33^ 



KTATURE 



[January 12, 191 1 



trace is clearly shown. From 11.35 to 11.38 there was a 

 very rapid easterly movement of about 4' in the declina- 

 tion trace, of a non-oscillatory character. The close agree- 

 ment in time of this movement with the arrival of the 

 preliminary tremors is very likely a purely accidental 

 coincidence ; but the movement is of an unusual character, 

 and it would be interesting to know what was being re- 

 corded at the time at other magnetic observatories. The 

 movement may, of course, have been due to some purely 

 local source, e.g. abnormal electric-tram currents. 



C. Chree. 

 Kew Observatory, Richmond, Surrey, January 7. 



Singularities of Curves and Surfaces. 



There is a distinction between multiple points and 

 what, for want of a better word, I have called singular 

 points. The curve aWp+ //^+] = o has at A a multiple 

 point of order p, but not a singular point. The latter 

 points are defined in § 169 of my " Geometry of Surfaces," 

 reviewed in Nature of December 22, 1910 (p. 231), and 

 the definition may be illustrated as follows. Let multiple 

 points of orders p. q, r . . ., where p is not less than 

 q, r . , ,, move up to coincidence along a continuous curve ; 

 then the compound singularity thereby formed is a 

 singular point of order p. The curve of lowest degree, 

 which can possess a singular point of given order, depends 

 on the way in which the singularity is formed. Thus if 

 four nodes move up to coincidence along a conic, the 

 resulting singular point is of the second order ; but a 

 quintic is the curve of lowest degree which can possess 

 such a singularity. Also, if three nodes move up to 

 coincidence along a straight line, the singular point is 

 still of the second order, but no curve of lower degree 

 than a sextic can possess such a point. 



The reviewer's statement in the second paragraph is 

 misleading, and calculated to convey a false impression, 

 since the investigations referred to are applicable to 

 surfaces of any degree. The fact is that a quartic surface 

 is capable of possessing most of the simpler singularities. 

 The principal exceptions are triple lines, which cannot be 

 completely discussed without the aid of a surface of the 

 seventh degree, and cuspidal twisted curves, which necessi- 

 tate the employment of a quintic surface, since a quartic 

 surface, which possesses a cuspidal twisted cubic curve, 

 is a developable surface, and is therefore not sufficiently 

 general for the purpose in question. 



As science advances, the introduction of new words is 

 essential. Thus lithotrity, ovariotomy, scleroderma, &c., 

 have been introduced during the last century to designate 

 operations and diseases of which our ancestors were 

 ignorant, whilst algebra has been enriched by such words 

 as catalecticant, evectant, protomorph, &c. the choice of 

 suitable words requires care, but I adhere firmlv to my 

 opinion that Latin and Greek are the best languages to 

 employ. A, B. Basset. 



December 23, 1910. 



It is unfortunately impossible to give a very brief 

 rejoinder to Mr. Basset's letter ; and it is perhaps as well 

 to take the opportunity of giving a further statement of 

 my position in reference to singularities on a plane curve. 



In the first place, the distinction drawn in Mr. Basset's 

 letter between multiple points and singular points of order 

 p does not seem to be in agreement with the practice 

 followed in his book, where the two terms appear to be 

 used indiscriminately : thus in §§ 171-4 and § i8i the 

 term multiple point is invariably applied to singularities 

 which, according to his letter, he would now call singular 

 points. At any rate, the singularities considered in these 

 articles cannot occur (in their general forms) on curves of 

 degree (p+i), and, as I understand Mr. Basset's letter, he 

 intends the use of the term multiple points to be restricted 

 to those singularities which do occur on curves of degree 

 (^+1). Naturally such a restriction would justifv the 

 assumption made in § 165, which was criticised in my 

 review ; but no modification of terminology will answer the 

 question as to whether all types of singularitv can be 

 obtained by Mr. Basset's treatment of the subject. 



NO. 2150, VOL. 85] 



The singularities which were in my mind when 1 raised 

 this question were those considered by Zeuthen {Math. 

 Annalen, Bd. x.) and Jordan (" Cours d'Analyse," t. i> 

 chap. V.) ; a fairly simple example is given by the origin 

 on the curve .x = t^, y = t'^ + 1" + 1'". 



Zeuthen 's method enables us to determine the Pliick' 

 equivalents of the singularity, and Jordan shows how l.^ 

 find quadratic transformations which reduce the singularity 

 to a simpler character. But I do not see that Mr. 

 Basset's limiting process (as briefly indicated in his letter) 

 would enable us to handle any singularity of this- type 

 (called a cycle by Jordan), nor have 1 found any reference 

 to the existence of such types in Mr. Basset's book. 



T. J. I'A. B. 



Scottish Natural History. 



I SEE that Nature of December 29, 1910, refers to two 

 statements made before a natural history society by Mr. 

 Symington Grieve, viz. :— 



(i) That half a century ago white-tailed eagles w*"-^^ 

 more abundant than golden eagles, or words to t!. 

 effect. 



(2) That Mr. Grieve is of the opinion that wild cats are 

 on the increase in Scotland owing to the instructions 

 issued by proprietors and factors for their protection. 



With regard to the first, naturalists would like to hu. 

 further data. It is certainly true white-tailed eagles utfc 

 then vastly more abundant than now, and that they are 

 now verging on extinction as an existing species. But 

 that they were " far more numerous half a century ago 

 than the golden eagle " requires more exact statistics. 

 Forty years ago there were quite eighty eyries of golden 

 eagles occupied over all Scotland, but I cannot find any 

 evidence to prove that white-tailed eagles at any time 

 anywhere in Scotland even approached that figure, and 

 during at least forty years I have paid considerable atten- 

 tion to all statements made as to their distribution and 

 their subsequent decrease. Locally in some few districts 

 white-tailed eagles were more numerous than golden 

 eagles, but not generally, and I believe all ogeupied 

 eyries could at any time have been easily counted. 



As regards the increase of wild cats, that is also quite 

 undoubted, but the true reason is not the direct instruc- 

 tions given by proprietors or factors generally, though that 

 may have some local value also, but to the protection 

 afforded by the increased area of lands devoted to dr • 

 afforestation. T. A. Harvie Brows. 



Dunipace, Larbert, Stirlingshire, N.B., 

 December 29, 1910. 



The Origin of Man. 



The following extract from a review in " Dodsley's 

 Annual Register for 1767 " of Dr. Adam Ferguson's essay 

 on the " History of Civil Society " may be of interest : — 



"Many of the authors who have written on man, and 

 those too, some of the most ingenious, have set out by 

 considering him as an animal. . . . Nay, one in particular 

 has thrown out doubts of his having been originally a 

 monkey or baboon." (The reviewer goes on to speak of 

 this theory as " too ridiculous for serious animadversion.") 



Could any of your readers say who was the " one in 

 particular "? Charles E. Benham. 



Colchester, January 7. 



COLLIERY WARNINGS. 



WHEN an appalling collien,- disaster, like that ai 

 Hulton Colliery, happens to coincide with a 

 "colliery warning," public attention is naturally 

 attracted to the fact, and the warning at once becomes 

 invested with an appearance of importance that i>; 

 out of all proportion to its true value. There appear 

 to be an impression that tliese colliery warnings ar 

 issued by some central responsible authority, such :.■■• 

 the Meteorological Office might be, and that they ar 

 based upon sound scientific principles, but as a mattt 

 of fact they are issued by the Press Association, and ar 



