of Young's Modulus for Glass. 417 



sometimes a matter o£ importance ; whilst in experiments on 

 rods, hammer and rod may be enclosed in a tube, which is 

 then immersed in a water or steam bath. 



The beats produced by the simultaneous vibration of the 

 glass and steel rods were, as a rule, simply estimated by com- 

 parison with those of a watch. The most successful of more 

 exact methods tried consisted in timing the oscillations o£ a 

 heavy ball attached to a string to coincide with the period 

 o( the beats, by altering the length of the string, the rate of 

 the pendulum being subsequently ascertained by means of a 

 watch. But a moderate amount of practice enables one to 

 make a pretty exact estimate of the frequency of the beats 

 when this is in the neighbourhood of four or five per second. 

 It i> not advisable to attempt to bring steel and glass rod 

 more closely into unison : as a rule the vibrations of thin 

 glass rods, especially if these are rather irregular, die out so 

 rapidly that the apparent absence of beats is no criterion of 

 exaet synchronism. 



In every case, the sense of the difference between steel and 

 glass rod was positively ascertained in the usual way by 

 means of a spring-brass rider which could be fixed on the 

 steel bar. This was more than usually important, since the 

 fundamental tone of an irregular rod is certain to be accom- 

 panied by anharmonic overtones. 



In the way described, the product nx2l is easily and 

 rapidly found for a number of thin rods. The correction, 

 A/, to be applied to the observed length / of a free-free 

 irregular rod vibrating longitudinally in its gravest mode, is 

 (see Appendix) 



A7 f'SS 2tt~ 



A/=l —.cos - dz, 

 Jo ^o t 



where 68 is the difference, positive or negative, between the 



cro ection at the point : and its mean value, S , for the 



whole rod. 



Now an exact determination of S throughout even a single 

 rod (jf considerable length would be a matter of some dif- 

 ficnlty; and as rod> and tubes are never quite free from 

 knot- and streaks, very often not homogeneous throughout, 

 and only exceptionally properly annealed, would in the end 

 lead to no high degree of accuracy. In these experiments I 

 have, as a rule, been -atisfied to divide each rod into ten 

 nearly equal lengths : after suitable trimming of the ends of 

 each piece on the emery disk, to determine its length to 

 the nearest tenth millimetre, and its weight to within one 



milligramme; and to take .---- s as a measure of S, supposed 



