December i, 1904J 



NATURE 



LETTERS TO THE EDITOR. 

 [The Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the -writers of, rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.] 



Average Number of Kinsfolk in each Degree. 



As Dr. Galton has completely misunderstood the point 

 of my last remark, I fear it will be necessary again to re- 

 open a discussion which I had thought was satisfactorily 

 closed. 



My point is this : If we take a large number n of families 

 containing in the aggregate nd sons and nd daughters, and 

 remove on an average one child of specified sex from each 

 family, we shall have n preponderance of the opposite sex 

 in those that remain. The average numbers under this con- 

 dition will be d and d~i, and not d — i and d — j, and this 

 was how I was originally led to my first conclusion. 



If, however, we wish to test the question whether a girl 

 has the same average number of brothers as sisters, we are 

 only concerned with families containing at least one girl, and 

 therefore families containing only boys must be left out of 

 account, as I stated. When these have been removed there 

 will be a preponderance of girls in the families that are left. 

 It is this cause which enables us to reconcile the fact that, 

 while the probable total numbers of girls and boys in any 

 family may be equal, the probable numbers of brothers and 

 sisters of a single individual of specified sex, say a girl, may 

 still be equal. This may not be such a rigorous method as 

 Dr. Galton employs, but it at least shows that the result 

 is not necessarilv opposed to what one would naturally infer 

 from general considerations. G. H. Bry.^n. 



Compound Singularities of Curves. 



The compound singularities of algebraic curves may be 

 divided into three primary species. First, point singulari- 

 ties, or multiple points, which are exclusively composed of 

 nodes and cusps ; secondly, line singularities, which are 

 exclusively composed of double and stationary tangents ; 

 thirdly, mixed singularities, which are composed of a com- 

 bination of simple point and line singularities. Amongst 

 compound line singularities may be mentioned (a) a double 

 tangent which osculates a curve at one of its points of 

 contact, the constituents of which are one stationary 

 and two ordinary double tangents ; {$) a tangent having 

 a contact of the fourth order with a curve, the constituents 

 of which are three double and three stationary tangents. 



The third species comprises the majority of compound 

 singularities, and may be divided into the following sub- 

 sidiary ones : — 



(i) Nodes and multiple points, any tangent at which has 

 a contact of a higher order than the first with its own 

 branch, and does not touch the curve elsewhere. The 

 flecnode and biflecnode are the most familiar examples of 

 this species. 



(2) Nodes, cusps, and multiple points, any tangent at 

 which has a contact of the first or some higher order at 

 some other point or points on the curve. For example, it 

 is possible for each of the six nodal tangents of a trinodal 

 quintic to touch the curve elsewhere, and it can be shown 

 that the six points of contact lie on a conic. 



(3) Two or more nodes, cusps or multiple points may 

 have a common tangent. Thus the reciprocal of a biflec- 

 node is a pair of cusps having a common cuspidal tangent, 

 whilst a septimic curve may possess a node and a rham- 

 phoid cusp having a common tangent. 



(4) Singularities of the tacnode and oscnode type. When 

 the number of constituent double points is unequal to 

 nu((i — i), where n is a positive integer, the singularity can- 

 not be a multiple point, but must be of the tacnode type ; 

 and since the constituents of a tacnode are two nodes and 

 two double tangents, every singularity of this species must 

 contain double or stationary tangents, or both. When the 

 number of double points is equal to hn{n—i), the singularity 

 may be a multiple point, but when it contains line as well 

 as point singularities, it is of the same type as the oscnode, 

 which is composed of three nodes and three double tangents. 



(5) A tangent at a node or a multiple point, which has 



NO. 1831, VOL. 71] 



a contact of a higher order than the first with its own 

 branch, may coincide with some other tangent at the 

 singularity. When both tangents at a flecnode coincide, 

 the resulting singularity is a tacnode ; but the coincidence 

 of two or more tangents at a multiple point, any of which 

 possess this property, gives rise to a variety of peculiar 

 singularities which do not appear to have been completely 

 examined. 



It is also possible for a mixed singularity to be formed 

 in more than one manner ; in other words, it may possess 

 more than one penultimate form. Thus an oscnode may be 

 formed by the union of two cusps and two stationary tan- 

 gents, and additional singularities of this character are 

 possessed by quintic and sextic curves. 



To call a cissoid or a cardioid a nodal curve appears to 

 me a glaring misuse of language, since both curves are 

 nodeless. A. B. Basset. 



November i8. 



The Origin of Life. 



No doubt " Geologist " points out a literal Haw in my 

 statement, but I thought it would be obvious that by the 

 "potentiality of life," which would be destroyed by heat, 

 I meant potentiality of life, appearing within the time of 

 the experiment. Given countless ages, then, on the evolu- 

 tion hypothesis, the potentiality of life, as of the rest of 

 nature as we know it, existed in the fluid mass of the un- 

 cooled earth, and I did not mean to say anything inconsistent 

 with this. Nor, on the other hand, did I mean to say that 

 by the heat applied the potentiality of life in the matter 

 under test would be destroyed for all time. I meant 

 potentiality of appearing within a given time, the time of 

 the experiment, and I cannot help thinking this was the 

 natural sense of my words. 



In asking me to explain the introduction of life or its 

 potentiality into this planet, " Geologist " shows that he 

 has entirely mistaken the purport of my letter. My aim 

 was only logical, not constructive. If I could explain how 

 life first appeared on the earth, I should probably be able 

 to suggest a more promising line of experiment than that 

 hitherto followed, which I find myself unable to do. My 

 sole object was to point out a logical error, as it seemed to 

 me, in the view commonly taken by men of science of the 

 results of these experiments, an error, if my memory serves 

 me, fully shared by Huxley — in admiration for whom, I 

 hasten to say, I yield to no one. Huxley, if I remember 

 rightly, was so impressed with the strength of the evidence 

 against the contemporary origination of life that he 

 practically gave up the idea, and put the date back. In 

 this, I am venturing to suggest, he was illogical ; through 

 having overlooked the fact that in all the experiments the 

 agent, which was used to destroy actual life and its germs, 

 would probably be efficacious in destroying the potentiality 

 of life in non-living matter on the point of assuming life, if 

 any such there were, and, consequently, the positive result 

 having artificially been made impossible, the negative result 

 meant nothing, and should not be allowed to influence 

 opinion. George Hookham. 



Change in Colour of Moss Agates. 



The following observations may perhaps throw light on 

 the colour changes in moss agate and flint noted by Messrs. 

 Whitton and Simmonds in your issues of November to 

 and 17. Specimens of the flints from Bournemouth referred 

 to by Mr. Simmonds were brought to this laboratory some 

 months ago, and, though they were not submitted to any 

 very searching examination, it was found that the colouring 

 matter could be removed on boiling a fragment with hydro- 

 chloric acid, while the solution gave well marked reactions 

 for iron and phosphoric acid. Now the compound 

 Fe3(POj),.8H20, whether prepared in the laboratory or 

 occurring as the mineral vivianite, is colourless when pure, 

 but becomes oxidised to ferrosoferric orthophosphate, and 

 turns blue, when exposed to the atmosphere. It seems prob- 

 able, then, that the change of colour of these flints is due 

 to a layer of vivianite which alters on exposure. 



In considering the case of the agate penholder, it 

 should be noted that such objects are but rarely made 

 of agate in its natural condition, it being the practice of 



