of minute Forces on the Rate of the Seconds Pendulum. 247 



a tangent-screw, so that they could be adjusted to any depth 

 in the teeth of the wheel. This shape afforded the means of 

 giving about three fourths of the impulse in the descent. Ex- 

 periment showed that the clock now gained about 2 seconds 

 in 24 hours. The extra friction in this case was in the ascent. 



It is known that if a pendulum have at the point of rest 

 impulse sufficient to reach 2°, with a certain quantity of fric- 

 tion, it will require a greater impulse with a greater quantity 

 of friction. The greater impulse will of course cause the first 

 increments of motion to be quicker in the latter case than in 

 the former; but this incidental quickness will have gradually 

 decreased, and vanished when the pendulum has arrived at 

 the extent of 2°; and consequently, the entire vibration will 

 be quicker. Pendulums having strong adjusted suspending 

 springs require a maintaining power in weight about double 

 of that which they would require with a thin spring, or on a 

 knife-edge, in order to make them vibrate to the extent of 2°. 



The change of rate occasioned by the use of strong suspend- 

 ing springs, led to the consideration of some other practical 

 means for obtaining isochronism, cycloidal cheeks being ad- 

 mitted to be objectionable in practice. It occurred to me that 

 by placing a cylinder, or a portion of it, at the point of suspen- 

 sion of a pendulum, and making it roll on a plane, the point 

 of oscillation would move in a cycloid, at least as far as the 

 extent of the vibrations of the pendulum required. For this 

 purpose, I constructed an appropriate apparatus. I described 

 the central portion of a cycloid on a sheet of brass, and fixed 

 it on a wall, with a horizontal plane on the same, at a proper 

 distance above for the length of the seconds pendulum. After 

 several trials with cylinders of different sizes, it appeared that 

 one of about 2 inches in diameter caused the point of oscilla- 

 tion to traverse in the curve, at least as far as could be sensibly 

 determined. 



These trials led to the construction of a cylinder the size of 

 which was a very near approximation to the proper magni- 

 tude. This cylinder was then fixed to a convertible pendu- 

 lum, which I had previously constructed; but in the present 

 case it was used as a common pendulum. The result of more 

 careful and repeated experiments showed that a cylinder of 

 1*8 inch in diameter caused the seconds pendulum to perform 

 its vibrations in times more nearly equable than could be ob- 

 tained by cylinders of any other size. 



Thinking, however, that the property of isochronism might 

 possibly depend on some minute size or proportion, I first 

 shortened the pendulum, making use of the cylinder which 

 gave the nearest approximation. I then gradually and sue- 



