But the most wonderful of these mechanical arrangements is the machine for analysing the curves drawn by a self-registering tide gauge, so as to exhibit the constants of the harmonic curves, and thus enable the prediction of tidal heights to be carried out either by the tide-predicting machine, or by calculation. One day in 1876, Thomson remarked to his brother, James Thomson, then Professor of Engineering at Glasgow, that all he required for the construction of a tidal analyser was a form of integrating machine more satisfactory for his purpose than the usual type of integrator employed by surveyors and naval architects. James Thomson at once replied that he had invented, a long time before, what he called a disk-globe-cylinder-integrator. This consisted of a brass disk, with its plane inclined to the horizontal, which could be turned about its axis by a wheel gearing in teeth on the edge of the disk, and driven by the operator in a manner which will presently appear. Parallel and close to the disk, but not touching it, was placed a horizontal cylinder of brass, about 2 inches in diameter (called the registering cylinder), and between the disk and this cylinder was laid a metal ball about 2½ inches in diameter. When the disk was kept at rest, and the ball was rolled along between the cylinder and disk, the trace of its rolling on the latter was a straight horizontal line passing through the centre. Supposing then that the point of contact of the ball with the disk was on one side, at a distance from the centre, and that the disk was then turned, the ball was by the friction between it and the disk made to roll, and so to turn the cylinder. The angular velocity of rolling, and therefore the angular velocity of the cylinder, was proportional to the speed of the part of the disk in contact with it, that is, to y. It was also proportional to the speed of turning of the disk.