320 

One is tempted, indeed, to go on quoting Samuel 
Butler, who, whatever the quality of his rhymes, 
summed up the truth of this matter in a few caustic 
passages. For language adequate to describe the 
obscurity and tedium of such books one would need 
the powers of a Swift or a Pope. 

Our Bookshelf. 
(1) A New Manual of Logarithms to Seven Places of 
Decimals. Edited by Dr. Bruhns. Thirteenth 
Stereotype edition. Pp. xxiv+6r1o. (London: 
Chapman and Hall, Ltd., 1922.) 12s. 6d. net. 
(2) Tables of 1-1? and 1-7? for Use in Partial 
Correlation and in Trigonometry. By Dr. J. R. 
Miner. Pp. 49. (Baltimore, Md.: The Johns 
Hopkins Press, 1922.) 1 dollar. 
(3) Two-figure Tables. Compiled by C. R. G. Cosens. 
On Card, 10 in. x 4% in. (Cambridge: Bowes and 
Bowes; London: Macmillan and Co., Ltd., n.d.) 
6d. Quantities of one or more dozens supplied at 
4s. per dozen. 
(1) Tue first table in this edition of Dr. Bruhns’ 
Manual is a reprint of Kohler’s table of logarithms of 
integers from 10000 to 100000, covering 180 pages. 
Auxiliary tables of proportional parts at the side of 
each page give all necessary assistance to a computer 
in finding the logarithms of six- and seven-figure 
numbers. LEight-figure logarithms of integers between 
roocco and ro80co are not given, as in the original 
Kohler and the modern Chambers, “ since the addition 
of logarithms of numbers from rooo0o to 108000 does 
not appear to offer a sufficient advantage.” With 
this we do not agree. Eight places of decimals in 
logarithmic work in dealing with numbers that slightly 
exceed 1:0 are only equivalent to seven places for 
numbers in the neighbourhood of g:o. Within recent 
years the present reviewer was engaged in computing 
work in which the eight-figure logarithm was essential 
for numbers just greater than 1-0. In fact it was only 
regretted that the eighth figure was not available from 
100000 tO II5000. 
There follow tables of the logarithms of sin x, cos x, 
tan x, and cot x, the entries being given at intervals 
of one second from x=o° to x=6°, and at ten-second 
intervals from 6° to 45°. In the latter range six pages 
are assigned to each degree of arc, whereas one page is 
given to each minute from o’ to 10’. The tables of 
differences and proportional parts on each page give 
every help needed in interpolation. 
A few minor tables are added to the above main 
ones. The tables on each page are set out in an 
attractive way, and the new edition will be found to 
be a very serviceable one. 
(2) The tables in this pamphlet give the numerical 
values of ,/(1—r*) and 1-7? to six decimal places for 
values of r between o-o and 1:0 at intervals of o-o0o0r. 
Differences and subsidiary tables for interpolation are 
not appended. Thus the table gives the consecutive 
entries 
,/(1—1?) =0°567026 when r=0°8237, 
J/(a — 7?) =0°566881 when r=0:8238, 
NO. 2784, VOL. 111} 
WNATORE 
[Marcu 10, 1923 
and a slide-rule calculation is necessary to evaluate the 
function when 7 =o: 8237463. 
The tables were ‘calculated with a view to their 
bearing on partial correlation coefficients: they serve 
equally to determine cos @ and cos? @ from sin 6 by a 
single reading. bo 
(3) On the two sides of this card are printed the 
numerical values of sixteen functions, x2, x3, ./x, 9/x, 
xi, 1/x, logyy x, loge x, e*, e~*, Sin x, Cos x, tan x, sinh «, 
cosh x, and tanh x, the intervals for « being o'r between 
o-o and 50, and o-5 between 5:0 and roo. In tabulat- 
ing the circular functions, « is measured in radians and 
not in degrees. Except in special cases two-figure 
accuracy is retained throughout. This amount of 
accuracy is sufficient for plotting many elementary 
graphs for the purpose of which the card is primarily 
intended. WES Des 
Essai d’optique sur la gradation de la lumiére. Par 
Pierre Bouguer. (Collection ‘‘Les Maitres de la 
Pensée scientifique.”) Pp.xx+130. (Paris: Gauthier- 
Villars et Cie, r921.) 3 francs. 
PIERRE BoucuER was born at Croisic in 1698. At 
an early age he was initiated in mathematics and 
problems of navigation by his father, who was one of 
the best hydrographers of his time. When only 
fifteen years of age he occupied the chair of his father, 
who had just died, and afterwards distinguished 
himself by his researches in physics, astronomy, and 
navigation. He is remembered to-day principally 
by his work on photometry, and by his expedition to 
Peru in 1735 to carry out a measurement of a degree 
of latitude, thus contributing to the solution of the 
important problem of the figure of the earth. It was 
during this expedition that he obtained an estimate 
of the mean density of the earth from pendulum 
observations in the neighbourhood of Chimborazo. 
The present essay, in which he laid down the funda- 
mental bases of the science of photometry, is repro- 
duced from the original text of 1729. The author 
discusses methods of measuring the intensity of light, 
the manner in which the intensity is changed by reflec- 
tion or by absorption, and explains how to calculate the 
diminution in the intensity after the light has pass 
through various thicknesses of the absorbing medium. 
His work is distinguished by its clarity and the masterly 
realisation of the essential points in the problem to be 
solved. 
The Internal Combustion Engine: a Text-book for the 
Use of Students and Engineers. By H. E. Wimperis. 
Fourth edition (revised and enlarged). Pp. xvi+320. 
(London, Bombay and Sydney: Constable and Co., 
Ltd., 1922.) 12s. 6d. net. 
Ir is not surprising that a fourth edition of this valuable 
work should have been called for within thirteen years 
after its first publication. As is well known, the pro- 
gress of the internal combustion engine during the war 
was very rapid, due largely to aviation. By rearranging 
some of the older matter, the author has been able to 
give an account of these advances, including recent — 
experimental work on explosions in closed vessels, and 
modern fuels and fuel mixtures suitable for use in petrol 
engines. The chapter on the efficiency of petrol engines 
has also been brought up-to-date and now includes 

