January 6, 1923] ; 
NATURE 17 

down movement of the naked thorax is induced in a 
way similar to that recorded by Prof. Andrade. It 
is possible that murderers brought into the presence 
of the corpse of their victim exposed in a dim light 
must frequently have seen such movements of the 
hands especially as they will probably stare fixedly at 
the body. Any apparent movement will of course be 
intensified by suggestion. This may account for 
many old superstitions. 
Finally I should like to compliment Prof. Andrade 
on having described certainly two of the prettiest 
methods of demonstrating the movements of the 
visual purple. I find that the phenomena described 
by him are readily seen by people who have not been 
told what they are expected to see, an essential point 
in such experiments. 
F. W. EpRIDGE-GREEN. 
London, December 26. 

Experiments on Hardness and Penetration. 
I AM greatly interested in the letter on ‘‘ A Curious 
Feature in the Hardness of Metals,’’ by Mr. Hugh 
O'Neill and Dr. F. C. Thompson, which appears at 
- 773 of Nature of December 9, for in my paper 
“Experiments with Clay in its relation to Piles,” 
read before the Society of Engineers on March 10, 
1919, will be found an account of the “ pressure of 
fluidity ’’ of clay. Briefly this may be described 
thus. When a horizontal disc resting on clay is 
gradually loaded it slowly sinks into the clay, each 
increment of load producing a corresponding incre- 
ment of penetration, but when the load on the disc 
reaches a certain critical value the disc continues to 
sink at about ten times the speed without any further 
increase of the load. This load divided by the area 
of the disc I have called the pressure of fluidity of 
the clay. This quantity has been found, within a 
considerable range, to be independent of the area of 
the disc used for its determination. The only factor 
easy which it depends, in the case of the London 
clay used, is the percentage of water in the clay, and 
4 this it is very greatly affected, as will be seen from 
e following equations, which fit the results closely 
within the ranges stated, and the table below. 
From 28 per cent. to 38 per cent. of water; 
,__ 1073 X 10° 
p 22. (w’)? 
ms per sq. cm. and w’ is the percentage of water 
in the clay. 
The same equation may be used with small error 
down to w’ =25-7 per cent., but with values of w’ 
from 25:7 per cent. to 22-0 per cent. the relation is 
? (kilograms per sq. cm.) = 39°5 - 1-48w’. 
I have experimented with spheres in place of discs 
and have not detected any difference in the values of 
the pressures of fluidity thus determined. The 
reason for this is probably due to what other experi- 
ments have disclosed, namely, that the descending 
disc carries down with it the clay which was 
immediately under it at the start of the experiment, 
this stagnant clay forming roughly a hemisphere 
below the disc. ether a disc or sphere is used, a 
clean hole is left behind. 
Expecting to find a similar phenomenon in the case 
of metals, a corresponding experiment was made 
with cast lead. The result was the same. At a 
certain critical load the disc continued to sink into 
the lead without further increment of load. The 
ressure of fluidity of lead was thus found to be 1233 
ilos per sq. cm., as recorded at pp. 152-4 of my 
fourth paper on ‘‘ The a oer Properties of Clay,’ 
read before the Society of Engineers on June 12, 1922. 
NO. 2775, VOL. 111] 
, where ~’ is the pressure of fluidity in 
From the rate of penetration (after the pressure of 
fluidity had been reached) and by a modification of 
Stokes’ Law, the viscosity of the lead at 60° F. was 
found to be 
7°37 x 10” dyne-seconds per sq. cm. 
Taking the Brinell formula given by Messrs. O'Neill 
and Thompson, when the ball is below the surface of 
the material d=D, and the Brinell formula they 
give becomes L 
2 
And when d=D the Meyer formula becomes 
Pee a, 2 eS. Mee ABD 
Substituting (2) in (1) we have 
aa = } barb od 6 eps) 
The Brinell hardness number is the stress in kilograms 
per sq. mm. on the curved surface of the indentation. 
The pressure of fluidity, p, is the critical load L 
divided by the area of the disc (or great circle of the 
ball). Thus: 
) 
aa STye pe 
4 + 
: Pee 
Hence p is seen to be equal to 2H, where H= sp 
aD” _ 42 pa-2, £7 eed 
TT 
and L is the critical load. 
This result also immediately follows from the fact 
that in the case of the Brinell No. the load is divided 
by the area of the curved surface of the indentation, 
whereas in the case of the pressure of fluidity the 
load is divided by the projected area of the sphere, 
and the ratio of the area of the curved surface of a 
hemisphere to its flat surface is 2. 
As A="D', -, D=113 VA, 
Therefore Meyer’s formula 
L=aD" becomes L=a(1-13 ./A)" 
=a(1-13)"A?. 
But in the case of clay, L« A, this being one of 
the most definite and carefully determined results. 
Consequently, if Meyer's formula is also true for clay, 
n must be= 2:0, in which case L=a(1-13)*A=1-275aA, 
and L/A=p=1:'275a or a=p/1‘275. 
Using this relation the following values of @ are 
obtained for London clay :— 


















Per cent, of Water. Pikiloe pes aps 
37°8 0'083 
~ f babe o*100 
31°0 0°251 
30°0 O'4I4 
29'0 o’471 : 
28°0 0°663 
25°4 I°521 
23°6 3°69 
22°0 5°65 

A. S. E. ACKERMANN. 
17 Victoria Street, Westminster, S.W.1, 
December 11. 
