59 



the motion of the table. When placed near the edge of 

 the table, so as to be conveyed throngh the circvunfevence 

 of a circle, the plane of the disc is always parallel to its 

 first position, for the reason stated in (1). If it Avere 

 placed in the centre of a circle at the pole of the earth, 

 the plane of the disc would appear to move round a 

 vertical axis in twenty-four hours. This property of 

 maintaining the plane of rotation unchanged has been 

 proposed as a means of proving experimentally the rotation 

 of the earth on its axis. If the instrument be placed at 

 any point between the pole and the equator, the time of 

 an apparent revolution round a vertical axis will be more 

 than twenty-four hoiirs, and the time is greater the nearer 

 it approaches to the equator. When at the equator it will 

 not move round the vertical axis at all. 



In order to explain this satisfactorily, it is necessary to 

 state what is meant by saying that the revolving disc 

 maintains its plane of rotation unchanged. The plane of 

 rotation is not absolutely unchangeable, since it alwa^-s 

 coincides with a great circle of the earth (when clamped 

 as described) passing through the station, and therefore 

 it partakes of the diurnal motion of the earth, except when 

 situated at one of the poles. 



Let A (Fig. 11) be the station, and let it be carried through 

 the small arc AB by the diurnal motion of the earth, the 

 plane of rotation of the disc at the point B, is not BY, which 

 is a small circle, but BDV, a great circle intersecting the 

 great circle APV in two points W, diametrically apposite. 



Since APV = 90°, and AP is the distance of A from the 

 pole P, therefore PV = latitude of A. And when the arc 

 AB is very small, BDV = APV = 90°. Hence, in the 

 spherical triangle VPB, (Fig. 4.) 



Sin VPB : sin PBV = sin VB : sin VP. 

 or Sin p : sin = R : sin lat. 

 or Arc ab : arc c d = 1 : sin lat. 



