May 24, 1901.] 
Fortunately one case has been studied which 
is not thus complicated, 7. e., the arc in mer- 
cury vapor between mercury terminals. In 
this case only one element is to be considered, 
and here Arons* found that the greater fall of 
potential was at the anode. In the light of the 
work now described we may interpret this to 
mean that the positive ions in such an arc move 
the more rapidly. 
Warburg + found that in case of discharge in 
a vacuum tube containing some mercury vapor 
the fall of potential at the cathode was approxi- 
mately the same as it was in nitrogen. Arons 
in discussing this calls attention to the fact that 
when discharge is taking place through a gas 
the greater fall of potential is at the cathode, 
when through a metal vapor at the anode. 
Possibly we may now modify this statement 
and say that when gases are ionized the negative 
ions move the more rapidly, but that when metal 
vapors are ionized the positive ions move the more 
rapidly. All the facts that have thus far been 
observed could be explained by such a hypoth- 
esis. If this should be shown to be correct, 
it will no doubt lead us to modify somewhat 
our ideas concerning the relation of metals to 
electricity. 
C. D. CHILD. 
MODULUS OF CONSTANT CROSS SECTION. 
THE longitudinal rigidity of a solid, repre- 
sented by Young’s modulus, depending as it 
does upon both the volume elasticity and 
simple rigidity, leaves one condition unpro- 
vided for viz.: the case of longitudinal exten- 
sion with cross section remaining unchanged. 
This case probably does not occur with an un- 
restricted stress, but it is easily conceived in 
theory. I can find no mention anywhere of a 
modulus of constant cross section, and have 
undertaken to approach the problem in this 
wise. Addto Young’s modulus that fraction of 
the simple rigidity represented by Poisson’s 
ratio. This preserves the longitudinal rigidity 
and restores to the new modulus the numerical 
measure of that portion of the strain called 
out by the change in lateral dimensions. 
If this be a true modulus, it offers an easy 
*Wied. Ann., 58, 78. 
t Wied. Ann., 40, 10. 
SCIENCE. 
831 
method of determining approximately the 
mechanical equivalent of heat, and provides a 
practical experiment for laboratories not sup- 
plied with costly and complete apparatus. 
Thus a brass wire of density 8.5; sp. heat, of 
.09, coefficient of expansion .000018, volume 
elasticity 10 X10", simple rigidity 3.7 < 10", 
and Young’s modulus 10.4 10" gives roughly, 
[ 10.4 <Ige +e (Fs x 3.7 X 10") |3 < .000018 
8.5 <X .09 
3 
‘=41+ x 107 
as the value of the calorie in C. G.S. units. 
Bens. H. BRown. 
NOTES ON INORGANIC CHEMISTRY. 
WITHIN the past few years much has been 
added to our knowledge of the chemistry of the 
alums. To the aluminum, chromium, iron, 
gallium, and indium alums have been added 
those of titanium, vanadium, manganese, and 
cobalt. This completed the series of alums of 
the metals of the period from titanium to cobalt, 
but beyond this no alums were known of 
metals outside of the third group. In the last 
number of the Zeitschrift fiir anorganische Chemie 
Professor Piccini of Florence, the discoverer of 
the titanium and vanadium alums, has de- 
scribed a series of rhodium alums, including 
those of potassium, ammonium, rubidium, 
cesium and thallium. This is of peculiar in- 
terest, since rhodium belongs to a period in 
which no alums have been known, and opens 
the question as to whether there may be other 
alums in the same period, which includes mo- 
lybdenum and columbium. Picciniis at present 
endeavoring to form iridium alums, which the 
preparation of the rhodium alums makes seem 
possible. 
In a paper in the last Berichte of the German 
Chemical Society, on radio-active lead, Pro- 
fessor K. A. Hofmann of Munich and Eduard 
Strauss describe two new substances which ap- 
pear to be new chemical elements. Both are 
found in the lead chlorid obtained from pitch- 
blende, and are separated from the lead by 
fractional crystallization. The one substance 
possesses no radio-activity and resembles some- 
