48 LECTUEE V. 



applied to the measurement of time, but more frequently, and more successfully, 

 to the regulation of the motions of machines. Thus in Mr. Watt's steam 

 engines, two balls are fixed at the ends of rods in continual revolution, and 

 as soon as the motion becomes a little too rapid, the balls rise considerably, 

 and turn a cock, which diminishes the quantity of steam admitted. (Plate II, 

 Fig. 28.) 



The same laws are applicable to many other cases of rotatory motion ; for 

 instance, if we wish to determine the height, at which a ball, revolving with a 

 given velocity, will be retained in a spherical bowl ; or the inclination of a 

 circular road, capable of counteracting the centrifugal force of a horse, running 

 round it : for the horse, like the ball of the revolving pendulum, has a cen- 

 trifugal tendency, which is greater as his velocity is greater : this centrifugal 

 force, combined with the force of gravity, composes a result, which, in the 

 case of the pendulum, is completely counteracted by the force of the thread or 

 wire, and must therefore be in the direction of the thread, and which obliges 

 the horse to place his legs in a similar direction, proceeding from an imaginary 

 point of suspension above; since he would otherwise be liable to fall out- 

 wards, if his velocity were sufficiently great. But in order to withstand the 

 pressure of the horse's legs, the road must be in a direction perpendicular to 

 them; otherwise its materials will naturally be forced outwards, until they pro- 

 duce an elevation sufficient to give the road the required form. Thus, if the 

 diameter of the ring were 40 feet, and the horse moved at the rate of 12 miles 

 an hour, he would perform about 500 revolutions in an hour, and half a revo- 

 lution in 3 seconds and a half. Now the length of a pendulum vibrating in 

 34- seconds, must be 39 inches multiplied by the square of 34^, or a little more 

 than 80 feet : the road must therefore be perpendicular to the direction of a 

 line drawn to it from a point 80 feet above the centre of the ring; and its ex- 

 ternal circumference must be higher than its internal circumference by one 

 fourth of its breadth. It would however be improper to have a road of this 

 form in a manege, since the horse must be taught to perform all his evolutions 

 on a perfect plane. 



There is a general principle of curvihnear motion, which is in itself of lit- 

 tle importance or practical utility, but which so far deserves to be noticed, as 

 it has been magnified by some philosophers into a fundamental law of nature. 



