202 
——_—_—_———— ee 
For Book iv. we find the proposal ‘that all proposi- 
tions be omitted, as formal propositions, except 2, 3, 4, 
5, 10, and that these be taken with earlier books, the rest 
of the book being treated as exercises in geometrical 
drawing.” 
Coming to Book vi., it is recommended “that an 
ordinary school course should not be required to include 
incommensurables ; in other words, that in such a course 
all magnitudes of the same kind be treated as com- 
mensurable.” This at once relieves teachers from an 
enormous task—that of explaining Euclid’s definition of 
proportion. There is now nothing to be said beyond 
that the ratio of ato 4 is the fraction a/. To meet this 
change, two alternative proofs are given for vi. 1, 
though attention is called to the continental practice of 
making the proof of vi. 2 self-supporting. 
With regard to areas, the tendency of the report is to 
make the treatment algebraic. Euclid vi. 14, 15, 16, 
17,°23 contain merely the one fact that the area of a 
parallelogram is ad sin @; nothing is gained by con- 
cealing this fact from the student. It is definitely sug- 
gested that “numerical” trigonometry shall be taught 
concurrently with Book vi. ‘In connection with the 
formal course, as soon as the proposition that equiangular 
triangles are similar has been proved, the sine, cosine 
and tangent can be defined (if this has not been done 
earlier in the experimental course). In order to make 
the meanings and importance of these functions sink 
deeply into the pupil’s mind, numerical examples should 
be given on right-angled triangles (heights and distances) ; 
these should be worked with the help of four-figure 
tables.” 
“Tn accordance with the spirit of the above proposals, 
the committee suggest that the following proposition be 
adopted :—If two triangles (or parallelograms) have one 
angle of the one equal to one angle of the other, their 
areas are proportional to the areas of the rectangles 
contained by the sides about the equal angles.” 
“ All statements of ratio may be made in fractional 
form, and the sign = used instead of the :: sign. In the 
ordinary school course reciprocal proportion should be 
dropped, and compounding replaced by multiplying.” 
The report may be described as an attempt, on con- 
servative lines, to simplify the study of geometry and to 
make it interesting. If the attempt is judged to be 
successful, now is the time to make examiners unstop 
their ears. G..G: 
SEISMIC FREQUENCY IN JAPAN. 
N no country has seismology been more carefully 
nurtured than in Japan. At the University we find 
a professor and assistant professor of this branch of 
science ; in the Meteorological Department there is a 
bureau controlling more than 1000 observing stations, 
and, lastly, there is a committee composed of engineers, 
architects and men of science who, as an aid to carrying 
on investigations which will lead to a better understand- 
ing of earthquake phenomeng, are supported by a 
‘Government grant. 
This body, since its establishment eleven years ago, 
has already published thirty-six quarto volumes in 
Japanese and eight in English, and it is to the last of 
these, by Dr. F. Omori, professor of seismology, to 
which we now refer. Unlike many of the volumes by 
which it is preceded, which treat of construction to 
resist earthquake effects and kindred branches of applied 
seismology, this particular publication deals with ques- 
tions which are purely scientific. Its title is ‘“ Annual 
and Diurnal Variations of Seismic Frequency in Japan,” 
the investigation of other periodicities being left for 
a future occasion. 
NO. 1704, VOL. 66] 
NATURE 
“may. practically be divided into two groups. 
[JUNE 26, 1902 
The materials analysed are 18,279 entries contained 
in earthquake registers from twenty-six meteorological 
stations which are distributed in a fairly uniform manner 
over the Japanese Empire. These registers, which for 
the most part are dependent on instrumental observation, 
are discussed separately, and it is in consequence of 
this method of treatment that conclusions new to 
seismology have been reached. 
The first out of a series of seventy-six curves shows 
the monthly frequency of earthquakes in Tokio. In 
plotting this, as in plotting curves for other stations, 
those months where the ordinary seismic frequency has 
been affected by “‘after shocks” have been Gmitted ; that 
is to say, the curves represent the normal frequencies 
in various districts. These omissions, all of which 
refer to the settlements which follow destructive earth- 
/ quakes, are carefully epitomised. Dotted curves drawn 
through the mean position. of monthly curves show 
annual and semi-annual periods. A comparison of the 
curves for seasonal seismic frequency shows that these 
In one 
group the maximum frequency is in winter, whilst in the 
other group the maximum frequency isin summer. When 
we turn to the geographical distribution of the stations 
the records from which give these curves, it is found 
that they are distributed over two distinct areas—those 
which show a winter frequency lie ina district chiefly 
shaken by earthquakes having an inland origin, whilst 
those where the greater number of disturbances are noted 
in summer occupy anarea shaken by earthquakes having 
a suboceanic origin. 
In an endeavour to explain this striking result, the 
annual, monthly and diurnal frequencies are compared 
with corresponding fluctuations in barometric pressure. 
The general result arrived at is that the curves showing 
the winter frequency follow those of changes in baro- 
metric pressure, from which it may be inferred that an 
increase in barometric pressure has a marked effect upon 
the yielding of a land area. With the curves relating to 
earthquakes of suboceanic origin, it is seen that the 
annual variation is the reverse of the barometric pressure 
on Jand. 
With regard to diurnal variation in seismic frequency, 
Dr. Omori concludes that this is probably due to 
corresponding variations in atmospheric pressure, but 
such frequency is not confined to earthquakes originating 
on the land. Single barometric fluctuations, even if they 
amount to 20 mm., are not generally related to any 
marked increase in seismic frequency. 
Although the last two observations apparently contra- 
dict the more important result indicating a relationship 
between fluctuations in barometric pressure and the 
seasonal frequencies of earthquakes originating beneath 
the sea and on the land, arguments are adduced to show 
how such contradictions may be harmonised. 
The distinction in the rules which governs the frequency 
of earthquakes with these distinctive origins, now brought 
forward for the first time, may probably be emphasised 
when, rather than analysing the registers from different 
stations—the entries in which may frequently be common 
to a number of such stations—an analysis is made of 
registers of earthquakes classified according to their 
origins. As illustrative of such materials we may refer 
to a catalogue of about 9000 shocks, published as vol. iv. 
of the Sezsmological Journal of Japan, in which each 
entry is referred to a district from which the shock it 
represents may have originated. y 
In conclusion, not only do we congratulate Dr. Omori 
on this new departure in seismology, but we also con- 
gratulate the Earthquake Investigation Committee on the 
admirable manner in which it has presented its results 
to those outside the pale of eastern ideography. 
J. MILNE. 
ee = 
