OF FLUIDS ON THE MOTION OF PENDULUMS. [97] 



theory as the observation of the time. Indeed, if it should be inconvenient to observe the 

 time, the observation merely of the arc would be very valuable as a test of theory. In that 

 case an approximate value of the time of oscillation in air would be required. 



In the system proposed, Nos. 1 and 3 are the principal pendulums, Nos. 2 and 4 are intro- 

 duced for the sake of making certain small corrections to the results of Nos. 1 and 3. No. 2 

 is meant for the elimination from No. 1 of the effect of the wire, and No. 4 for the elimination 

 from No. 3 of the effect of the resistance experienced by a small portion of the rod near its 

 end. The times of vibration of the four pendulums ought to be nearly the same, although 

 for that purpose slightly different lengths of wire would be required in Nos. 1, 2, and 4. 



It follows from theory that for a given pendulum the factor It is a function of the time of 

 vibration. This is a result which seems to have been hardly so much as suspected by those 

 who were engaged in pendulum experiments, or at most to have been mentioned as a mere 

 possibility*, and therefore it might be thought advisable to verify it by direct experiment. 

 For my own part I regard it as so intimately connected with the fundamental principles of the 

 theory, that if the theory be confirmed in other respects I think this result may be accepted on 

 the strength of theory alone. The direct comparison with experiment would be inconvenient, 

 because it would require a clock which kept excellent time, and yet admitted of being adjusted 

 so as to make widely different numbers of vibrations in a day. The result could, however, be 

 confirmed indirectly by observing the arc of vibration, an observation which is as easy with one 

 time of vibration as with another. 



82. Second object. According to theory, the index of friction may be deduced from 

 experiments either on the arc or on the time of vibration. It must be left to observation to 

 decide which give the more consistent results. Should the results obtained from the arc appear 

 as trustworthy as those obtained from the time, it would apparently be much the easiest way of 

 determining p for an elastic fluid to observe the arc, because no particular accuracy would then 

 be required in the observation of time. As to the form of the pendulum, a cylindrical rod 

 would apparently be the best if only a single pendulum were employed. The observation of 

 the arc seems the only practicable way of determining the influence of temperature on the index 

 of friction, unless the pendulum be extremely light, or unless the observer be content with the 

 limited range of temperature which may be procured by making observations at different times 

 of year. For in an apparatus artificially heated or cooled, it would be difficult to prevent 

 small unknown variations of temperature, which would cause variations in the rate of vibra- 

 tion, in consequence of the expansion and contraction of the pendulum ; and these variations 

 would vitiate the result of the experiment, so far as the time of vibration is concerned, because 

 the effect of the gas on the time of vibration is deduced from the small difference between two 

 large quantities which are directly observed. But the effect of the gas on the arc of vibration 

 produces by far the greater part of the whole diminution observed, and therefore small fluc- 

 tuations of temperature would not be of much consequence, except so far as they might 



* It should be observed however that in a subsequent I deduced from other experiments that the value of k was larger 

 memoir ( Astronomhche Nachrichten, No. 223, p. 106), Bcssel for the long than for the short pendulum. 



Vol. IX. Paet II. 37 



