Marcu 28, 1907 | 
NATURE 
o1 
07 
Medizeval ships are briefly described and excellently 
illustrated, this section ending with an account of 
the famous Sovereign of the Seas, built about the 
middle of the seventeenth century. A long chapter 
on modern wooden  sailing-ships concludes _ this 
volume, and brings the history up to the construction 
of the great sailing three-deckers in the Royal Navy, 
which formed our most powerful war-ships until the 
middle of the nineteenth century. On the mercantile 
side the gradual development of sailing-ships is 
traced, and the famous ‘‘ clippers ’’ are described. 
In the second volume steam navigation and the 
use of iron and steel for shipbuilding form the main 
topics. An interesting account is given of early 
wooden steamers. It is worth note in passing that 
this year is the centenary of the completion of the 
Clermont by Robert Fulton, and her trials on the 
Hudson River. The development of types of mercan- 
tile steamers is described, and numerous examples 
are included, amongst them being the Great Eastern 
and many vessels now employed on ocean or cross- 
channel service. Tables of dimensions and_par- 
ticulars for Transatlantic steamers are given in an 
appendix. On the structural side the book is valu- 
able; it traces the influence of the use of iron and 
steel on dimensions and strengths of ships, and the 
differences between mercantile and Admiralty methods 
of construction. A brief discussion of the external 
forces acting upon a shiprat sea, and the resultant 
stresses on the structure, is given in one appendix; 
in another the puzzling subject of tonnage measure- 
ment is made as clear as it can be made to general 
readers. This necessarily brief notice leaves many 
points unmentioned; the volumes should be read by 
all interested in the history of shipbuilding. 
W. H. W. 
FREQUENCY CURVES AND CORRELATION. 
Frequency-curves and Correlation. By W. Palin 
Elderton. Pp. xiiit+172. (London: Published for 
the Institute of Actuaries by C. and E. Layton, 
n.d.) Price 7s. 6d. 
Na stated in a short preface by the president of the 
Institute of \ctuaries, the object of this little 
volume is “to give a detailed description of the basis 
and practical application of those modern statistical 
methods that are associated with the name of Prof. 
Karl Pearson.” The work was undertaken, 
understand, by Mr. Elderton, at the invitation 
of the council of the institute, and we not only concur 
with the president in his commendation of the 
‘““public-spirited manner” in which Mr. Elderton 
acceded to their request, but think that the action of 
the council of a professional society in thus en- 
deavouring to place the results of recent research 
before the members in a convenient form for con- 
sideration is well worthy of note. 
In view of its purpose, the illustrations introduced 
are, of course, mainly of an actuarial character, but 
we have no hesitation in saying that the volume 
NO. 1952, VOL. 75 | 
we 
will be of great service to statisticians in other fields. 
Much of Prof. Pearson’s work has been given im 
the Philosophical Transactions of the Royal Society, 
the Philosophical Magazine, and other publications 
which are not readily accessible to the ordinary statis- 
tician, and Mr. Elderton’s worl will be most useful 
to the student by providing a short and handy sum- 
mary of some of the more important results. 
After a brief introductory chapter, the author passes 
at once to the subject of frequency distributions, and 
the mean and standard deviation are defined (chapter 
ii.). The method of moments is then treated in some 
detail, including the calculation of moments by the 
direct and the summation methods (iii.). The de- 
duction of Prof. Pearson’s curves from the hyper- 
geometrical series is then given (iv.), and their fitting 
by moments (v.). 
The subject of correlation is introduced in 
chapter vi.; this is treated mainly from the standpoint 
of the normal distribution, but it is also shown 
that the formula may be regarded as obtained by the 
fitting of straight lines to the points in a “dot dia- 
gram,’’ using the method of moments. In chapter vii. 
Prof. Pearson’s method of calculating the coefficient 
of correlation from any fourfold table, for measured 
or unmeasured characters, is described, and there 
follow two short chapters on probable errors (viii.), 
and on Pearson’s test for goodness of fit (ix.) respec- 
tively. The concluding chapter gives briefly the 
theory of the coefficient of contingency. A few 
appendices deal with frequency curves other tham 
Pearson’s, with the integrals of the normal functiom 
and other matters. 
The exposition is careful and lucid, but some of the 
actuarial illustrations will prove rather a stumbling 
block to the non-actuarial reader. Proofs are given 
which assume a fair mathematical knowledge, neces— 
sarily including the integral calculus, but the more: 
lengthy and difficult proofs are omitted. In some 
respects the work strikes one as a little limited in 
scope, but this arises naturally enough from the fact 
of its being addressed to a special public. 
There are only one or two points we have noted in 
reading that seem to call for mention. In connee- 
tion with the summation method of calculating 
moments, we would direct attention to the work of 
G. F. Lipps (Wundt’s Phil. Studien, xvil., 538 ef 
seq., 1901), and to the chapters on “die Summen- 
methode” in the Wahrscheinlichkeitsrechnung of 
Bruns (1906). Even if the name “method of least 
squares” be avoided, we would submit that this is 
no reason for omitting the short and simple proof that 
X(v@—éy) is a minimum if b=70,/o,. Without this 
proof the meaning of the coefficients of regression re- 
mains, in the general case, vague and indefinite. In 
the chapter dealing with the coefficient of con- 
tingency, it might be as well to point out that the 
coefficient cannot attain the value unity unless the 
number of classes be indefinitely great; it cannot, in 
fact, exceed ,/(¢—1)/¢for a txt-fold classification, at 
the best. 
We cordially commend the volume to the attention 
of all students of statistics. Ga Ue Ye 
