. 
ON THE ABSOLUTE MEASUREMENT OF HARDNESS.* 
By F. AUERBACH. 
Translated by Cart BARUS. 
Hardness, aside from its practical importance, is one of the most 
remarkable properties of solid matter. This is shown at once by the 
difficulties which have been encountered in the endeavor to arrive at 
an accurate interpretation of it. Indeed, the attempts to solve questions 
relating to hardness are of very great variety, and are exceptionally large 
in number, and they have in a measure led to some interesting results; 
but the subject in its broader bearings has not yet been attacked with 
success, nor has a rigorous definition of hardness been established. 
Problems which present themselves in dealing with any of the physical 
properties of a body may usually be divided into three sub-problems: 
The first among these includes the scientifically exact description of the 
conception in question, so that the property may henceforth be treated 
as a purely mathematical variable. Then this quantity is to be meas- 
ured, and methods and apparatus must be devised for that purpose. 
Finally, the measurements are themselves to be generalized by being 
extended to as many bodies under as many different circumstances as 
possible. At the outset, however, it is by no means necessary that the 
procedure adopted should be so simple as to be of immediate practical 
utility. As arule this will only be attained at a much later stage of 
the research. The chief aim at the beginning is to work forward from 
some theoretically perfect basis, and-to so fashion the methods that the 
end in view may be reached with a reasonable degree of accuracy as 
wellas certainty. To within a few years none of the three sub-problems 
which I have mentioned can be said to have been solved. To Hertz 
belongs the credit of being the first to push the question to an issue. 
His ingenious reasoning is particularly fortunate, inasmuch as it har- 
monizes the general conception of hardness and the earlier definitions 
which were given of it in all essential and necessary points and to the 
exclusion of errors of principle and vagueness. Taking Hertz’s con- 
clusions as a point of departure, I believe I have solved the second of 
the sub-problems, and in the present paper submit a method, which (with 
*From the dAnnalen der Physik und Chemic, April, 1891; (new series) vol. XLII, pp. 
61-100, 
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