APPARATUS FOR ASCERTAINING MINUTE STRAINS. 89 
APPARATUS ror ascertaining tHe MINUTE STRAINS 
WHICH occur IN MATERIALS wuen STRESSED 
WITHIN THE ELASTIC LIMIT. 
By W. H. Warren, wWh.Sc., M. Am. Soc. C.E., M. Inst. C.E., 
Challis Professor of Engineering, University of Sydney. 
[Read before the Royal Society of N. S. Wales, July 7, 1897.] 
THE coefficient of elasticity is usually defined as the ratio of the 
stress to the strain which it produces. It is necessary to know 
the coefficient of elasticity whenever it is desired to calculate the 
deformation or strain produced by a given load or stress, or to 
calculate the stress from an observed deformation. Such calcu- 
lations are of frequent occurrence in connection with the design 
of structures and machinery. 
The deformations produced by the stresses under normal work- 
ing conditions are exceedingly minute, and require very delicate 
instruments to measure them accurately. This remark is 
especially true in connection with the determination of the elastic 
constants for stone, concrete, and cements, where a stress of one 
ton per square inch may produce a compression of only one hundred 
thousandth part of an inch (zsssss") per inch, in which case the 
Coefficient of elasticity would be expressed as 100000, the units 
2 Stress being tons per square inch. In the case of a certain 
kind of Sandstone, for example, Prof. Bauschinger obtained a 
Coefficient of 240,000 with the same units in compression. So 
that a Stress of one ton per square inch on this sandstone would 
Produce a compressive strain of one two hundred and forty 
thousandth of an inch. 
In the case of metals the deformations produced by s J 
are much larger, and the elasti ficient p lingly smaller, 
80 that their accurate determination is more easily accomplished, 
But even in this case it is necessary to be able to measure strains 
