Nov. 12, (885] 



NATURE 



29 



very admirable manner, showing that they possess a 

 perfect acquaintance with the subject. 



There are, however, a few minor blunders ; thus, for 

 instance, the substitution of the word "length" for 

 "longitude " in connection with the perihelion and node, 

 plays havoc with the elements of a comet's orbit, given 

 on p. 584, while the diagram on p. 387, illustrating the 

 change of wave-length, is rendered unmtelligible by the 

 misplacement of the figures indicating miles per second. 



A Practical Arithmetic on an entirely New Method. By 



John Jackson. (London: Blackie, 1885.) 

 Principles of Arithmetic. By Homersham Cox, M.A. 



(Cambridge : Deighton, 1885.) 

 As the title-pages indicate, these Attack the subject from 

 quite different sides : the former is eminently practical, 

 and everything unpractical is carefully eschewed : the 

 latter goes into the principles and considers all from the 

 theoretic side, giving very little practice. 



Mr. Jackson aims at giving the easiest and shortest 

 rules he can ; explanations are few, the deficiency to be 

 met by black-board illustration. The fractional form for 

 the solution of questions is adopted in the advanced rules ; 

 but the most noticeable feature is the exclusion of the rule 

 of " subtraction " and the substitution of what the writer 

 calls " incremental or complementary addition." To take 

 an example in compound complementary addition : — A 

 pays a bill of 15^-. %\d. with a sovereign ; the tradesman 

 says, " 15.?. %\d. with a farthing (puts it down) make 

 I5.f. ()d., and yl. (puts it down) make 16^-., and 4^. (puts it 

 down) make one pound.'' There is no new difficulty in- 

 troduced here, and a beginner is taught a good practical 

 lesson. There is a vast collection of examples, numerous 

 e.xamination papers, and a good store of sums worked 

 out on the usual plan, as well as on that put forward by 

 the writer. There are 25 pages of tables containing 

 specific gravities, a mariner's compass, a perpetual calen- 

 dar (to A.D. 1925), compound interest results, square and 

 cube numbers, prime numbers and logarithms. Some 

 space, as might be expected, is devoted to "mental arith- 

 metic." We have shown, we think, that this book well 

 merits its title of a " practical " arithmetic. 



IVIr. Cox at once states " the object is to give an ac- 

 count of the principles of arithmetic, omitting all merely 

 mercantile applications." The author takes as his guide, 

 in the main, Cantor's " Geschichte der Mathematik," 

 consulting also Hankel and Nesselmann (" Algebra der 

 Griechen ") ; but " the conception of the subject as a 

 whole, and many of the details, have been taken from the 

 mathematical portions of the works of Auguste Comte, 

 and in especial from his last great work, the ' Synthese 

 subjective.' " 



There is no index nor table of contents, which is a 

 drawback to the ready use of the book. There is an in- 

 troduction, and then come seven chapters. Chapter I. 

 discusses Numeration ; Chapter II. is devoted to the first 

 four rules in four sections ; Chapter III., on Properties of 

 Numbers, is divided into four sections: (i) Theorems 

 (the commutative, the associative, and distributive) ; (2) 

 G.C.M. ; (3) Prime and Composite Numbers ; (4) 

 L.C.M. Chapter W., in four sections, treats of the four 

 rules for fractions, and in the fifth section discusses Ratio 

 and Proportion. Chapter "V., in six sections, treats of 

 Decimal fractions. Chapter "VI., in four sections, dis- 

 cusses powers and roots, with geometrical illustrations 

 and resumes (in Section IV.) the subject of Ratio and 

 Proportion (applied to incommensurable quantities). 

 Chapter VII., in three sections, resumes the discussion 

 of Properties of Numbers, as regards Permutations, the 

 Arithmetical and Geometrical Progressions, and Figurate 

 Numbers. There are a few exercises appended to the 

 sections. The book in parts reminds us much of De 

 Morgan's Arithmetic : it will be valuable for teachers, 

 even if they have read the works cited in Mr. Cox's pre- 



face. It is by no means a school-book, though senior 

 boys may derive much interest as well as profit from its 

 perusal. 



