length of the pendulum 



below the axis of rotation. The mean total arc of vibration in both the Tokio 



and Sapporo exjieriment« was about one degree and a half. 



The next correction is that depending on the temi>erature of the pendulum. 



The discordance in the coefficients of expansion given by dillerent authorities 



as well iw the didicuity of e.xacliy identifying the quality of the metal on which 



they experimented shows that it would have been deeirablo to determine the 



