NATURE 



551 



THURSDAY, JULY 31 1913. 



PROF. PERRY'S PRACTICAL 



MATHEMATICS. 

 Elementary Practical Mathematics. With Numer- 

 ous Exercises for the Use of Students, and 

 especially of Mechanical and Electrical Engin- 

 eering Students. By Prof. John Perry, F.R.S. 

 Pp. xiv + 335. (London: Macmillan and Co., 

 Ltd., 1913-) Price 6s. 



DURING the past ten or fifteen years a great 

 deal of work has been done by ■ mathe- 

 matical teachers in wiping old scores off the slate 

 and redeveloping their teaching on more sensible 

 and rational lines. It is well known that this 

 revolution owes its success largely to the inde- 

 fatigable exertions of Prof. John Perry. We 

 cordially agree with many of the remarks con- 

 tained in the preface to the present book. It is 

 impossible to quote the whole of the author's 

 attacks on the old-fashioned drudgery in algebra 

 which has disgusted many would-be mathe- 

 maticians in the past, and made it quite impossible 

 for the present reviewer ever to appreciate any- 

 thing but applied mathematics. We can only 

 quote the first few lines : — 



"Academic methods of teaching mathematics 

 succeed with about five per cent, of all students, 

 the small minority who are fond of abstract 

 reasoning ; they fail altogether with the average 

 student. Mathematical study may be made of 

 great value to the average man if only it is made 

 interesting to him." 



Now one difficulty that most teachers have 

 experienced in developing mathematics on more 

 rational lines has certainly been the difficulty of 

 constructing suitable exercises, examples, and 

 examination questions. It is not that it is intrin- 

 sically more difficult to construct practical ques- 

 tions than it was to devise the old "pretty" 

 question to the effect that "if tweedledum" 

 (meaning one jumbled mass of symbols) "shew" 

 (never show) "that tweedledee " (an equallv 

 meaningless formula). Still, to stock a book with 

 practical intelligent questions is so difficult a task 

 that the author's statement, "In many cases each 

 of the questions has taken several hours, and in 

 some cases several days, to construct," will be 

 well understood by everyone who has worked or 

 tried to work on similar lines. 



If Prof. Perry had only published his collec- 

 tion of questions under the title " Exercises in 

 Practical Mathematics," we should have given the 

 book our unqualified praise. Unfortunately, how- 

 ever, when he comes to deal with bookivork, we 

 no. 2283, VOL. qi] 



fail to find much difference between his "practical " 

 mathematics and the old-fashioned " academic " 

 mathematics, except that his methods are less 

 logical, less interesting, and less convincing than 

 those now adopted by our best teachers. 



In fact, most of the bad features of our existing 

 methods of teaching, which the author so violently 

 attacks in his preface, will be found reproduced 

 in his own text. The book, to some extent, re- 

 sembles a recent volume which might be called 

 "The Fool's Calculus," and which justified this 

 title from the way the author had made an easy 

 subject appear difficult. Let us now examine a 

 few points in detail. 



Prof. Perry is quite correct in saying that 

 "when calculating from observed quantities it is 

 dishonest to use more figures than we are sure 

 of," although, perhaps, this mistake might be 

 rather described as " unmathematical inaccuracy," 

 than as dishonesty. But the only remedy he 

 can suggest in the case of contracted multiplication 

 is to multiply by 8651 when he wants to multiply 

 by 1568. Very few teachers adopt this absurd 

 and unnecessary method. A boy who has any 

 common sense ought to learn not only to multiply 

 numbers the right way round, but to be able to 

 fix the position of the decimal point in any line 

 of the products. 



His definition of a logarithm is as foiiows : — 



"If a n = N then n = log„N and we read this 

 as ' n is the logarithm of N to the base a.' " 



Now the average schoolboy ought to learn to 

 multiply and divide by means of a table of logar- 

 ithms long before he knows what is the meaning 

 of a n . Besides, the definition is not a logical one 

 unless n is a positive integer, because the very 

 existence of quantities with fractional indices 

 depends for its proof on the existence of a system 

 of logarithms. By making up successive integral 

 powers of i"oi or I'oooi or rooooooi, we can 

 prove the existence of logarithmic scales capable 

 of performing numerical calculations to any re- 

 quired degree of accuracy, and these lead to the 

 conception of the natural scale. Prof. Perry then 

 says that "in many important calculations we 

 need to use Napierian logarithms, whose base is 

 271828." "Why 271828?" asks the intelligent 

 student. No answer is given ; and this is what 

 Prof. Perry calls "practical mathematics." We 

 should call it cram. But the author continues to 

 drag in this apparently useless and meaningless 

 symbol e throughout the book, and when it occurs 

 in such examples as the following (p. 30) : — 



" If loefp— — + o'Q x —2_ = loe e — — + " — x, find the 

 5 493 ?53. 493 677 



value of x to three significant figures " 



Z 