LETTERS TO THE EDITOR 

 [ The Editor does not hold himself responsible/or opinions extiresseti 

 by his correspondents. Neither can he undertake to return^ 

 or to correspond with the writers of, rejected manuscripts. 

 iVo notice is taken of anonymous communications. 

 [The Editor urgently re(]uests correspondents to keep their letters 

 as s/iort as possible. The pressure on his space is so great 

 that it is impossible otherwise to insure the appearance even 

 of communications containinginteresting and novel facts.\ 



The Recent Total Eclipse of the Sun 



By last mail I sent you a brief account of my eclipse observa- 

 tions at Tahoraite on the 9th inst. , and a diagram illustrating the 

 corona. Owing to a miscalculation as to closing time of mail 

 the account had to be very hurriedly written ; there was no time 

 to revise it or to find out the longitude and latitude of the point 

 of observation, but this information I am now able to supply 

 from the Trigonometrical Survey Records at Napier : — 

 Centre of railway station 1 Longitude Latitude 



at Tahoraite, Hawkes- / 176° 5' 7"'o7 ... 40° 13' I7"'22 



bay ) 



The longitude and latitude of the nearest Trigonometrical Station, 

 No. 83, from which the above were calculated, seems to have 

 been origin.ally fixed with reference to Trigonometrical Station 

 No. 60, Lighthouse Reserve, Napier, whose latitude then, ac- 

 cording to observations taken in January 1871, was 39° 28' 47"'30. 

 According to fresh observations taken in February 1S85 the lati- 

 tude of the same point is 39° 28' 43" '52 ± 0° o' o"'04. If both 

 series of observations are correct, a reduction in latitude to the 

 extent of about 3"'78 must have taken place since 1871. 



Considering the position of New Zealand at the Antipodes of 

 Europe, where a reduction of latitude seems to have occurred, a 

 reduction like the one above indicated, bearing as it does on a 

 very interesting question, has particular importance and urgently 

 calls for confirmation. As mentioned in my last letter, the 

 corona reminded me of an auroral display. The rays all seemed 

 radially disposed and perfectly straight with well defined edges. 

 The differences in length were very remarkable. All the ob- 

 servers I have spoken to agree as to the position of the longest 

 ray, but not as to that of the others. The public attention was, 

 however, fixed on the red protuberances and the other pheno- 

 mena of the eclipse, and little notice was evidently taken of the 

 corona. N. A. Graydon 



Hastings, Hawkesbay, New Zealand, September 25 



Ophthalmologic Education in the United Kingdom 



I DID not see your notice of my translation of Fuchs's 

 " Causes and Prevention of Blindness" imtil to-day. I find two 

 accusations brought against me, which I do not admit to be 

 well founded. 



(l) I am accused of "mistranslation" because I have often 

 rendered " Augenheilkunde " by the word "ophthalmology." 

 You state that "the treatment of diseases of the eyes' 

 would be the correct translation. "Ophthalmic medicine," 

 which is my altern.ative. translation, is more correct than the 

 translation you offer ; but ophthalmology is quite sufficiently cor- 

 rect, and in many cases is employed by the author indifferently 

 with " Augenheilkunde," to express the same thing. No doubt 

 "ophthalmology," etymologically considered, is a more com- 

 prehensive word than " Augenheilkunde " or its English 

 synonym " ophthalmic medicine ;" but custom has sanctioned its 

 employment in the limited sense of the latter word in Germany, 

 in France, and in this country. Thus the Professor of 

 Ophthalmic Medicine in Vienna was Professor of Ophthalmology. 

 Fuchs constantly speaks of " ophthalmological clinics," and in 

 many of the medical schools of this country the lecturers on 

 what is in other schools called "ophthalmic surgery," " diseases 

 of the eye," &c., are called lecturers on "ophthalmology" (King's 

 Ciillege, Yorkshire College, Liverpool University College, 

 Owens College, Catholic University School of Medicine, 

 Dublin). 



• (2) I am blamed for not correcting Fuchs when he says, "As 

 a rule no regular lectures on ophthalmology (Augenheilkunde) 



