Feb. 2, 1888] 



NA JURE 



319 



a direct denial. There is a systematic arrangement in the whole 

 book, or rather in the whole scheme embodied in both books. 

 Because " H. E. A." fails to discover that plan which finds 

 favour with him, it does not follow that systematic arrangement 

 is absent. To say that the arrangement is not that which one 

 would like to see adopted is fair criticism ; but to imply that 

 there is no alternative between one's own system and chaos is to 

 expose one's own ignorance. And what is the feature of that 

 system of practical chemistry in which alone the reviewer thinks 

 the student can find salvation? He says, "in a properly chosen 

 series of experiments everything should be proved ; no assump- 

 tion should be necessary." In another part of the review he 

 tells us that "air and the phenomena of combustion should be 

 first studied : the composition of air should be determined, and 

 oxygen should be discovered by the student . . . The com- 

 position of water should next be qualitatively a'^cerlained." I 

 should be deeply indebted to " H. E. A." if he would kindly 

 describe experiments on these subjects, suited to beginners in 

 chemistry, in which no assumptions are made, and which convey 

 sound teaching. He must not get over the difficulty by cleverly 

 hiding the assumptions made, and so appearing to make none ; 

 everything must be proved, and proved by experiments which the 

 beginner can satisfactorily conduct. I hold, and I am convinced 

 that the history of science bears me out, that all scientific reason- 

 ing starts with certain assumptions, and that in every particu- 

 lar train of reasoning assumptions are made. If the beginner 

 can be taught to recognize the assumptions which are involved 

 in his reasoning on experimental data, he will do well. In the 

 " Practical Chemistry " we have tried to emphasize the assump- 

 tions which the beginner must make. In our opinion the fatal 

 thing is to cover over and hide away the assumptions ; by doing 

 this, the student acquires a habit of confounding hypotheses with 

 facts, and so unconsciously he slides into loose methods of 

 reasoning. I fancy I can detect the effects of such a method in 

 the whole review : has not " H. E. A." tacitly, probably un- 

 consciously, assumed that chemical truth abides with him and 

 with him only ? 



We thank " H. E. A." for indicating some points in the 

 descriptions of certain experiments which might be improved, and 

 also for reminding us that the drawings of apparatus are not as 

 good as they might be. These things can and will be improved. 

 The mistake in the description of the diffusion-experiment, on 

 p. 30 of the " Elementary Chemistry," to which " H. E. A." 

 alludes, has been already pointed out to us, and a slip has been 

 inserted in all copies except the first few hundred correcting this 

 mistake. We cannot congratulate the reviewer, nor do we 

 think he will be inclined on second thoughts to congratulate 

 himself, on the trifling quibbles in which he has indulged regard- 

 ing one of our experiments on the electrolysis of water. 



Cambridge, January 23. M. M. Pattison MuiR. 



"Physical Science and the Woolwich Examinations." 



I AM afraid that the moderation of your article on the regula- 

 tions for admission to the military colleges may give some readers 

 the impression that science is merely being discouraged more or 

 less seriously in their examinations. The fact is, however, that 

 it is being ousted with absolute certainty, for hardly anyone can 

 afford to take up an optional subject which is at a disadvantage of 

 1000 marks. Severity of competition has within the last few years 

 quite doubled the number of marks qualifying for admission to 

 Sandhurst, and it will soon be impossible, even if it is not so at 

 present, for a candidate to gain a place if he takes up any subject 

 other than Latin, French, German, or mathematics. 



This making all the men fit square holes whether they are 

 round or not can hardly be for the advantage of the service, and 

 one's curiosity is aroused as to the reason for such retrogressive 

 changes — whether it is due, as has been asserted, to the action of 

 head masters who do not desire to accumulate or encourage new- 

 fashioned lore ; or whether the military authorities really opine 

 that to an officer who may have to deal with telegraphy, to 

 choose a camping-ground, or perhaps direct a search for water, 

 Latin is half as important again as electricity or physical 

 geology. 



