184 REPORTS ON THE STATE OF SCIENCE.—1913. 
repetition for some particular very large number of times will just produce 
fracture. If unlimited time were available for testing, the very large 
number referred to would be indefinitely great or would exceed the 
number of repetitions which the material would be required to withstand 
in service. 
The cycle of stress having its maximum and minimum respectively of 
equal (or nearly equal) positive and negative values is the most important 
practically ; and the bulk of experimental work has been done with this 
cycle. The usual method of finding experimentally the resistance of a 
material is to make a number of tests to destruction with a series of ranges 
of stress of this (equal +) cycle; the first of the series having an appropriate 
high range, and subsequent series a successively less and less range. This 
succession of tests is continued until the number of the repetitions before 
fracture is at least a million. Plotting the ranges of stress, ‘f’ (or half the 
range of the cycle of equal + and — stresses), against the respective number 
of repetitions, ‘ »,’ before fracture, an ‘f, n’ curve, or ‘ endurance curve,’ 
is obtained. This curve (at any rate for iron and steel) becomes less and 
less inclined to the axes of ‘n’ as ‘n’ becomes larger. Where the curve 
becomes sensibly asymptotic to a line parallel to the axis of ‘n,’ the 
ordinate—i.e., the range of stress—between the asymptote and the axis of 
‘mn’ is called the ‘limiting range,’ or the ‘ Wohler safe range.’ This range 
is a definite measure of the ‘ endurance ’ under the type of stress and con- 
ditions of test. The term ‘endurance’ has been somewhat loosely used, 
and it is not employed herein to denote any particular measure of the 
resistance to alternating stress. 
Testing Machines. 
The machines used in making the alternating stress tests that have been 
published are referred to in the bibliography and the notes contained 
therein. 
Data from Published Tests. 
It has been suggested * that a list of all published data of tests should 
be made out. Such a list should include (if available) information con- 
cerning the chemical composition, manufacture, previous heat treat- 
ment, testing machine, shape and preparation of specimen, and an attempt 
to estimate how nearly the Wéhler safe ranges have been approached in 
each case. This matter is one of some magnitude, and is at present left 
over for further discussion. 
Bauschinger’s Theory. 
This theory is thus concisely stated by Bairstow (No. 2,f page 168, 
Vol. VI. ‘Collected Researches,’ N.P.L.) :—‘ The superior limit of elas- 
ticity can be raised or lowered by cyclical variations of stress, and at the 
same time the inferior limit of elasticity will be raised or lowered by a 
definite, but not necessarily the same, amount. The range of stress be- 
tween the two elastic limits has therefore a value which depends only on 
the material and the stress at the inferior limit of elasticity. This elastic 
range of stress is the same in magnitude as the maximum range of stress 
which can be repeatedly applied to a bar without causing fracture, no 
* By Prof. J. E. Petavel. 
{ The numbers refer to the bibliography of this Section. 
