208 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. _ 
the exception of a single point as yet in need of further elucidation), 
seems to lead to satisfactory results, both from a theoretical and a 
practical point of view. My paper is therefore divided into the follow- 
ing parts: . 
§*1. A review of the earlier work. 
§ 2. The theory, in so far as it enters into my work. 
§ 3. The method in general. 
The deseription of the apparatus. 
General remarks on the observations. 
§ 6. The constants and the sources of error. 
\ 7. Theexperinental verification of the method. 
§ 8. The measurement of the elasticity and the hardness of certain sub- 
stances. 
ao) 
With reference to the last I will state at once that the data are given 
solely with the object of evidencing the utility and accuracy of the 
method. They show to what degree the second sub-problem has been 
solved. Systematic work relative to the third sub-problem, as well as 
many investigations which the present paper suggests or implies, I have 
reserved for future communications. 
I. A REVIEW OF THE EARLIER WORK. 
Relative to the definition and the measurement of any physical 
quantity like hardness, the observer may proceed from three points 
in view. He may only wish to find out whether the hardness of any 
given body is greater or less than the hardness of another given 
body; and he may therefore be satisfied with a typical series, any mem- 
ber of which is conventionally harder than the preceding and softer 
than the succeeding body. The elements of such a series may even be 
numbered; but the numbers are obviously not significant quantities. 
Furthermore, if even these members are reliable it is clearly to be 
shown (1) whether if B be harder than A, A is always necessarily less 
hard than 6; (2) if when C is harder than Band B harder than A, C 
is always harder than A. Inthe case of many physical properties these 
conditions do not hold, or do not hold at least for all substances; and_ 
it is, therefore, not generally possible to classify bodies in a seale of the 
kind in question. Only after these fundamental conditions have been 
fixed in principle, is it permissible to make the second step, namely, to 
replace the more or less arbitrary members in the scale of hardness, by 
data which actually measure the property, and which therefore, for any 
two bodies, will express the hardness ratio. The scale so obtained is 
relative, and the term of comparison conventionally chosen. Thus, for 
instance, the hardness in a given definite body may be taken as the unit. 
But here again it is necessary to reflect that the data may differ not only 
as to their actual value, but in their relations, depending as they must 
on the experimental method by whieh they were obtained. Only the 
final or absolute method is, therefore, always satisfactory, for here the 
