582 



NA TURE 



[April 19, 1900 



He has now a sum of 30/. of unspent income. Suppose, 

 to make the argument quite clear, that with this sum he 

 engages another typist in his own office. Is this not a 

 new opening in the industry ? And granted that Miss 

 Dives has displaced another typist, if this displaced one 

 gets the new situation, has this competition taken the 

 bread out of Miss Lazarus' mouth? The position, of 

 course, practically, is that the new typist has added a new 

 sum of wealth to the community, and is paid by the 

 value of this new sum." 



In this way the author deals with the popular fallacy 

 that there is in a community only so much work to go 

 round, and that if some are unemployed, the way to get 

 this margin into work is to shorten the hours of those 

 who are employed. The exact reverse is the truth. The 

 way to produce more employment is to increase the pro- 

 duction of those who are already employed, and so cause 

 a greater demand for labour upon which the value of 

 that increased production is spent. 



The author discusses at great length, m the second 

 part of the book, the principles of distribution, and we 

 are sorry that we have not left ourselves space to follow 

 him as much as we should like. The demonstration is 

 clear, however, that no distribution of the aggregate 

 income of a community upon any principle of equal needs 

 or other such principle dreamed of by Socialists is even 

 conceivable, and that the only way, in fact, that rough 

 justice can be done is by the income of each individual 

 being assessed at what his services fetch in the open 

 market. This is the essence of the individualistic struc- 

 ture of society, and its justification is that there is no 

 other way of measuring individual services against each 

 other. 



Altogether, we must commend the book very highly as 

 a careful study of most difficult problems. The author's 

 style is clear and pointed, and there is not an obscure 

 page in the book. It is an excellent work to put into 

 the hands of the economic student. R. GiFFEN. 



PRACTICAL MATHEMATICS. 

 Practical Mathetnatics. Summary of Six Lectures de- 

 livered to Working Men by Prof. John Perry, D.Sc.^ 

 F.R.S., February and March 1899. (London : Eyre 

 and Spottiswoode, 1899.) 



THESE Lectures were delivered as introductory to the 

 new subject of Practical Mathematics, recently 

 established in the examinations of the Science and Art 

 Department ; but, incidentally, they serve to show how 

 we have come by our state of lethargy, out of which we 

 have had so rude an awakening. 



Recent events in South Africa have given a shock to 

 our insular self-sufficiency, and made the reflective tremble 

 to think what would have happened, remembering the 

 fate of France, if we had been involved with a real 

 European power, with no opportunity of gaining time 

 for a reorganisation of our antiquated methods. 



We have lost initiative and flattered our own superi- 

 ority, instead of observing the marvellous progress of 

 other countries ; and this self-sufficiency is especially 

 ■noticeable in our scientific and practical methods, so that 

 among us it was considered hopeless for a benighted 

 foreigner, French or German, however hard he might 

 work, to rival methods we could acquire without effort. 

 NO. 1590, VOL. 61] 



Our practical men have been content to jog along by 

 rule of thumb and the knowledge acquired from endless 

 mistakes, imagining the rest of the world felt its way in 

 the same blind fashion ; holding no communication with 

 the theorists, who, as mostly engaged in the educational 

 line, were high up in an sethereal plane of thought, and 

 despised all practical applications of theory to nature, 

 ignoring the ideas which are in the course of trans- 

 forming the conditions of civilisation. 



These Lectures on Practical Mathematics are useful 

 in lifting the thoughts of the working man out of his 

 narrow groove ; and are also worth the study of the pure 

 theorist, in showing him how to take the additional and 

 difficult steps, hitherto neglected, but required for making 

 his theory of immediate practical utility ; at the same 

 time to give him some useful hints for smoothing the 

 initial path of mathematics from needless difficulties. 



The Lectures begin with some valuable advice on the 

 proper method of performing the simple arithmetical 

 operations, a subject which is carried out with us in a 

 scandalously antiquated manner. The keynote of prac- 

 tical numerical computation is given in § 3 : — 



"When calculating from observed quantities, it is dis- 

 ho7iest to use more figures than we are sure of." 



Suppose TT is to be squared, taking its value as 3T416 ; 

 according to our obsolete methods, the result would be 

 worked out to nine significant figures, even if five only 

 were to be retained ; the proper method, of writing the 

 multiplier in reverse order, is explained on p. 4 ; so, too, 

 with division on p. 5. Mantalini had the true arith- 

 metical sense when he passed his remark on the bill of 

 sale ; but our schoolmasters proceed on the proverb— 

 " Take care of the pence, and leave the pounds to take 

 care of themselves " — thus reversing the relative import- 

 ance of the figures. 



Prof. Perry is a true disciple of Squeers, the discredited 

 inventor of our modern system of technical education, 

 hampered as he was by an incompetent demonstrator. 

 After giving the smallest possible preliminary explana- 

 tion, he makes the student think out the principles for 

 himself in the course of a variety of well-chosen applica- 

 tions of actual interest. The Slide Rule, never mentioned 

 in scholastic treatises, is introduced at once for practical 

 calculations ; this instrument rejects automatically all 

 the unimportant and dishonest figures in the arithmetical 

 operations of multiplication, division, involution and 

 evolution. After a short description with a diagram. 

 Prof. Perry finishes with the sound advice : — 



" Think it out for yourself ; practise multiplying siniple 

 numbers ; ask nobody to help yoii, and you will rapidly 

 get familiar with, and fond of, the Slide Rule." 



The celluloid scale of the latest patterns enables the 

 figures to be read off with such increased accuracy that 

 the Slide Rule may now supplant all books of Mathe- 

 matical Tables and Logarithms for physical and engineer- 

 ing purposes, as measurements can rarely be made beyond 

 four significant figures in Lord Kelvin's opinion. 



A Table of four-figure Logarithms and Antilogarithms 

 is appended, and further on a method is given (due origin- 

 ally to Mr. Edser) of calculating these logarithms, with 

 which must be contrasted the elaborately difficult treat- 

 ment of ordinary mathematical treatises; depending on 



