In this machine the annual arbor does not revolve in an assumed solar year, but in 365 days only, as limited by the train of connexion.
Whenever the screw is met with, which will be fre quently the case when a very slow motion is wanted, it will always be found to be a driver, and must be made a denominator f 1 or 2 to its wheel, according as it is a single or a double screw ; and in some cases, a single wheel will be nt•oduced merely for the purpose of chang ing the dire*ci on of motion, from direct to retrograde, or the reverse. In such case, the number of this wheel, which may be considered both as a driver and driven wheel, may stand both as numerator and denominator of a compo nent part of a compound fraction, to shew that such wheel is employed ; but in computing the value of the period produced by such train, the wheel may be omitted, as in creasing the products, without altering the value of the fraction.
In machines where the rotation of any planetary body is introduced, some additional wheel work will be found placed on the revolving bar or arm, that carries the said body round in its periodic time, according to its appropri ate train. When such additional mechanism is used, the motion of the rotation is usually produced by a centralfix ed wheel, round which its fellow wheel or pinion is carried in the course of the revolution of the revolving arm. In this case, the period of the rotation will depend on the two wheels, or train of wheels, considered as the fraction of the time of revolution of the bar. If the numerator and denominator, i. e. in this case, the moveable and fixed wheels, have their teeth equally numerous, the period of rotation will be the same as the period of the revolution ; but if the fixed wheel, which may be considered always as the driver, is larger than the driven one, or carried round it, while their teeth are in connexion, then the period of revolution, multiplied by the driven wheel, and divided by the driver, will give the period of the rotation. But some times it will happen that the central wheel, round which the revolving bar is carried by its appropriate train, is it self one of the rotation train, and is consequently always in motion. When this happens, the period of the rotation
is affected thereby, and either an addition or subtraction may take place, according as the wheel carried round the i central one has its motion derived from the train, direct or retrograde, as compared with the additional motion it receives by virtue of its connexion with the central wheel. An example will render this observation more intelligible, and at the same time slim the necessity of a rigid notice with respect to this particular.
If we suppose a wheel A of 50 teeth, placed on one of the central revolving tubes of any machine, to have 80 re volutions given it in a solar year, in a direction from west to east ; and another smaller wheel B of 25 teeth, placed on a moving bar, and carried round it once in the same pe riod in a contrary direction, or from east to west, while their teeth are in connexion ; the consequence would be, that the motion given to B would be derived from two sources ; for first, this small wheel would have 50 of 80 = 25 160 rotations, communicated in the ordinary way, suppos ing the bar on which it is placed stationary ; and secondly, it will rotate twice more by virtue of the motion of the bar that carries it in a contrary direction while their teeth are connected, and ihe whole number of rotations will be 160 + 2 = 162. On the contrary, if the motion of the larger wheel A be from east to west, with the arm carry ing B moving once in the same direction as before, the wheel B will receive 160 rotations in a direction contrary to that of wheel A, and two in the same direction, by vir tue of its journey round the central wheel A, and the whole number of its turns will be 158 only.
The Tellurian of Benjamin Martin, which is seen in the different shops of mathematical instrument makers in London, has an error, arising from a want of attention to this source, in the rotations of the earth round its axis. The train which turns the year in days into this machine, 59 10 8 10 —365d. oh.