482 
NATURE 
[ Marcu 21, 1907 
volts, and hysterical crises result. The patient 
alternately passionately repudiates her sexual instinets 
and brazenly asserts them. It is hard to imagine 
how a creature without memory or logic could per- 
form all the mental processes involved in this assimil- 
ation and repudiation. 
Weininger now turns on man. Woman is nothing, 
and therefore non-moral, not immoral; but man in 
his relations with her is always immoral. For he 
always regards her as a means to an end, and not 
as an end in itself; in sexual congress as the instru- 
ment of pleasure and physical reproduction; in love 
as the instrument of self projection and mental re- 
production; but woman is part of humanity, and 
must be regarded as an end in herself. The present 
writer, for one, fails to comprehend how a person 
who has no ego and is nothing can be regarded as 
an end in herself ! 
Specious and persuasive as our author shows that 
he can be, it is clear that he is very far from establish- 
ing his principle. The book is a remarkable one for 
the author’s years—he was only twenty-one when 
he wrote it—remarkable in the learning and thought 
which he brings to bear no less than in the large- 
ness of its conception and the breadth with which 
the matter is treated. It is brilliantly written, and 
contains at profound reflections and almost 
laughably unfounded statements of fact. It at 
times stimulating and suggestive, but, nevertheless, 
often irritating, because the central idea seems rather 
an obsession of a brilliant but inexperienced mind 
than a conception to which the writer has been driven 
by carefully considered facts. 
Weininger died by his own hand in 1903, and we 
are told by the friend who collected his posthumous 
papers that he felt within him criminal tendencies, and 
could no longer continue the struggle between these 
tendencies (Nichts) and his intelligible ego (All). 
once 
is 
Ie: 1\6 
SOME RECENT LOGARITHMIC TABLES. 
Tableaux logarithmiques, A et B. By Dr. A. 
Guillemin. Pp. 48 of explanation, with two tables 
35X35 and 46x35 cm. (Paris: 
Price 4 francs complete. 
Félix Alcan, 1906.) 
Clive’s Mathematical Tables. Pp. 49. (London: 
University Tutorial Press, Ltd., 1906.) Price 
Is. 6d. 
Five-figure Mathematical Tables for School and 
Laboratory Purposes. By Dr. A. Du Pré Denning. 
Pp. 21. (London: Longmans, Green and Co., 
1906.) Price 2s. net. 
R. GUILLEMIN’S two tables possess several 
interesting features. Taking, in the first place, 
Table A, which is used for working to six places of 
decimals, this contains the antilogarithms, calculated 
to six decimal places, of all decimals of three places 
from 0.000 to 0.999. In a third column are given 
the values of log «, corresponding to values of 
log (1+4), from 0.000000 to 0.000999. When it is re- 
quired to calculate logarithms to six places of 
decimals, the principle employed is as follows :—Let 
N@. 1951, VOL. 75] 
| N be the number the logarithm of which is re- 
quired, m the nearest number in the column of anti- 
logarithms, so that log m=log N to three places of 
decimals. Then if N=m(1+2) we have 
log N=log m+ log (1+2). 
By subtraction we find N—m, which is equal to ma. 
From the tables we can find by inspection log ma to 
three decimal places, and subtracting log m, which 
is known, we have log z to three decimal places. The 
table then gives log (1+2) to three significant figures, 
and these figures are the second three decimals to be 
written after log m in order to give log N to six 
places. 
In the second table (Table B) the values of the 
antilogarithms are given to nine places of decimals, 
and the values of log to six places. In each table 
the number of entries is one thousand, the logarithms 
With Table B, which 
measures 35 cm. by 46 cm., it is possible to calculate 
any logarithm to nine decimal places, but the work 
involves something more than a repetition of the 
process used for Table A. If, for example, it is re- 
quired to find log 7, there is no difficulty in obtain- 
ing the first six figures 0.845098, but the remainder 
to be operated on in order to fyid the next three 
figures cannot be got until we have worked the 
whole thing backwards and calculated the anti- 
logarithm of 0.845098 to nine decimal places. 
It is not offen that logarithmic calculations have 
to be taken to nine decimal places, but if this has to 
be done the present method, which is very fully ex- 
plained by the author, avoids the use of cumbersome 
books of tables, and it will probably be found, with 
a little practice, not to tale much longer—perhaps 
not even to take so long as the interpolation methods 
which such books of tables would necessarily involve. 
The other tables under review .are good examples 
of a number of small tables which have been issued 
during the last few years with the object of saving 
elementary students in mathematics, as well as 
students in physics and chemistry, from the tedious 
work of looking out seven-figure logarithms in the 
large ‘‘ Chambers.’’ It has been felt for a long time 
past that working with four figures is sufficient for 
teaching purposes; on the other hand, the student of 
experimental science often requires the additional 
accuracy obtained by an extra decimal place. But 
though several cheap books of four-figure tables have 
been issued during the past few years, we had to 
retain ‘‘Chambers’”’ for teaching and examining. 
junior students until about four months ago, as none 
of the other books we saw contained what was neces- 
sary. One contained natural sines and cosines, but 
not their logarithms; another contained natural and 
logarithmic sines, but no cosines. 
Junior students are very fond of using natural sines 
when they ought to learn to use their logarithms. 
They invariably get inaccurate results by clumsy 
methods, and it would not be a bad plan to remove 
the tables of natural sines from the books supplied 
for examinations. 
The proper arrangement for a table of trigono- 
going from 0.000 to 0.999. 
