Fesruary 18, 1897 | 
NATURE 
383 
a square one is vacant. The 6 square beds thus become occu- 
pied, and an octahedron of 19 balls is formed, each plane face of 
which is an equilateral triangle of 6 balls with 3 in each edge. 
Each triangular face presents 4 triangular beds, of which the 
middle one is shallow, and the 3 around it deep (tried with a 
probe pin). There being now no square beds, wandering 
molecules take triangular beds; but the rule (to make the 
whole assemblage homogeneous and equilateral) must be that 
only deep triangular beds are eligible. Thus procedure 
according to rule adds 24 balls, and we have a cluster of 43 
balls (model shown), which presents 2 kinds of triangular or 
3-contact beds and 12 equal and similar 5-contact beds, but 
no square beds. The 12 5-contact beds are next to be filled. 
These give us a cluster of 55 balls (model shown), presenting 
6 square faces of 9 balls, with 4 square beds, and 8 triangular 
faces of 6 balls each. The 24 square beds are next to be 
filled, and we have a cluster of 79 balls presenting 6 square 
beds. The next action, according to rule, fills these, and gives 
us a regular octahedron of 85 balls, with 15 balls in each face and 
5. in each edge. Each triangular face contains 16 triangular 
beds, of which 10 are deep and 6 shallow. To continue the 
crystallisation, we may suppose all the deep triangular beds 
equally eligible; and any one of them may be taken by a 
molecule deposited from the solution, and any one of the 6 
equal and similar q-contact beds between it and neighbours 
may be taken next. We shall never find any 6-, 7-, 8-, or 
g-contact beds formed if the following rule is rigorously 
observed in continuing the crystallisation. Five-contact beds 
must be occupied when any are vacant. When none of these 
remain, 4-contact beds must be occupied, and whenever no 
5-contact or 4-contact beds remain, we shall find that we have 
a regular octahedron. To continue the crystallisation, any one 
of the deep triangular beds may be taken by a wandering 
molecule, and the process continued rigorously according to 
rule. The formation of garnet (rhombic dodekahedron) was 
illustrated on similar principles by cubic molecules cohering 
by attractions between ‘‘corners” and relatively oriented by 
quasi-repulsions between edges. Definite laws of force between 
molecules are suggested, according to which an ideal ‘‘ com- 
plete’” crystal of anorthic system, or of any system possessing 
symmetry, would be a figure of minimum potential energy, and 
would be of perfectly determinate figure. The number of such 
configurations would be infinite if the number of molecules 
were infinite; but practically for a crystal in nature the 
number that could probably occur might be hundreds, or might 
be only one. And fhe one configuration of absolutely least 
potential energy would be a perfect crystal of unique quality. 
PaRIs. 
Academy of Sciences, February 8.—M. A. Chatin in the 
chair.—On fictitious waterspouts, by M. H. Faye. It is con- 
tended that the name of waterspout (¢7oe) has been given to 
two quite distinct phenomena solely on account of their ex- 
ternal resemblance. The true waterspout is in rapid rotation 
destroying whatever it touches, has a definite direction, moves 
with a high velocity, has no aspirating power, and comes from 
above. The false waterspout is distinguished by having a small 
and uncertain rotation, no definite course, aspirating and ascend- 
ing movement, and also by the fact that its source of motion is 
at its base, on the earth.—New researches on the estimation of 
pyrophosphoric acid, by MM. Berthelot and G. André. The 
pyrophosphate is precipitated as the magnesium salt by a mix- 
ture of magnesium chloride, ammonium acetate and chloride, in 
the presence of a large excess of acetic acid. © The precipitate 
thus obtained is of complex composition containing sodium and 
ammonium in addition to magnesium. The composition of the 
precipitate, moreover, appears to depend upon the amount of 
washing it has received.—Some historical remarks on metaphos- 
phoric acid, by MM. Berthelot and G. André.—The reduction of 
nitrates in arable earth, by M. P. P. Deherain. As the result 
of the study of the destruction of nitrates in aqueous solutions 
by denitrifying organisms present in manure, it isshown that the 
treatment of farm manure with dilute sulphuric acid, previously 
recommended as a means of destroying denitrifyng organisms, 
is not only expensive, but is, moreover, useless and harmful.— 
Results of the solar observations made at the Royal Observatory 
of the Roman College during the second half of 1896, by 
M. P. Tacchini.—On the zeros of certain analytical functions, 
by M. Desaint.—On the comparison of the times of oscillation 
NO. 1425, VOL. 55 | 
of two pendulums of very nearly the same period, by M. G. 
