274 



REPORT — 1898. 



rest. Sometimes the motion goes on for three or four houi-s after the 

 initial disturbance, usually much less. I can offer no explanation of these 

 anomalies. I merely mention them here to show that the amount of 

 material at my disposal is not so great as I could wish : that a much 

 longer time is necessary to remove the instrumental and systematic errors, 

 and that the present result is a preliminary inquiry now offered to show 

 what use has been made of the instrument entrusted to my care. 



However distrustful one may be of the result, and however cautiously 

 one may feel it necessary to speak of the numerical values obtained, it is 

 impossible to doubt the general character of the motion of the mirror, 

 notwithstanding the small angles M'ith which we have to deal. A mere 

 glance at the record for any one day is sufficient to show the general 

 features of the curve, and herein I believe the motion in the pi-ime vertical 

 agrees with that derived from meridional displacement, though to what 

 extent the motion precedes or follows that on the meridian I have no data 

 to offer. On all days on which the photographic trace has offered no 

 suspicion of unsteadiness in the scale value, or where no interruption of 

 the trace has been made for more than twenty-four hours, the ordinates 

 of the curve have been measured from the time traced for each hour. 

 These ordinates have been read off to the tenth of a millimetre, corre- 

 sponding usually to about 0-004 of a second of arc, consequently the third 

 place of decimals has been retained, but simply as a matter of calculation. 

 These measures have been grouped in monthly periods, for it was soon 

 apparent that the time of maximum displacement was not constant 

 throughout the year. The mean values of the ordinates for each month 

 have been compared with Bessel's Interpolation Equation for expressing in 

 the usual periodic formulfe the reading at any hour of the day, reckoned 

 from noon, in terms of the mean value and the hour of the day. Sup- 

 posing the general expression for the value of the measured ordinates at 



the hour after noon to be represented by the formula 



D.c=I) + a sin(a;+A)-l-i sin(2a; + B)-f c sin(3.?; + C), 



the following table will give the value of the constants D, a, b, c, A, B, C, 

 derived from the solution of the equations formed by the substitution of 

 the mean monthly ordinates for every two hours in the general 

 expression : — 



Table I. 



The principal maximum values, both positive and negative, for each 

 month as derived from the forementioned equation are as follows : — 



