48 DR. F. HORTON ON THE EFFECTS OF CHANGER OF TEMPERATURE 



with the coefficient of expansion, melting-point, and atomic weight of the metal in 

 question, rather than to obtain great accuracy in the investigation of the efl'ects of 

 alteration of temperature on the rigidity modulus. 



Although observations of the logarithmic decrement of the amplitude of the 

 torsional oscillations were not the main object of this research, the results obtained 

 throw considerable light on the internal viscosity of the wires used, and it seems 

 desirable, therefore, to compare them with similar observations by other observers. 



The diminution of amplitude of the torsional vibrations of a wire suspended as in 

 the present experiments is due to two causes : 



(1) loss of energy By the vibrating system to the surrounding air; 



(2) the internal molecular friction of the suspended wire. 



In order, therefore, to obtain accurate information as to the internal friction of the 

 wire, it is necessary to deduct from the observed logarithmic decrement that portion 

 which is due to the viscosity of the air. An exact calculation of this is impossible in 

 the present case on account of the various objects fixed inside the box enclosing the 

 vibrator, but an approximate value was found by using MAXWELL'S formula for the 

 cuse of a disc vibrating between two fixed plates. The value thus found for the 

 logarithmic decrement due to air-damping was of the order 10~ 5 . The increase in 

 this value due to an increase of the temperature of the air of 100 0. (about 25 per 

 cent.) would not be within the limits of accuracy of. the observations, and hence the 

 variation in the observed logarithmic decrement on increasing the temperature of the 

 jacket enclosing the vibrating system may be taken as being due entirely to the 

 alteration of the internal viscosity of the suspending wire. 



Observations of the effects of changes of temperature on the internal viscosity of 

 metal wires have been made by most of the observers who have investigated the 

 modulus of rigidity by the dynamical method, notably by KUPFFBR, PISATI, and 

 TOMLINSON. KVPFFER was probably the first to observe that the rate of subsidence 

 of torsional oscillations increased with the temperature of the wire. He did not 

 investigate this effect very fully, merely stating that at each temperature the 

 amplitudes of successive oscillations decrease in geometrical proportion, a conclusion 

 which is not borne out by the numbers given. PISATI, who experimented over a 

 range of temperatures from C. to 300 C., investigated this effect more fully, and 

 gives a series of formulae for calculating the amplitude of the n" 1 oscillation after the 

 amplitude was 90, over different ranges of temperatures. He found a marked 

 increase in the rate of subsidence at higher temperatures except in the case of iron, 

 in which the number of oscillations made by the wire in damping down from an 

 amplitude of !M) to an amplitude of 10 at first increased with rise of temperature 

 and reached a maximum at 100 C., afterwards decreasing again and Incoming 

 constant between 20CT C. and 300 (\ This minimum internal viscosity for iron at 



