Oct. 17, 1889] 



NATURE 



593 



Key to Todfiunter' s Integral Calculus. By H. St. J. 

 Hunter, M.A. (London : Macmillan and Co., 1889.) 



All the examples in Todhunter's " Integral Calculus " 

 are fully worked out in this volume. In the earlier chap- 

 ters, the solutions are exhibited with considerable detail, 

 so that the " Key " will be a valuable aid to those who are 

 beginning the subject without the help of a teacher. 

 Throughout the work many references are made to the 

 text, the edition referred to being that of 1886. 



The Ha7id-book of J ainaica for 1 889-90. By A. C. Sinclair. 

 (London: Edward Stanford. Jamaica: Government 

 Printing Establishment.) 



This is the ninth annual issue of Mr. Sinclair's "Hand- 

 book," and to those who have already had occasion to 

 consult the work we need hardly say that it contains all 

 the information, clearly and compactly presented, that is 

 likely to be wanted by its readers. The writer provides 

 a good description and historical sketch of Jamaica, and 

 full details are given with regard to all the leading institu- 

 tions of the island. The volume is published by authority, 

 and has been compiled from official and other trustworthy 

 records. 



LETTERS TO THE EDITOR. 



f The Editor does not hold himself responsible for opinions ex- 

 pressed 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. ^ 



The Method of Quarter-Squares. 



May I point out, by way of note to Mr. Glaisher's article 

 (October 10, p. 573) on the method of quarter-squares, that 

 the method is indicated in the second edition of Sir John 

 Leslie's "Philosophy of Arithmetic" (Edinburgh, 1820; see 

 pp. 246-57). Leslie gives what he calls a " specimen " table, 

 extending as far as 2000, whereby any two numbers containing 

 not more than three digits each can be multiplied ; and he also 

 points out the application of the table for any two numbers less 

 than 2000 by using the formula — 



ab — 2 



Ir 



4 4 4 - 



Apparently, Leslie was an independent discoverer of the method ; 

 at least this seems to be implied in the remarks v»hich follow his 

 table in the work cited above : — " This application of a table 

 •of quarter-squares, as it is derived from the simplest prin- 

 ciples, might have readily occurred to a mathematician ; yet I 

 have nowhere seen it brought into praccical use till, last summer, 

 I met with, at Paris, a small book by Antoine Voisin, printed 

 dn 1817. It contains a table of quarter squares for the multi- 

 plication of whole numbers from i to 20,000, with an explanation 

 •of the mode of employing them." G. Carey Foster. 



University College, London, October 13. 



Marine Biological Association. 



The British Association, at the recent meeting at Newcastle 

 placed a grant of money in the hands of a Committee, consist 

 ing of Prof. W. H. Flower, Prof. M, Foster, Prof. E. Ray 

 Lankester, Prof. S. H. Vines, and myself (Secretary), " for 

 the purpose of nominating students to work at the Laboratory 

 of the Marine Biological Association at Plymouth." Arrange- 

 ments are being made with the Council of the Marine Biological 

 Association, by which the Committee hope to obtain the use of 

 a table at the Laboratory at Plymouth for twelve months. 



May I ask you to assist, through the medium of Nature, in 

 making this information public ? Persons who wish to take 

 advantage of the opportunity, afforded by the British Associa- 

 tion, of working at the Plymouth Laboratory should address 

 their applications to me at the earliest possible date. The 

 application should contain full particulars as to the nature of the 

 investigation which it is proposed to carry on, together with a 



statement of the period of time during which the applicant would 

 be able to work at Plymouth. S. F. Harmer. 



King's College, Cambridge, October 15. 



Section Work at the British Association. 



The recent meeting at Newcastle has emphasized what has 

 been frequently noticed before, that the British Association week 

 undoes the benefil of previous holiday, and that the conditions 

 under which the work of the Sections is ca'rried on are preju- 

 dicial to health, and have this time resulted in a considerable 

 list of sick and wounded. I speak especially of Section A, but 

 have no reason to suppose it different from others. 



The principal difficulty is the elementary one of food. A 

 satisfactory midday meal is at present practically unattainable, 

 unless one is willing to sacrifice everything else to it. The time 

 of meeting (from 1 1 to 3, or, for those more intimately con- 

 nected with the business of the Sections, from 10 to 5) and the 

 practice of non-adjournment for lunch are to blame for this ; 

 and I write to raise the question, whether it may not be wise to 

 reconsider the time-honoured meeting-hours both of Sections 

 and of Committees. Several proposals can be made, but the one 

 I wish to bring forward is, to postpone the Sectional Committee 

 meetings till after the Section has sat, and to begin the Section 

 work at 10 a.m. The work should begin then more freshly 

 than it does now after an occasionally tedious, though occasion- 

 ally interesting. Committee meeting ; and it may go on steadily 

 till 1.30, when it will usually stop for the day. At 2.30, or 

 possibly, but less advantageously, at 2, the Sectional Commit- 

 tees can meet and transact their business comfortably. It will 

 be easier to arrange the papers for next day when it is known 

 how many stand over from the recent meeting ; and as the 

 Secretaries usually have things pretty well arranged beforehand, 

 there need be no difficulty or delay in getting the list to the 

 printer in good time. The important business of appointing 

 Committees and such-like can be discussed very rationally after 

 the Committee or individual has just reported to the Section, 

 instead of, as at present, before such report. At 3.30 the 

 General Committee and the Committee of Recommendations 

 can meet, instead of at 3. This apparent lengthening of the 

 day's work by half an hour will be more than compensated by 

 a comfortable sit-down lunch, and one useful function of the 

 Association, viz. the interchange of ideas in conversation, will 

 be much assisted. It may be objected that, if all the Sections 

 rise at 1.30, the luncheon-room will be inconveniently crowded, 

 but there are usually many clubs and private houses available ; 

 and if a midday meal became a feature, there is no lack of 

 hospitality. The usual difficulty is how to fit anything social 

 into the crowd of engagements and evening lectures. 



My proposal curtails the Section time by half an hour. 

 Whether this is regrettable or not, I am not sure : there are 

 ways of avoiding it if it is. If any hard-pressed Section 

 chooses, it might meet again at 3.30 on every day but Monday, 

 and sit, concurrently with the Committee of Recommendations, 

 for an hour or two without essential hardship. What I feel 

 sure ought to be reconsidered, is the present health-destroying 

 practice of continuous session. Oliver J. Louge. 



Anthropometric Measurements at Cambridge. 

 I quite agree with your correspondent " F. M. T." that the 

 head measurements are not sufficiently accurate to warrant their 

 use as data for coming to any conclusion as to increased cranial 

 capacity, much less as the foundation for the theories of Mr. 

 Francis Gallon. On a comparison of the head measurements of 

 any one individual, they are found to be so variant that one is 

 forced to conclude that the errors of observation are far greater 

 than the maximum error which could exist without completely 

 vitiating the trustworlhine s of the data. The following measure- 

 ments of my head during the last two years are sufficient to 



render this obvious — 



Above line 



Breadth. Length, from brow Total, 

 to ear-lobe. 



May 28, 1887 ... 57 - 74 - 5'3 - 22355 



November 19, 1887... 56 ... 7'3 ■■• 5"5 ••• 224-84 



June 14, 1888 ... 58 ... 7'4 - 5*5 — 236x6 



Fcbiuary 4, 1889 ... 57 ... 7 3 - 5'2 ... 216-37 



August 23, 1889 ... 58 ... 7-5 ... 5'4 ••• 234-90 



August 30, l!i89 ... 58 ... 74 ... 5"5 - 24035 



