May 14, 1914] 
NATURE 
277 
tion of unexplained differences which occasionally exist 
in the indications of ordinary and _ self-registering 
rain gauges. The report is accompanied, as in pre- 
vious years, by several interesting scientific papers. 
One of these, by Dr. Hellmann, ‘‘On the determina- 
tion of air temperature,” bears particularly on the re- 
cent discussion on that subject in this country 
(Nature, April 9, p. 143). Comparisons of readings 
in a ‘*Stevenson’”’ screen with those of an aspiration 
thermometer showed that on a sunny day the tempera- 
ture by the latter might change more than ign OF 
within a minute, while the readings in the screen 
are not so quickly affected by sudden changes. The 
results seem to indicate, as was also inferred by Dr. 
J. Aitken, that the screen readings give trustworthy 
mean values for short intervals (say two to three 
minutes); a closer agreement than this in the time 
of observing, as Dr. Hellmann remarks, can scarcely 
be expected. 
A new form of Gauss’s principle of least constraint 
forms the subject of a short note by Dr. H. Brell, of 
Graz, in the Vienna Sitzungsberichte, vol. cxxii., 
p. 7, in which the author obtains a single formula 
for Appell’s equations. 
An addition to the numerous tables of logarithms 
and anti-logarithms that have been published by 
various writers for special purposes is the ‘‘ Table 
auxiliaire d’Intéréts composés” of M. A. Trignart 
(Paris: Gauthier-Villars, 1914, price 2 francs). This 
table gives the various powers of the base, 1-001, 
for all integral indices from 1 to 1000, for 
indices in ‘‘thousands’’ from 1000 to 100,000, 
and for the ten indices completing the range 
from 100,000 to 1,000,000. In the first two tables the 
anti-logarithms to this base are calculated to fifteen 
decimal places. Those in the third table are given to 
twenty significant figures. It will be observed that 
to all intents and purposes these anti-logarithms differ 
from those of the natural system of logarithms in that 
the fundamental base differs from unity by 1 in 10,000 
instead of by an infinitesimal quantity; at the same 
time it would appear that a similar difference existed 
in the case of the original logarithms of Napier. The 
present table is obviously adapted to meet require- 
ments of a special character, such as might perhaps 
occur in actuarial computations. 
AMONG the reports of recent investigations at the 
Imperial Institute the first quarterly issue of vol. xii. 
(1914) of the Bulletin includes papers on the little- 
known economic products of Somaliland, and on the 
composition of monazite, which is used extensively 
in the manufacture of incandescent gas mantles. An 
illustrated article describes an important plant of 
rubber-testing machinery set up at the Institute for 
the purpose of carrying out a systematic investiga- 
tion of samples of plantation Para rubber specially 
prepared in Ceylon in different ways, in order to 
secure accurate data for comparison. <A note of 
agriculture in the Gold Coast states that the cultiva- 
tion of cocoa is still being extended, and that the 
crop in 1913 was valued at nearly two and a half 
millions sterling. The interesting fact, probably not 
commonly known, is stated that more than one-third 
NO. 2324, VOL. 93] 
of the world’s production of cocoa is produced under 
the British flag. 
In part vi. of the Verhandlungen of the German 
Physical Society Dr. F. A. Lindemann shows how the 
simple method of dimensions may be applied to the 
construction of atomic models which shall have many 
of the properties of the actual atoms. Taking the 
frequency of the electronic oscillations in such an 
atom to depend only on the distances between the 
negative and positive charges, the mass of the carriers 
of the charges, the force between the charges at unit 
distance apart, and on Planck’s constant h, he shows 
| that if the frequency is proportional to the nth 
power of the force, it must also be proportional to 
the (n—1)th power of the mass, the (n—2)th power of 
the distance and to the (1—2n)th power of h. Taking 
n in succession equal to 0, 1, and 2, he shows how far 
the model will represent the behaviour of an actual 
atom without further hypothesis, and what additional 
hypotheses must be brought in to reproduce given 
atomic properties. In this way he arrives at the 
relations previously given by Balmer, Moseley, Bohr, 
Gehrcke, and others, as holding for the actual atoms. 
Tue flow of sand and other fine materials through 
openings of various shapes and in different circum- 
stances is not 2 subject which has received much 
attention from experimentalists, although it is of con- 
siderable practical importance. We welcome therefore 
the recent work of Prof. E. A. Hersam, of the Uni- 
versity of California, on sands of various degrees of 
coarseness, on crushed slate, crushed shale, mustard 
seed, and lead shot. From Prof. Hersam’s paper in 
the April number of the Journal of the Franklin Insti- 
tute we gather that the following are his principal 
results. The velocity of flow is determined mainly 
by the size of the particles and of the opening, but 
is slightly diminished by angularity of the particles 
or by moisture on them. The specific gravity of the 
particles, the height of the material above the open- 
ing, and the shape of the upper contour of the mate- 
rial have little effect. If D is the diameter of the 
opening, d that of the particles, both in inches, the 
mean velocity of flow V in feet per second is given 
with sufficient accuracy for most practical purposes 
by the equation, V=(D—2d)/¥7D. 
WE have received a report by Prof. Ph. A. Guye 
on the unification of the bibliographic abbreviations in 
chemical memoir: which was presented at the third 
session of the council of the ‘Association inter- 
nationale des Sociétés chimiques,” held at the Institut 
Solvay at Brussels in September, 1913. The author 
points out the inconvenience which arises from the 
same periodical being represented by several different 
abbreviations, and suggests that a uniform system 
should be adopted by scientific societies and by authors 
of chemical works. It appears there are only two 
systematic methods at present in use, namely, those of 
the Internationa! Catalogue of Scientific Literature 
and of the Conciiium Bibiiographicum de Zurich. 
Neither of these lists is complete, but the author is 
in favour of adopting the system of the International 
Catalogue, which is under the control of the Regional 
