34 Mr. W. Sutherland on a 



n being the rigidity, I the length of the wire vibrated, m its 

 mass, p its density, I the moment of inertia of the vibrator, 

 and t the time of a complete vibration. Using C.Gr.S. units in 

 the measurements, the rigidity is given in dynes per square 

 centim., but as the gramme weight is the unit of force most 

 employed by elasticians it will be used here. 



When the vibrator swung outside the chamber, a small 

 length of the wire was not heated directly but only by conduc- 

 tion ; to allow for this the small length was assumed to be at 

 the temperature of the external air. Let n x be the rigidity at 

 the initial temperature 1 of the surrounding air, n 2 that at 

 any higher temperature 2 , and A, the length of the small part 

 of wire outside of the chamber, a the coefficient of linear ex- 

 pansion of the wire, t x and t 2 the periods observed at the two 

 temperatures, then the ratio n 2 / w i is given by the formula 



n 2 _ I — X 

 n, I 



1 + 3<0 2 -<9j) " Wt x J l{l + u{0 2 -0 i )\J 



Lead. — Commercial wire. 



I. X. m. p. I. 



77*05 cm. 4 cm. 28*4 gm. 11*4 586500 gm. cm. 2 



Temperature C. 21° 60° 102° 



Half-period t/2 5-51 sec. 5*71 6*00 



Rigidity ratio /is/ft! 1*00 *924 -829 



Rigidity at 21° C. } 90 x 10 6 grammes weight per sq. cm. 



To control the absolute value found, a large number of 

 measurements were made on a longer wire with a lighter 

 vibrator ; length 238*7 centim., mass 88 gm., density 11*4, 

 moment of inertia of vibrator 3350 gm. centim. 2 , temperature 

 17° C, and half-period *7365 sec. These values give a 

 rigidity 90 x 10 6 at 17° C, in close agreement with the value 

 found from the shorter wire. 



To make still surer of getting this absolute value of the rigidity 

 of lead thoroughly tested, I carried out some experiments on 

 a much larger scale, using a piece of stout lead pipe instead 

 of wire. For vibrator a rectangular plank 179'7 centim. long 

 and 14*6 centim. wide was taken ; a hole was bored at its 

 centre through which the pipe was pushed till a short length 

 projected which was slit and hammered back in four flaps, 

 then strongly nailed to the plank ; a conical plug being driven 

 into the pipe, there was no doubt about the rigidity of the 

 connexion between pipe and vibrator. The plank weighed 



