Oct. 19, 1876] 



NATURE 



555 



square root of 39"2 inches ; thr.s the time of the swing 

 of a pendulum 61 inches long 



\/6i /6t 



= , = A / = i'25 = li seconds. 



V39'2 V 39-2 



On the other hand, if you wish to find the length of a 

 pendulum to swing in a given time, all you need do is to 

 multiply 39*2 by the square of the time ; thus the length 

 of a pendulum to swing in \ second ==• 39*2 X (i)* = 9'8 

 = gi inches. 



But with reference to an ordinary clock pendulum, such 

 as is shown in Fig. 10, you may ask me what is its 

 length ? do we measure its length from the point of 

 suspension to the end or centre of the bob, or to the point 

 at its extremity ? We measure it to none of these places. 

 Its true length is determined by multiplying every par- 

 ticle into the square of its distance from the point of 

 suspension, adding all these together and dividing by the 

 sum of every particle multiplied into its distance from the 

 poirt of suspension simply. Of course an operation of 



Fig. 13. 



this kind is not very easily performed, but the upshot of 

 the calculation is, in general, to give a distance to a cer- 

 tain point, o, called the centre of oscillation, just below the 

 centre of gravity, G, of the pendulum. This is the true 

 length of our pendulum so far as its time of vibration is 

 concerned, and if we could take a perfectly simple pen- 

 dulum (that is one with a rod without weight, and all the 

 matter of its bob accumulated in one point at its extre- 

 mity) of the same length, we should find that the times 

 of their swings would exactly correspond. 



What will happen if at any point above the centre of 

 oscillation we add a little weight to our pendulum, say at 

 point c ? Evidently the effect is just the same as if we 

 tied another short pendulum of length s C to our main 

 one — it will urge it on and make it swing faster. At a 

 point just hall-way up the pendulum, the effect of any 

 given weight will be greatest. From which follows the 

 curious fact that a weight moved upwards or downwards 

 away from this point will, in either case, increase the time 



of the swing of the pendulum, that is to say, make the 

 clock lose. 



The finer regulation of pendulums is performed upon 

 the principle of adding or withdrawing weight at a point 

 above the centre of oscillation. The collar c upon the 

 pendulum, is placed there to carry subsidiary weights for 

 the purpose. 



The Pendulutn Cotupensation. 



Pendulums, like other things, lengthen as they get 

 warmer, and shorten as they get colder, and the time of 

 their swing is varied in consequence. For instance, a 

 plain iron rod pendulum for every 10 degrees rise in the 

 thermometer, will expand sufficiently to make the clock 

 controlled by it lose nearly 3 seconds a day. 



The earliest and one of the best methods of correcting 

 or compensating this error is the mercurial pendulum 

 designed by Graham (see Fig. 10). The bob of the pen- 

 dulum is formed of a glass or iron vessel containing 

 mercur>', M M. When there is any increase of tempera- 

 ture, the rod R R expands and lets down the bob, but the 

 mercury in the bob also expands, and from the manner it 

 is confined expands upwards. The expansion of the 

 mercury therefore tends to raise the centre of oscillation, 

 and its amount is so calculated as exactly to neutralise 

 and destroy whatever error would otherwise result from 

 the lengthening of the rod. The action of this compen- 

 sation may very readily be increased by adding or with- 

 drawing a little of the mercury. • Of course after each 

 addition or withdrawal of mercury the clock will have to 

 be regulated to time again by altering the nut upon its 

 pendulum for the purpose. 



A slight tendency to vary its rate after first being 

 put up may sometimes be noticed in a clock fitted with 

 one of these pendulums. This arises from air bubbles in 

 the mercury, which gradually approach the surface ; as 

 they do so the mercury upon the other hand of course 

 falls. 



Another method of compensation is the gridiron pen- 

 dulum of Harrison. Different metals expand at different 

 rates, for instance — 



Steel expands "000064 of its length. 



Brass ,, "oooi ,, 



Zinc ,, 'oooiy ,, 



for every 10 degrees rise in temperature. 



Suppose we take a c^itral steel rod (see Fig. 11) about 

 3 feet long, and fasten to its extremity a cross piece ^, 

 upon which we erect two (for the sake of symmetry) brass 

 rods, one upon each side of it ; and to the summit of these 

 we attach two other rods of steel, and at the extremity of 

 these again two other rods of brass, and then let fall two 

 more rods of steel, joined at their extremities by a cross 

 piece, ard to the cross piece attach the pendulum bob by 

 another short length of steel so as to make up 39 "2 inches of 

 length between the centre of oscillation and the point 

 of suspension. Supposing that the four supplementary 

 lengths of brass and steel upon each side of the original 

 steel rod average 2 feet 1 1 inches long, we have, in between 

 the point of suspension and the centre of oscillation 

 1 09*2 inches of steel and 70 inches of brass, and further, 

 that the expansion of this amount of brass is exactly 

 equivalent to the expansion of the steeh But we have so 

 arranged that all the brass expands upwards and all the 

 steel downwards J therefore one destroys the other, and 

 the position of the centre of oscillation does not change, 

 whatever be the alteration of temperature. The worst of 

 this method of compensation is, owing to the great weight 

 of the rods, the centre of oscillation generally ceases 

 approximately to correspond with the centre of gravity of 

 the bob, and the true amount of compensation has to be 

 determined by experiment, which is seldom done. 



In the construction of compensation pendulums care 

 must be taken that they are formed so that each part shall 

 simultaneously take up any change of temperature. This 