Bigourdan. A. modification of the arrangement described by 
M. Lippmann, in which the pendulum clock is replaced by a 
chronometer, and in which no electrical apparatus is required. 
—On a new measurement of the coefficient of viscosity of air, 
by MM. Ch. Fabry and A. Perot. In the absolute electro- 
meter, described a short time ago, equilibrium was found to be 
only very slowly attained when the distance between the plates 
was very small (below 75 “), on account of the viscosity of the 
air between the plates. The experimental study of the motion 
produced by the addition of a small surplus charge on the centre 
of the moving plate has led toanew determination of the coefficient 
of viscosity of air, 1°73 x 1074 at 13° C.—Study of the variations 
of energy, by M. Vaschy.—On the principle of Avogadro- Ampere, 
considered as a limited law, by M. A. Leduc.—On the am- 
moniacal chlorides of silver, by M. R. Jarry. It is shown that 
solutions of silver chloride in ammonia contain the definite 
compounds AgCl.3NH, and 2AgCl.3NHs3, and the dissocia- 
tion pressure of the ammonia is the same in aqueous solu- 
tion as in a vacuum.—On some colour reactions, by M. E. 
Pinerua. Some colour reactions obtained by the use of 
£-naphthol-sulphonic-acid. Tartaric, citric, malic, and nitrous 
acids give characteristic reactions. —On a new method of prepar- 
ing primary amines, by M. Marcel Delépine. The alkyl 
chloride, bromide, or iodide is combined with hexamethylene 
amine, in presence of chloroform, and the product hydrolysed 
with aqueous hydrogen chloride. —Improvements in the match 
industry, with especial reference to the health of the operatives, 
by M. Magitot. The ameliorative measures proposed depend 
upon a good artificial ventilation, and a careful selection of the 
operatives, especial stress being laid on the necessity of the 
latter having no unsound teeth.—On the estimation of potassium 
bitartrate in wines, by M. Henri Gautier.—On the essence of 
basil, by MM. Dupont and Guerlain.—The argon and_ nitrogen 
in the blood, by MM. P. Regnard and Th. Schleesing. The gases 
obtained from a litre of blood gave 20°4 cc. of argon and nitrogen, 
0°42 cc. of which was argon.—On the colours of irradiation in 
short luminous impressions, by M. Aug. Charpentier.—On a 
new method of electrification, by M. Charles Henry.—Research 
on the evolution of the Urzes, by MM. J. Kunstler and A. 
Gruvel.—On the gum disease of the cocoa plant, by M. Louis 
Mangin.—On an apparatus for measuring the refractive indices 
of minerals in rocks, by M. Fred Wallerant.—-On the granite of 
Pelvoux, by M. P. Termier.—Generalisation of a formula in 
probabilities, by M. C. Maze. 
SYDNEY. 
Royal Society of New South Wales, December 2, 
1896.—Mr. J. H. Maiden, President, in the chair.—On the 
presence of a true manna on a “‘blue grass,” Andropogon 
annutatus, Forsk., from Queensland, by R. T. Baker and Henry 
G. Smith. The substance is found on the nodes of the stems 
in masses as large as marbles. This appears to be the first 
time that a substance of this character has ever been described 
from a grass. Not only is the grass indigenous in Australia, 
but occurs in tropical Asia and Africa. The manna is sweet, 
and nearly three parts of it consists of the substance 
mannite, which, although sweet, is not a sugar. Besides the 
presence of this interesting substance, a peculiar ferment was 
discovered in the manna, which apparently has the power 
to decompose cane-sugar without the evolution of carbonic 
acid or gases of any kind. It probably belongs to the Sacchoro- 
mycetes, and is allied to the ferments of which the yeast plant 
isa type. It has been isolated from the manna, and was shown 
at the Society working in a solution of cane-sugar, and also 
under the microscope. The investigations are not yet com- 
pleted ; but, so far, it appears to be probably the cause of the 
occurrence of the mannite in the manna, and not only has it the 
power to alter cane-sugar to mannite, but, with the assistance 
of yeast, to decompose mannite also—a fact of no little interest. 
—Remarkable hailstorm of November 17, 1896, in parts of 
parish of Gordon, by E. du Faur—On the determination of the 
meridian line by solar observations with any altazimuth instru- 
ment, by G. H. Knibbs. The paper dealt with the rigorous. 
mathematical theory of the subject ; tables and formule, for 
| facilitating the reducing of this class of observations with pre- 
cision, were supplied. The astronomical conditions of good 
results were fully dealt with, the matter being of considerable 
importance in practical geodesy. 
