554 



NATURE 



\Oct. 19, 1876 



fees at the meeting(993 roubles from 331 members) \yas 

 allowed for the publication of memoirs. The discussion 

 of these various subjects having taken up much time, the 

 members dispersed, and very few attended the lecture of 

 M. Kostareff " On the Inductive and Deductive Methods 

 of Reasoning and of Inquiry." The meeting was closed by 

 a short address by the president, Pi-of. Brodofsky. 



A. L. 



PRINCIPLES OF TIME-MEASURING APPA- 

 RATUS'^ 



II. 



The Pendulum. 



N that early apparatus I recently described, you will 

 remember that the balance, after being set swinging 

 in one direction, had its motion completely destroyed, 

 and was then set swinging in the other, all by the direct 

 agency of the clock-train. If it had possessed no other 

 property than that merely of vibrating against the earth's 

 attraction, the pendulum would have been an immense 

 improvement upon this state of things, because every 

 impulse delivered to it is, so to speak, stored up there, 

 and is gradually expended therefrom as occasion requires 

 in overcoming the friction due to its connections and the 

 resistance of the atmosphere. 



The discovery of the pendulum is generally attributed 

 to Galileo, whose attention was attracted to the subject 

 by watching the oscillations of a chandelier suspended 



I 



by a very long line at a church in Pisa. The story 

 is very likely to be a true one ; anybody observing the 

 shorter oscillations of a very long pendulum (fifty or sixty 

 feet in length say) could scarcely fail to be impressed by 

 them. 



The celebrated Dutch philosopher, Huygens, first 

 worked out its theory. He discovered that if a pen- 

 dulum, instead of swinging in a circular arc (which it 

 obviously does) could be made to move in a cycloidal, it 

 would perform all its oscillations, whether large or small, 

 in precisely equal times. 



He succeeded in obtaining this motion for his pen- 

 dulums by the following contrivance (see Fig. 9) : — Two 

 curves or cheeks, C C, starting from the axis of motion are 

 placed one upon each side of the pendulum, which is 

 suspended by a flexible line or spring S. As the pendulum 



' Lectures by Mr. H. Dent Gardner, at the Loan Collection, South 

 Kensington. Continued from p. 331. 



swings, this line wraps around either curve and deflects 

 the pendulum from its circular path, K u R, into the 

 cycloidal, D u L. As you could almost infer from inspec- 

 tion the time of a pendulum swinging a cycloidal, is rather 

 faster than when it swings a circular arc, the cycloidal 

 being the more rapid curve. Also the time of the swing 

 of a pendulum in a circular arc gets longer as the swing 

 increases, that is to say, as it travels further up the curve ; 

 for instance, if the arc of a pendulum which was swinging 

 2° was increased to 2^°, the loss of time due to the in- 

 creased length of its swing would be four seconds a day. 

 The invention of these cycloidal cheeks or curves must 

 have been looked upon as the iie plus ultra of perfection 



Fig. 10. 



Fig. 12. 



at the time ; but in the first place they did not deflect 

 the pendulum without a good deal of friction ; and in the 

 second it is, rather advantageous than otherwise that a 

 pendulum should gain in its shorter vibrations, because 

 it never gets into them without retardation (which implies 

 loss of time), and one error tends to correct the other. 



Huygens also discovered that the time of one swing 

 of a pendulum varies as the square root of its length. 

 The length of a pendulum swinging in one second is 

 nearly 39*2 inches, and if you wish to find the time in 

 which a pendulum of any other length will perform one 

 swing, you divide the square root of that length by the 



