June 21, 1906] 



NA TURE 



187 



said to be accompanied witli thunder and lightning ; some 

 of the storms are very heavy, and a lightning recorder has 

 been erected at Johannesburg which gives a permanent 

 record of their intensity and duration. On the High Veldt 

 the mean temperature of the twelve months ranged from 

 57° at V'olksrust to 65° in the VVaterberg, the extreme 

 maxima from 87° to 104°, and the extreme minima from 

 14° to 29°. Telegraphic messages are received and ex- 

 changed daily, and the Government has sanctioned the 

 appointment of an assistant, to be trained in weather fore- 

 casting at the Meteorological Office in London. 



THE THEORY OF FREQUENCY-DISTRIBU- 

 TIONS.' 



'THREE brief but important notes on the theory of the 

 law of error were communicated to the Royal 

 Academy of Sciences at Stockholm last year by Mr. 

 Charlier, director of the astronomical observatory at Lund. 

 The first of these (" Ueber das Fehlergesetr ") is a dis- 

 cussion on the lines, generally, laid down by Laplace. An 

 " error " is supposed to be given by the sum of a large 

 number of elementary errors, each with its own law of 

 frequency ; these laws need not be the same, but are sub- 

 ject to the condition that the frequency should not fall 

 off with great rapidity on either side of the mode. On 

 this condition, the law reached is the known expansion 

 in terms of the normal function and its differentials, re- 

 cently discussed in detail by Prof. Edgeworth (Camb. Phil. 

 Trans., vol. xx.). In his second note (" Die zweite Form 

 des Fehlergesetzes ") Mr. Charlier discusses the comple- 

 mentary case, in which the condition stated does not hold, 

 supposing, for instance, that each elementary error can 

 only take the value zero or a, and that the probability of 

 a is very small. The normal function of the former series 

 is now replaced by an auxiliary function of more complex 

 form. These two laws are referred to as Type A and 

 Type B. The third note (" Ueber die Darstellung 

 willkurlicher Funktionen ") bears on the general mathe- 

 matical method employed. 



The present memoir, which is written in English, is a 

 sequel to these purely mathematical notes, discussing the 

 practical work of fitting such curves to given statistics 

 and so forth. The method of fitting used throughout is 

 Prof. Pearson's " method of moments," which has proved 

 so widely applicable. The illustrations are numerous ; for 

 Type A, frequencies of stigmatic rays in Papaver, 

 Johannsen's distributions of weight in beans, cephalic 

 indices of .Swedish recruits, and deaths from typhoid fever 

 in groups of three successive days during an epidemic at 

 Lund ; for Type B, De Vries's statistics of numbers of 

 petals in Ranunculus, and Johannsen's figures for sterility 

 in barley. Davenport and BuUard's data for the numbers 

 of glands in the fore-legs of swine are discussed under 

 both heads. These illustrations are followed by a short 

 section on the dissection of a compound curve by Pearson's 

 method (Phil. Trans., 1893). One or two possible cases of 

 approximation are discussed, and an interesting suggestion 

 made as to the employment of a graphic method to lighten 

 the labour of solving the fundamental nonic. The text of 

 the memoir is followed by some tables giving, inter alia, 

 the third and fourth differentials of the normal function, 

 and values of the auxiliary function for Type B. 



There are several incidental points of interest ; a proof 

 of the empirically discovered rule that the difference 

 between mean and median is one-third of the difference 

 between mean and mode for Type A deserves mention, and 

 a suggestion as to an arithmetical check in calculating 

 moments is worth consideration from the practical stand- 

 point. If one may judge from a diagram (Fig. 5), curves 

 of Type A may be bi-modal. Is this so? The point does 

 not appear to receive special attention in the text. The 

 statement on p. 15 that " as a rule it may be advisable 



1 "Researches inio the Theory of Probability." By C. V. L. Charlier. 

 Pp. 51. (Meddelanden fran Lunds Astronomiska Observatorium, Sprie ii. 

 Nr. 4. Kongl. Fysiografiska Sallskapets Handlingar. Bd. 16.) {Lund, 

 1906.) 



NO. I912, VOL. 74] 



to take the class range smaller than the standard devi- 

 ation " would seem to be rather incautious. Surely, as 

 a rule, it should be not merely smaller, but a good deal 

 smaller — say one-third of the standard deviation or less? 



The memoir and its preceding notes must be commended 

 to the attention of all who arc interested in the theory of 

 frequency distributions either from the mathematical or the 

 statistical side. G. U. Y. 



A PLEA FOR AN EXPEDITION TO 

 MELANESIA. 



DR. A. C. HADDON, F.R.S., recently brought before 

 the research department of the Royal Geographical 

 Society a plea for the investigation of biological and 

 anthropological distributions in Melanesia. The Melancsian 

 islands constitute a fairly well-marked biological province. 

 Many of the islands are of large size, and there is reason 

 to believe that some of these are vestiges of an ancient 

 land-mass that probably became submerged in the 

 Mesozoic period. The islands of Melanesia have yet to be 

 studied from a geomorphological point of view, and their 

 geology is extremely little known. Botanists would 

 welcome a more ample knowledge of the flora of the 

 district as a whole and of particular portions of it, and 

 many problems of plant structure, distribution, and cecology 

 require detailed investigation on the spot. The same re- 

 marks apply to zoologists. Botanists and zoologists alike 

 would welcome an opportunity for extensive or intensive 

 study of the systematic distributional or biological problems 

 of plants and animals in Melanesia. 



There are also many anthropological problems in 

 Melanesia that require investigation in the immediate 

 future, since the dying out or modification of arts, crafts, 

 customs, and beliefs that is now taking place, and the 

 shifting and mixing of populations, will soon render their 

 solution difficult and even impossible. On the other hand, 

 there are many districts never yet visited by a white man, 

 and many islands of which science has no knowledge. 



There is a certain amount of variation in the physical 

 character of the people of these archipelagoes that requires 

 local study for its explanation. .\ good deal is known in 

 a general way about the arts and crafts of the Melanesians, 

 but an investigation of the kind proposed would verify 

 existing data, add an immense numljer of trustworthy 

 facts, and localities could be ascertained of unlocated speci- 

 mens in our museums, and the uses of doubtful objects 

 could in many cases be discovered. By a combination of 

 these two lines of inquiry, the physical and the cultural, 

 the nature, origin, and distribution of the races and peoples 

 of the West Pacific could be elucidated. Melanesia is 

 peculiarly suitable for studying the stages of the transition 

 from mother-right to father-right, and it would be 

 important to discover the causes that have led to this 

 transformation, and the steps that mark its progress. With 

 this is associated the evolution of the family and the dis- 

 tribution and inheritance of property. Melanesia is also 

 a favourable area for tracing the emergence of govern- 

 ment. What are required at the present day are intensive 

 studies of restricted areas, since it is only by careful 

 regional study that the real meaning of institutions and 

 their metamorphoses can be understood. The same applies 

 equally to all the manifold beliefs and usages that are 

 grouped under the term religion. The psychology of back- 

 ward peoples has been greatly neglected, and the oppor- 

 tunity of a well-equipped expedition would do much to 

 encourage students to undertake this research. 



It is superfluous to extend this plea, as all ethnologists 

 will agree that this work requires to be done, and that 

 without delay. The presence of Government officials, 

 missionaries, traders, and of returned indentured labourers 

 tends rapidly to modify or destroy the old customs. Much 

 has already disappeared in many places ; we are yet in 

 time in many others if we do not delay. 



Dr. Haddon is convinced that the best means of 

 accomplishing the end in view is to organise a prolonged 

 expedition to the Pacific with the absolute control of a 



