NOTICES AND BIBLIOGRAPHY. 
NOTICES. 
1. Edgeworth, F. y. The Law of Error. Transactions of the Cambridge Philosophical Society, 
1905, Vol. XX. pp. 36—65 and 113—141. 
2. . The Generalised Law of Error, or Law of Great Numbers. Journal of the Eoyal 
Statistical Society, 1906, Vol. lxix. pp. 497—539. 
3. Charlier, C. V. L. Ueher das Fehlergesetz. Arkiv for Mateniatik, Astrouomi och Fysik, 
Vol. II. Stockholm, 1905. 
4. . Die zweite Form des Fehlergesetzes. Ibid. 
5. . Ueber die Darstelhmg Willie iirlicher Functionen. Ibid. 
6. . Researches into the Theory of Probability. Meddelanden fran Limds Astronomiska 
Observatorium, Serie ii. No. 4. Lund, 1906. 
In (1) Professor Edgeworth, starting from various conditions, some of which he afterwards 
shows can be relaxed, gives four methods by which one can reach an " approximate expression 
of the frequency with which in the long run different values are assumed by a quantity which is 
dependent on a number of variable items or elements." These conditions are that the elements 
assume different values in random fashion and in the long run recur with a proportionate 
frequency capable of being represented by a single definite frequency curve ; that the variations 
are inde^^endent of each other* ; that the method of aggregation by which the elements are 
compounded is summation, etc. etc. 
Professor Edgeworth first gives a method which consists of equating the t^^ moment of the 
frequency with the same moment of the given locus. He then shows that the same curve 
can be reached by working on the lines followed by Professor Morgan Crofton and by the method 
originated by Laplace and developed by Poisson. He then gives confirmatory evidence by using 
Laplace's analysis with some of the conditions used by Crofton and inserts the fresh condition 
that if there be two or more magnitudes each fluctuating according to the law of error, then the 
sum of each must also fluctuate according to that law. 
* [The assumptions that the elementary cause-groups are independent and that the aggregate 
is obtained by summation have yet to be justified. lu particular the first assumption is opposed to the 
basis of every determinantal theory of heredity, and accordingly the frequency distributions of characters, 
which result from the fusion and throwing out of chromasomes, i.e. characters in living organisms, are 
extremely unlikely to comply closely with Professor Edgeworth's form of frequency. I have repeatedly 
urged the necessity for considering contributions to the aggregate as correlated, i.e. the hypergeometrical 
as distinguished from the binomial form of series, as the basis of frequency distributions. The skew 
curves I have introduced proceed from the basis that the " contributory cause-groups " give contributions 
to the aggregate which are correlated. See Biometrika, Vol. iv. pp. 196, 203 et seq. K. P.] 
