240 
NATURE 
[APRIL 29, 1915 


directing attention to the mineral wealth of the 
Dominion and of assisting all who may be inclined 
to take part in its development. A compact summary 
of the subject is to be found in a pamphlet of some 
eighty pages, ‘‘ Economic Minerals and Mining Indus- 
tries of Canada,” which has been prepared especially 
in view of the Panama-Pacific Exposition of San 
Francisco. It contains indeed no particularly novel 
features, but brings the subject well up to date. 
Messrs. H. T. Kalmus and C. Harper have published 
the second portion of their researches upon cobalt and 
cobalt alloys, this part dealing more particularly with 
the physical properties of the metal cobalt. Elaborate 
tests have been made, and are recorded with much 
minuteness of detail; it might be suggested that the 
full plate illustration of the testing machine used in 
making the tensile tests is decidedly superfluous. An 
elaborate report is published by L. H. Cole upon 
gypsum in Canada, From the technical point of view 
this appears to give all the necessary information, 
but somewhat more attention might have been devoted 
to the geological problems involved; thus there is no 
mention of the accessory minerals, such as the native 
sulphur and the borates, the existence of which in 
some of the Nova Scotian gypsum deposits has long 
been known, and which shed a very interesting light 
upon the probable mode of origin of these deposits. 
The third part is also issued of the Report on the 
building and ornamental stones of Canada, this deal- 
ing with the province of Quebec. This report also is 
very rich in detail, and contains much valuable in- 
formation; attention may be directed to the beautiful 
coloured plates illustrating the appearance of some of 
the more notable of the ornamental stones, which 
are admirably executed. 
In the Tohoku Mathematical Journal, vi., 2, 3, 
Mr. Kichiji Yanagihara, of Sendai, discusses the 
history of the Pythagorean equation connecting the 
sides of a right-angled triangle in Japanese mathe- 
matics. Methods of obtaining integral solutions of 
this equation were given by Matsunaga (eighteenth 
century), Ammei Aida (1747-1817), who gave a table 
of the first 292 primitive solutions, Sh6z6 Kilkuma, 
Tanehide Chipa (1830), and Séhei Kaneko (1845). The 
theorem of Pythagoras was in constant use in Japanese 
mathematics, and many wasanists gave their demon- 
strations in their works, but owing to the lack of sys- 
tematic establishment of geometry many of their 
demonstrations are found to resemble that of Bhas- 
kara’s ‘‘ Behold’? method in his Vija Ganita. 
Ir is easily shown that the ordinary linear differen- 
tial equation of the first order between two variables 
represents a family of curves such that the tangents 
at all points having the same abscissa pass through 
a fixed point on an associated curve S. This method 
was used by Czuber to obtain an approximate graphi- 
cal solution of the equation by building up the curve 
out of consecutive small elements much after the 
fashion of the common construction for the logarithmic 
curve. In the Science Reports of Tohoku Imperial 
University III., 6, Mr. Tetsuzé Kojima gives a method 
of obtaining a better approximation than that afforded 
by the original construction, and further employs 
NO. 2374, VOL. 95] 

| graphic methods of a similar character to the approxi- 
mate solution of certain other first-order equations, 
including the general equation of the first order and 
second degree. 
THE majority of recent researches on thermal radia- 
tion deal exclusively with stationary phenomena such 
as occur in a field when it has attained a state of con- 
stant temperature. In a note communicated to the 
Atti dei Lincei, xxiii, (2), 9, 10, Prof. T. Levi Civita 
has formulated a scheme applicable to the case of a 
, Variable field subject to given arbitrary initial and 
boundary conditions. The investigation is based on 
the assumption that energy of radiation is propagated 
with constant velocity, but that the specific intensity 
of radiation across any surface is not only a function 
of the temperature, but depends also on the direction 
of the surface. This hypothesis is necessary in order 
a cold region, Levi Civita represents this effect 
by the addition of a term in the expression for the 
intensity containing aS a factor the temperature gradi- 
ent along the direction of the normal. The analytical 
work leads to the deduction of an equation closely 
resembling that applicable to conduction of heat in a 
variable medium. 
Tue April number oi Science Progress contains an 
article by Mr. F. Hyndman in which the recent work 
of Prof. Kamerlingh Onnes and his pupils on the 
high electrical conductivity of metals at very low tem- 
peratures is summarised. In the case of mercury the 
conductivity at 2-5° absolute is 10’ times as large 
as at the freezing point of water, but Ohm’s law no 
longer holds—the electromotive force required to drive 
the current increases a thousandfold for a 10 per cent. 
increase in the current. If the metal is tested in a 
magnetic field a small increase in the field may pro- 
duce a similar large increase in the resistance. Dr. 
C. Davison, in another article, points out that increase 
of seismic disturbances along a geological fault may 
herald a serious earthquake and that attempts should 
now be made to foretell earthquakes in this way. In 
a further article Dr. J. Johnstone shows the useless— 
ness of considering the organism as a thermodynamic 
mechanism, since it is continually arresting the in- 
crease of entropy which goes on in inorganic bodies. 
In an essay review of mathematical text-books the 
author directs attention to the need of mathematical 
books which will help men of science to use mathe- 
matics without having to wade through the present- 
day text-books, which seem only intended for the use 
of schoolboys and undergraduates. 
Pusiication No. 9 of the Central Meteorological 
and Geophysical Institute of Chile consists of a dis- 
cussion by Dr. Walter Knoche of the Hertzian waves 
recorded at San Carlos de Ancud in 1913. The wire- 
less apparatus employed gives a continuous record 
from which the number of Hertzian waves, or atmo- 
spherics, can be enumerated. Assuming the apparatus 
equally sensitive throughout the whole period, and 
the nature of the atmospherics always the same, the 
| daily and monthly totals show remarkable variability. 
\ July had more than 16,900 occurrences, the total for 

to account for the. transference of heat from a hot to 
