600 Proceedings of Royal Society of Edinburgh. [sess. 
various suitably conducted series of experiments, the constant of 
proportionality being different in different series; and that, in 
each such case, it is possible to choose a y-unit which will make nb 
practically constant. 
ISTo doubt one cannot conclude, from the behaviour of one wire, 
anything regarding the possible behaviour of another under similar 
conditions. Yet the presumably identical cause of the decrease of 
the range of oscillation in each wire renders it probable that the 
same law applies in all — at least when the decrement is not exces- 
sively large. 
I cannot therefore account for the results which Mr Thompson 
has obtained, unless it be that the treatment to which his wires 
were subjected was such that 
log. nb = log. A + n log. y 0 
where y 0 is the angle of oscillation at which readings were taken 
on the average, and 1/A is the logarithmic decrement, so that a 
linear relation, similar to those above spoken of, held between log. 
nb and n. 
That this relation did not hold at values of y other than y 0 is evident 
from Mr Thompson’s observations. Indeed, Mr Thompson expressly 
points out that, when the wire was oscillated for some time through 
a considerably smaller range than y 0 , before observations were made 
on the decrement at y Q , the decrement at y 0 “as was to be expected, 
was lower than any hitherto found.” This statement seems to be an 
explicit recognition of fatigue. If a decrease in the value of the 
decrement at y 0 were essentially produced by previously keeping 
the wire oscillated for some time through a smaller range, much 
more should there be a decrease if it were previously kept entirely 
unoscillated. 