Is it really too much to expect that they might insist first on a 

 thorough knowledge of those parts of an ordinary education 

 which are specially necessary or helpful to an officer, and then 

 treat the unessential subjects on an equality as far as possible, 

 and let a boy do in his preparation as he will when a man — 



adequately fulfil the duties of his position, and then follow his 

 own bent ? W. A. 



January 30. 



" The Art of Computation for the Purposes of Science." 



Having read with much interest Mr. Sydney Lupton's 

 second article on this subject, I think it right to draw his atten- 

 tion, and that of your readers, to Table III. of my book of five- 

 figure and other logarithms published by Messrs. C. and E. 

 Layton in 1870. 



This table was framed by me for the purpose of enabling 

 computers who occasionally require to use logarithms to ten 

 places to get same with as little trouble as possible, and without 

 shifting to any other book. In fact, I believe results can be got 

 from my table almost as quickly as from the voluminous and 

 beautiful volume of George Vega. 



For instance, referring to Mr. Lupton's example, I find from 

 my table and the instructions that log I '0542482375 = log i "05 

 -(- log I '0040459405 — this by simple division ; then — 



By part A log 1-05 = 0-0211892991 



By part B log 1-0040459405 = 0-0017535845 



log 1-0542482375 = 0-0229428836 



correct by Mr. Lupton's solution from Vega. 



My whole table is contained in eight octavo pages, and I 

 believe is in as narrow a compass as is consistent with utility. 



I may add that in the preliminary part of my book will be 

 found a method of finding the logarithms of all numbers by nothing 

 more than simple multiplication. 



The late Prof, Augustus De Morgan, when I showed him this 

 Table No. III., I well remember, replied: "It is very good 

 indeed, but you will get no one to look at it," showing how rarely 

 logarithms are ever required for any practical use beyond five, 

 or at the most seven, figures. E. Erskine Scott. 



6 Bond Court, Walbrook, London, E.G., 

 January i8. 



The articles of Mr. Sydney Lupton on the above subject, 

 which have appeared in recent numbers of your paper, do not 

 profess to be complete ; still, as their declared object is to assist 

 those who are not mathematicians to work sums by the aid of 

 tables, it seems to me that the best methods should not be passed 

 over in silence, while others that are practically obsolete are dis- 

 cussed at length. 



I beg of you therefore to allow me to call attention to the 

 labours of the late Peter Gray, F.R.A.S., in the direction of 

 supplying facilities for computing logarithms and antilogarithms. 

 He contributed papers on the subject to various magazines ; 

 notably a series (with a table for formation of logarithms and 

 antilogarithms to twelve places) to the Journal of the Institute of 

 Actuaries in 1865. His most important work on this subject was, 

 however, published as an independent volume in 1876. It is 

 entitled " Tables for the Formation of Logarithms and Anti- 

 logarithms to Twenty-four or any less number of places " ; and 

 it contains, besides the tables, an explanatory introduction and 

 an exhaustive historical preface. The published price is only 

 7^, 6^/., and it is therefore not beyond the reach of those who 

 require such tools. 



Weddle's method, the last mentioned by Mr. Lupton, consists 

 in multiplying the given number down to unity, by means of a 

 series of factors of the form I - ('i),, x r, where r may take 

 any integral value from i to 9. The logarithms of the factors 

 are then obtained from a previously prepared table, and the 

 complement of the sum of these logarithms is the logarithm of 

 the given number. Weddle also used his method conversely, to 

 calculate antilogarithms. 



Hearn, of the Royal Military College, Sandhurst, improved 

 upon Weddle's method, by substituting factors of the form 

 I + (•!)" X ;- for the computation of antilogarithms, r, as before, 

 ranging in value' from i to 9 ; but he retained the factors 

 I - (•!)" X r for computing logarithms. 



Gray's improvements on Hearn were twofold. In the first 

 place, he gave r the range from i to 999, taking for factors 

 I -t- (-ooi)" X ;-, and he thereby brought within narrow compass 

 the arithmetical work involved. In the second place, by a 

 simple arrangement of the calculations, he showed how to use 

 factors of the form i -f- (-ooi)" x r, instead of i - (-ooi)» x r. 



