JUNE 27, 1912] 
account of the destructive eruption on January 30, 
1gt1, which Mr. Dean Worcester, Secretary of the 
Interior of the Philippine Islands, contributes to The 
National Geographic Magazine for April. The 
splendid collection of photographs procured at serious 
risk of life gives a most realistic picture of this great 
disaster. Even now it is dangerous to approach the 
neighbourhood of the volcano, and as since the erup- 
tion the waters of Bombon Lake have been flowing 
into the crater, it is well within the limits of prob- 
ability that the map of Batangas province may at 
any time be suddenly and materially altered, and the 
people of Europe and America may again have an 
opportunity of observing some of the wonderful red 
sunsets which fotlowed the eruption of Krakatoa. 
An account of the Taal eruption appeared in NATURE 
of November 2, 1911 (vol. Ixxxviii., p. 12). 
Tue Swiss Earthquake Commission is one of the 
oldest bodies established for the observation and regis- 
tration of earthquakes, it having been founded in 
1878 by Profs. Forel, Forster, and Heim, though its 
actual work began with the year 1880. Dr. J. Frith 
has recently published a summary of the first thirty 
years’ work, together with a description of the seis- 
mological observatory at Zurich ( Verhand. der 
Schweiz. Naturfor. Gesell., vol. i.,, pp. 57-80). The 
total number of Swiss earthquakes recorded in this 
period is 998, or about 33 a year, the annual number 
ranging from 7 in 1900 to 174 in 1881. The shocks 
are subject to a strongly marked annual variation 
in frequency, with its maximum epoch about the end 
of January. So far as can be judged from a some- 
what confused map on which the disturbed areas of 
more than 200 earthquakes are laid down, earth- 
quakes visit nearly all parts of the country, but seem 
especially concentrated towards the west and east 
ends. The disturbed areas seem for the most part to 
be elongated in the directions of the mountain-chains. 
In a note contributed to the Atti dei Lincei, xxi. 
(1), 7, Prof. G. Peano criticises the ordinary definition 
of probability, according to which the probability of 
an event is measured by the ratio of the number of 
ways in which it happens to the total number of ways 
in which it either happens or fails. This definition 
implies the assumption that all the different ways 
NATURE 
431 
construction for a fourth proportional, which enables 
any polynomial to be built up by suitably varying 
the segments representing the coefficients. In sub- 
sequent paragraphs, Dr. Muirhead describes modifi- 
cations suitable for solving simultaneous equations. 
Imaginary roots of an equation of degree n are to be 
got by finding an appropriate related equation of 
degree 3n(n—1); for example, the equation for the 
squares of the differences of the roots would be useful. 
Pror JosEPH BowbDeN has published a short note 
read before the American Mathematical Society on 
the Russian peasant method of multiplication, 
which is said to be in use in many villages in Russia. 
The method involves the operations of doubling, 
halving, and adding, but it requires no use of the 
ordinary multiplication table. It practically depends 
on expressing one of the factors in the binary scale 
of notation and multiplying the other factor by suc- 
cessive doubling. If we want to multiply 45 by 24 we 
divide 45 repeatedly by 2, obtaining 45, 22, 11, 5, 2, I, 
and against these numbers write the successive 
doubles of 24, thus, 24, 48, 96, 192, 384, 768, then 
we add together all the terms of the: second series 
standing opposite odd numbers of the first series (thus 
omitting 48 and 384), and their sum is the required 
product. The rule scarcely needs any further proof, 
and, we may add, can be used to multiply numbers 
| expressed in Roman numerals. 
Tue May number of the Journal de Physique, pub- 
lished by the French Physical Society, contains forty- 
five pages of memoirs and thirty-three pages of 
abstracts of important physical papers which have 
appeared elsewhere. The first section includes the 
address by Prof. Poincaré on the relations between 
matter and ether delivered to the Society on April 11, 
and that by M. Charles Maurin on recent researches 
in aérotechnics and aérial navigation. Of the abs- 
tracts, sixteen are from the March and April numbers 
of the Comptes rendus, eight from the April number 
of The Philosophical Magazine, ten from the March 
and April numbers of the Annalen der Physik, nine- 
teen from the Physikalische Zeitschrift of the same 
| dates, and thirteen from the Zeitschrift fir physikal- 
are equally probable, and thus assumes the concep- | 
tion of probability which it is attempted to define. 
Dr. Peano proposes a symbolic definition in the nota- | proceedings, but in matters of interest to physicists 
prop J Pp g pay 
tion of mathematical logic, which, being interpreted 
in words, is as follows :—If a and b are classes, and 
the total number of class a is finite, the symbol 
P(b, a) denotes the number of a that are b divided 
by the total number of a. 
Many devices have been proposed for finding the 
real roots of algebraic polynomial equations by 
graphical or mechanical methods. A novel form of 
mechanism based on principles resembling those em- 
ployed by Lagrange and Sequier is described by Dr. | 
R. F. Muirhead in the Proceedings of the Edinburgh | 
Mathematical Society, xxx. (1911-12). The principle 
is based on repeated applications of the geometrical 
NO. 2226, VoL. 89| 
ische Chemie, from December, 1911, to April,. 1912. 
It is clear from these facts that the Journal de 
Physique keeps the members of the French Physical 
Society well up to date, not only in regard to its own 
| which occur in the world outside. 
THE Institute of Metals has just published the 
seventh volume of its Proceedings, a book of 382+ ix 
pages, in addition which there are twenty-two 
full-page plates, and a frontispiece reproduced from 
a photograph of the president of the institute, Prof. 
W. Gowland, F.R.S. The major portion of the 
volume consist of a series of papers of scientific in- 
terest, which were read at the annual general meeting 
of the institute held in London in January last, of 
which summaries appeared in Narure of January 25 
(p. 427). The presidential address dealing with the 
subject of ‘‘Copper and its Alloys in Early Times,” 
to 
