140 Mr Sang on the Advantages of a 



The retardation of a clock, when the arc of vibration of its 

 pendulum is increased, is by no means so trifling as is generally 

 imagined ; the table, I am convinced, presents results much 

 greater than were anticipated by many, even of those who are 

 conversant with the subject. In the formation of the table, I 

 have taken every precaution to insure accuracy, having carried 

 the logarithms to ten decimal places, so long as I adhered to the 

 decimal division, and employed the ordinary tables to seven 

 places only, in passing from that to the ordinary division of 

 time. These circumstances, joined to that of its being new, will 

 render it acceptable to men of science. 



These statements may be confirmed by a very simple but 

 beautiful experiment. Having suspended a leaden ball by 

 means of a slender thread, let this simple pendulum be put in 

 motion, so that the ball may describe a curve known to bear a 

 considerable resemblance to the ellipse. If the times of vibration 

 along the two axes of this curve were exactly equal to each 

 other, the ball would repeatedly retrace the same orbit ; but these 

 times of vibration are different, and, during the passage from 

 end to end of the long axis, the ball has more than returned to 

 its position in reference to the short one, so that the axes of the 

 orbit are gradually displaced in the direction of the movement 

 of the ball. This displacement will be found to be most rapid 

 when the orbit is large ; as that orbit gradually contracts, the 

 displacement of the axes becomes more and more retarded, until, 

 when the evagations do not exceed three or four degrees, it 

 ceases to be perceptible. 



To these remarks on the advantages of pendulums with short 

 arcs of vibration, it must be added, that great practical objec- 

 tions lie against their being made very small; these objections, 

 however, are founded on the peculiar natures of the escapements 

 generally used, and, perhaps, derive additional strength from 

 the reluctance to depart from long established, although arbitrary, 

 rules. The beautiful escapement which lately gained the So- 

 ciety's highest prize, when applied, with proper precautions, low 

 down on the pendulum rod, obviates all these objections, and 

 offers the prospect of immense improvements in time-keeping. 

 A movement on this plan is already in a state of forwardness, 

 and I shall take pleasure in reporting to the Society the results 

 of experiments made with it. 



