September 2, 1909J 



NA TURE 



275 



LETTERS TO THE EDITOR. 



jThe Editor does not hold himself responsible for opinions 



~ expressed by his correspondents. Neither can he undertake 



to return, or to correspond with the ivrilers of, rejected 



manuscripts intended for tliis or any other part o/ Nature. 



No notice is taken of anonymous communications.] 



Beliefs and Customs of the Australian Aborigines. 



In May of last year (1911S) I had tne good fortune to 

 meet the Bishop of North Queensland {Dr. Frodsham) at 

 Liverpool, and he gave me in conversation some valuable 

 information as to the native Australian beliefs and customs 

 based on his personal knowledge of the aborigines. He 

 .told me that he had travelled among the Arunta as well 

 as among various North Queensland tribes, and he asked 

 me whether I was aware that the Australian aborigines 

 do not believe children to be the fruit of the intercourse 

 of the sexes. His Lordship informed me that this in- 

 credulity is not limited to the Arunta, but is shared by all 

 the North Queensland tribes with which he is acquainted, 

 and he added that it forms a fact which has to be reckoned 

 with in the introduction of a higher standard of sexual 

 morality among the aborigines, for they do not naturally 

 accept the true explanation of conception and childbirth 

 ■even after their admission into mission stations. The 

 Bishop also referred to a form of communal or group 

 marriage which he believes to be practised among aboriginal 

 tribes he has visited on the western side of the Gulf of 

 Carpentaria, but, unfortunately, I had not time to obtain 

 particulars from him on this subject. 



I pointed out to his Lordship the high scientific import- 

 ance of the information which he had volunteered to me. 

 and I requested that he would publish it in his own name. 

 He assented ; but as some time has passed without his find- 

 ing leisure to draw up a full account, he has kindly 

 authorised me to publisli this brief statement, which has 

 heen submitted to him and approved by him as correct. I 

 need not indicate to anthropologists the great interest and 

 value of the Bishop's testimony as independently confirming 

 and extending the observations of Messrs. Spencer and 

 frillen on the tribes of Central Australi.i. Tn the interest 

 of science it is much to be desired that the Bishop, or 

 those of his clergy w'ho know the natives, would publish 

 fuller information on these topics. J. G. Fr.\zer. 



Cambridge, August 23. 



A Question of Percentages. 



In Nature of .August 5 (p. 159) Mr. Cunningham asked 

 a question as to the proper method of arriving at the mean 

 percentage of marks obtained on papers of different values 

 in an examination, and this has been very clearly answered 

 by Mr. WHialley. The same question, however, arises in 

 ■e.v'perimental work, particularly in agricultural and horti- 

 cultural experiments, and there the answer is by no means 

 so evident. An examiner may be supposed to have 

 sufficient knowledge to weight his papers properly, but 

 in an experiment no data may be available for the purpose. 



Take a case where three sets of different varieties of 

 tress are subjected to some particular treatment, and com- 

 pared with three similar sets not so treated, and suppose, 

 as an exaggerated example, that the actual measurements, 

 say, of growth, are as follows : — 



Treated Untreated Ditf. per cent. Ditf. per cent. 

 A B 



... 240 ... 120 ... -1- 100 ... +100 

 60 ... 50 ... + 20 ... + 20 

 4 ... 8 ... - 50 ... - 100 



I. 



II. 



in. 



Sum ... 304 

 Mean diff. +71 



178 ... 



+ 23 



+ 7 



If the numbers of trees in the various sets are not the 

 ■same, the results may, of course, be easily weighted to 

 correct for this ; but there are other differences for which 

 they cannot be weighted, namely, those dependent of the 

 differences in nature of the different varieties and of 

 attendant circumstances beyond the control of the experi- 

 menter. The mean deduced from working each result out 

 separately (-I-23) ignores all such differences, and is clearly 

 incorrect ; but that deduced from the sums of the measure- 



NO. 2079, VOL. 81] 



ments ( + 71) is equally so, for it ignores the difference 

 in habit of the different varieties, and gives undue weight 

 to the results from that variety which happens to be the 

 most rampant grower. This difficuUy has been alluded to 

 more than once in the reports of the Woburn Experimental 

 Fruit Farm, and the only way out of it appears to be 

 to lake the mean of the means deduced in these two 

 ways ; at any rate, it is rarely safe to draw any con- 

 clusions as to the results of experiments unless these two 

 means agree fairly with each other. 



