232 IOWA ACADEMY OP SCIENCE 



in amplitude in the two types the loss of energy is smaller in 

 the first than in the second, or we would expect to find that the 

 amplitude-vibration number curves would be different in slope, 

 since one would be damped more rapidly than the other. To 

 see whether or not this reasoning was correct several curves 

 of the two types were compared. In every case the curve of 

 type III fell slightly above the curve of type II. This is shown 

 in figure 40. As we should expect, the two curves tend to coin- 

 cide again in the small amplitudes. This is easily explained by 

 the fact that the period of type II again increases after the 

 minimum at 4 degrees per cm. length. Again, as we should ex- 

 pect, type I continues below type III throughout the life of 

 vibrations. 



Logarithmic decrement. In ordinary damped vibrations the 

 logarithmic decrement is constant and is expressed by log K, 

 Where A 1 , A 2 , A. 6> A 4 „, .are the successive amplitudes and bear the 

 relation, 



~~J. V 2 X X "' = K n_1 



A2 Aj A4 A n 



A n 



then log A' 



K n-i 



log Ai — log An 



n-l 



Table V below shows how the log K varies in a sample of wire 

 No. 4. These tables have been compiled for several curves of 

 each type for several diameters of wires and all are found to be 

 very irregular with a general tendency for the log K to fall off 

 in the smaller amplitudes. Thus nothing of value can be learned 

 from the log K curves of the different states. The log K has 

 no real meaning in these cases. 



TABLE V. 



Wire No. 4 in state II. (Length=8.9 cms.) 

 Mean Amplitude Log K 



