TRANSACTIONS OF SECTION A. : 757 
number of small Hertzian oscillators. In the case of a long linear oscillator, it is 
easy to see that, calling % the strength of a Hertzian oscillator, then we must have 
the electrification e at any point oe! while the current at the point must be 
s 
that in the oscillator. Thus, if 
e=e, cost sin s, 
we have 
h= h,—e, cost coss, 
and then, in order that the distribution of current may be greatest in the centre 
where s=0, we must have the strongest Hertzian oscillator there, and consequently 
hg =0. Applying similar considerations, any distribution can be built up, and 
Hertz’s, z.e., Maxwell’s, equations applied to the case of large conductors, as, for 
example, to telephone circuits, alternating current circuits, and to the superficial 
conditions in reflection at metallic surfaces, or to calculate the force between two 
; neighbouring Hertzian receivers, as in Mr. Boys’s experiment. 
; 3. Report of the Committee on Molecular Phenomena attending the 
by Magnetisation of Iron.—See Reports, p. 145. 
_ 4, Note on the Relation between the Diffusion of Motion and Propagation of 
___— Disturbance in some turbulent Liquid Motions. By Professor G. F. Frrz- 
GERALD, F'.R.S. 
5. A Coefficient of Abrasion as an Absolute Measure of Hardness. 
By ¥. T. Trovron. 
Mohs’s scale of hardness, though probably affording all that is wanted by the 
practical mineralogist, can hardly be considered as very satisfactory from the 
_ physical point of view. .The scale is constructed by the selection of a number of 
substances (ten in all) of unequal hardness, ranging from the softest to the hardest 
of ordinary minerals—from tale to diamond. The process of determining hard- 
ness ultimately resolves itself to finding by scratching the given substance with 
the selected minerals in turn whereabouts in the scale the substance stands. In 
this way hardness is said to be 4 or between 4 and 5, &e., according to the results 
of comparative operations. 
One of the principal objections which has been urged to a method of this kind 
for measuring hardness is its being completely arbitrary, in so much as there can be 
no guarantee, that between successive numbers on the scale there is the same advance 
in hardness, whatever may be the proper meaning to be attached thereto. Thus it 
has been a subject of regret that, since this method is independent of all methods of 
_ measuring other quantities, there can obviously be no dimensional equation repre- 
senting the dependence of the unit of hardness on the units of other physical 
quantities. 
An altogether different way of measuring hardness suggested itself to me nearly 
two years ago, on seeing an apparatus which was constructed for the purpose of 
_ testing the durability of paving setts to traffic wear. In this apparatus a rotating 
iron or steel rubber (not unlike a pointless drill) was employed to wear away the 
stone, and in this way various stones could be compared by weighing the loss under 
similar circumstances. It occurred to me that an absolute scale of hardness might 
be invented, through the device of simply supposing each substance to be rubbed by 
itself, thus eliminating out the arbitrariness introduced into this method through 
the arbitrary selection of the material of the rubber. 
In this way for various substances the amount worn off could be determined, on 
the passage at a certain velocity of two portions of the same kind of matter over 
each other, under a certain pressure. The ratio of what might be called the 
