220 Mr. W. Sutherland on a 



applicability of the formula, I made copper and magnesium 

 wires vibrate unloaded both in the two vertical positions and 

 in the horizontal ; calling n z the number of vibrations per 

 second in the horizontal position, I found that wj + w|=2w|, as 

 should be, to a high degree of accuracy. But there is another 

 check which can always be applied to any set of experiments. 

 The equation (A) shows that 



so that n\ — n\ is quite independent of the elastic properties of 

 the bar, and has a calculable value. It is therefore a check 

 on the method to see that the observed value of n\—n\ is equal 

 to the calculated. In the experimental values about to be 

 given this method of verification will be applied, and it will 

 be seen that in any case where it is possible to make observa- 

 tions with only one vertical position of the bar, the equation 

 (A) can be safely used for the calculation of Young's 

 modulus. 



Of course, where the Young's modulus of a substance varied 

 appreciably with stress, it would not be possible to eliminate 

 the action of gravity, as in equations (B) and (0), but equation 

 (A) could be used. 



Experiments. — The vibrations were carried out in the same 

 box heated in the same manner as in the Rigidity experiments. 

 The rod or wire that was to vibrate could be clamped at the 

 middle point of either the top or the bottom of the box, and 

 executed its vibrations freely inside. To secure accuracy in 

 determining the period of the swing the vibrations had to be 

 reinforced, and this was done by means of a thread passing 

 horizontally from the free end of the wire to the outside ; 

 by means of the thread a slight periodic impulse could be im- 

 parted to the vibrating wire at the middle of a swing ; a 

 little practice enabled one to attain a high degree of accuracy 

 with even lead and tin wires in determining the number of 

 vibrations per second. Every value given in what follows 

 was derived from several hundreds of swings. 



In all cases except that of tin wire, the wires vibrated un- 

 loaded, and accordingly equation (C) applies. 



Lead. — Commercial wire, the same as that used in the 

 Rigidity experiments. I 38*1 cm., m 14*05 grm., p 11*4. 



ni denotes the number of vibrations per second when the 

 free end is down, and n 2 when up ; q denotes Young's 

 modulus, and will be given in terms of grammes weight per 

 sq. cm. 