Similar difficulties arise in interpreting the results of 

 other e.^periments ; with a number of analyses, for 

 instance, in which different quantities of material were 

 taken, the mean of the individual results assumes that 

 none of the errors is proportional to the quantities taken, 

 whereas a mean deduced from the sum of the quantities 

 taken and found assumes that all the errors are directly 

 proportional to these quantities, neither of which assump- 

 tions is correct, as a rule. 



.Another source of error in horticultural experiments is 

 that the differences observed are not unfrequently of 

 different signs, and since a plus difference of 50 per cent, 

 has a very different value from a minus difference of 

 50 per cent., the algebraic sum of such differences is 

 fallacious. This is evident from the values given above 

 for I. and IIL, in which the proportions are exactly re- 

 versed, but which figure under A as differences of +100 

 and —50 respectively. A more correct way of calculating 

 such differences is to take the lowest (or highest) value 

 in each pair of plots as the standard of comparison, instead 

 of the value in the check plot, and to affix a -t- or — sign 

 to the difference, according to whether the plot under 

 treatment has given a larger or smaller value than the 

 untreated plot. Such differences are given under B, and 

 correctly represent the ratios of the experimental measure- 

 ments. It would be well if such a method of calculating 

 percentage differences could receive some special designa- 

 tion, so that it might become recognised, for without this 

 its use is likelv to lead to misunderstanding. 



Spencer Pickering. 



The Planar Arrangement of the Planetary System. 



In your issue of July 29 your reviewer devotes some 

 space to my paper on the origin of the planetary system 

 (.istronomische .\'achrichten, No. 4308), and closes by ask- 

 ing, " Why, for instance, on the hypothesis of capture, are 

 the vast majority of the orbits near the plane of the 

 ecliptic and their motion direct?" This is because our 

 sj-stem was formed by the unsymmetrical meeting of two 

 streams of nebulosity or by the mere gravitational settling 

 of a single nebula of curved and unsymmetrical figure, 

 giving a rotating cosmlcal vortex, or spiral nebula, but 

 without hydrostatic pressure as imagined by Laplace. In 

 Lick Observatory Publications, vol. viii., Plate 38, you 

 will find an illustration of H.V. 2 Virginis, a spiral nebula 

 of unsymmetrical figure just beginning to coil up and 

 form a system. What will happen in the later stages of 

 this nebula is sufliciently shown in the Lick photographs 

 of other nebula5 given in this volume. As the mass whirls 

 and condenses under resistance, it will necessarily retain 

 and draw do%vn most of the nebulosity into the plane of 

 motion. This is exactly what has given the planar 

 arrangement of the bodies in the solar system. In .45(ro- 

 nomische Nachrichten, Nos. 4341-2, your reviewer will 

 find a fuller explanation of the method of capture, and 

 other papers yet to come will make the theory so clear 

 that it need not take up more of your valuable space at 

 present. T. J. J. See. 



Naval Observatory, Mare Island, Cal., August 12. 



The Benham Top. 



Mv attention has been directed to a paper in the Trans- 

 actions of the Ophthalmological Society, by Mr. A. S. 

 Taylor, entitled " Colour Phenomena due to Intermittent 

 Stimulation with Light : Note on the Colours of Benham 's 

 Top." 



It is to the conclusions in the latter part of the paper 

 that I desire to refer, as last year, in a paper before the 

 Phvsical Society (see Nature, June 18, iqo8, p. 166), I 

 endeavoured to explain this phenomenon in a somewhat 



