626 report— 1884. 



when, the framework is held with the axis of the flywheel and the line of knife 

 edges hoth horizontal, and the knife edges downwards in proper position for 

 performing their function. The apparatus, when supported on its knife edges with 

 the flywheel not spinning, may be dealt with as the beam of an ordinary balance. 

 Let now the framework bear two small knife edges, or knife-edged holes, like those 

 of the beam of an ordinary balance, giving bearing points for weights in a line, cutting 

 the line of the knife edges as nearly as possible, and of course (unless there is reason 

 to the contrary in the shape of the framework) approximately perpendicular to 

 this line, and, for convenience of putting on and off weights, hang, as in an ordinary 

 "balance, two very light pans by hooks on these edges in the usual way. Now, 

 with the flywheel not running, adjust by weights in the pans if necessary, so that 

 the framework rests in equilibrium in a certain marked position, with the axis of 

 rotation inclined slightly to the horizontal in order that the axis of the flywheel, 

 whether spinning or at rest, may always slip down so as to press on one and not 

 on the other of the two end plates belonging to its two ends. Now, unhook the 

 pans and take away the gyrostat and spin it ; replace it on its knife edges, hang 

 on the two pans, and find the weight required to balance it in the marked position 

 with the flywheel now rotating rapidly. This weight, by an obvious formula 

 which w 7 as placed before the Section at Southport, gives an accurate measure of 

 the vertical component of the earth's rotation. 1 



Gtrostatic Model of the Dipping Needle. 



I also showed at Southport that the gyrostatic balance described above, If 

 modified by fixing the knife edges, with their line passing as accurately as possible 

 through the centre of gravity of the flywheel and framework, and with the faces 

 of the knives so placed that they shall perform their function p-operly when ih 

 axis of the flywheel is parallel to the earth's axis of rotation, and the rotation of 

 the flywheel in the same direction as the earth's, will act just as does an ordjriarj 

 magnetic dipping needle; but showing latitude instead of dip, and dipping the 

 South end of the axis downwards instead of the end that is towards the North, as- 

 does the magnetic dipping needle. Thus, if the bearing of the knife edges be placed 

 East and West, the gyrostat will balance with its axis parallel to the earth's axis, 

 and therefore dipping with its South end downwards in northern latitudes and its 

 North end downwards in southern latitudes. If displaced from this position and 

 left to itself, it will oscillate according to precisely the same law as that by which 

 the magnetic needle oscillates. 



If the bearings be turned round in azimuth the position of equilibrium will 

 follow the same law as does that of a magnetic dipping needle similarly dealt with. 

 Thus, if the line of knife edges be North and South, the gyrostat will balance with 

 the axis of the flywheel vertical, and if displaced from this position will oscillate 

 still according to the same law ; but with directive couple equal to the sine of the 

 latitude into the directive couple experienced when the line of knife edges is 

 East and West. Thus this piece of apparatus gives us the means of definitely 

 measuring the direction of the earth's rotation, and the angular velocity of the 

 rotation. 



These experiments will, I believe, be very easily performed, although I have not 

 myself hitherto found time to try them. 



Gteostatic Model of a Magnetic Compass. 



At Southport I showed that a gyrostat supported frictionlessly on a fixed 

 vertical axis, with the axis of the flywheel horizontal or nearly so, will act just as- 

 does the magnetic compass, but with reference to ' astronomical North ' (that is to 



1 The formula is 



gw = - Wk J o>y sin I ; 

 a 



where w denotes the balancing weight ; gw the force of gravity upon it ; a the arm 

 on which this force acts ; W the weight of the flywheel ; k its radius of gyration ; 

 ^ its angular velocity ; y the earth's angular velocity ; and I the latitude of the place. 



