1914 - 15 .] 
The Theory of the Gyroscope. 
153 
XIV. — The Theory of the Gyroscope. By Professor H. Lamb, F.R.S. 
(MS. received March 13, 1915. Read May 3, 1915.) 
The object of this note is to obtain briefly the intrinsic equations of 
motion of a gyroscope, and to show how they lead immediately to the 
solution of a number of problems. So much has been written on the 
subject of the gyroscope that these equations are hardly likely to be new^ 
but I do not remember to have met with them in their explicit form. 
Apart from their use as a basis for calculation, they have a simple 
interpretation which enables us to foresee the general character of the 
motion in cases where the actual calculation would be difficult. 
1. It is assumed that two of the principal moments of inertia at the 
“ flxed point” (0) are equal, and the three moments are accordingly denoted 
as usual by A, A, C. We may also denote by C one of the two points in 
which the axis of symmetry meets a unit sphere having its centre at 0. 
For definiteness we choose that point of the pair which is such that the 
angular velocity {n) about the axis OC shall be right-handed. This point C 
may be called the pole of the gyrostat, and it is with its path that we are 
concerned. 
c 
Fig. 1. 
We draw from C, on the unit sphere, a quadrant CA tangential to the 
path and in the direction of motion, and a quadrant CB at right angles. 
