NEW BOOKS.

Dominion, Volume 3, Issue 834, 4 June 1910, Page 9

NEW BOOKS.

"The Theory of Elementary Trigonometry." By Professor Picken. Wellington: Whitcombe and Tombs. 2s. 6d. Although there have been many capable mathematicians on the staffs of the University Colleges in this country, wo have had next to nothing from them in the way .of treatises or text-books. Professor Steadman Aldis, of course, is the notable exception to liiis rule, and he not' only was a fine mathematician and a good teacher, but also had the extra faculty of writing text-books rich in freshness, precision, and vigour. One's inclination is therefore to give a hearty welcome to Professor Picken's little 48-page book. Unfortunately, while much praise is due to him for the excellence of his intention, we cannot feel either that the object he set before him was :: very useful one rr that he has in carrying out his design.- Mathematics, he tells us in his preface, "is suffering much loss of dignity in these days from iho tendency to write the elementary books with special reference to the need of schools." .Surely tins cannot be correct. 'This "tendency," which is a natural and necessary tendency, !:as been operative for far more than half a century. Kvory mathematician of eminence in that time has been brought up along the lines set by this tendency. This trndeney was the bone and bio id of Todhunti-rs treatises, and if there is one character common to those books and to the more modern text-books '.hat are not writjen by men of the graphic and geometric school of teaching, it is the tendency which the present little volume, h intended to counteract. Our author's emk'ivour is stated as having been "to follow a line of logical development, siicb Ilitil <-:»:li step sjiall commend ilsHf In intelligent readers, .'.•veil if their ac.'jUaiiiUu'.fi.' '.villi mathematics be bi't slight: ot the same time to satisfy ill!. , demands that more advanced students must make upon fundamental theory." One should expect very grent simplicity in a book written with such, a purpose, but v.i- are hound to confess that Professor Picken is very difficult and obscure in his treatment, of simple points. It is hardly exaggeration to say that one who has had a long familiarity with the calculus and with its applications to statics and dynamics may easily ■lintl the professor's opening pages very hard to grasp. The reason for this is not at first obvious, but it soon appens on a little rellection. The very !ii>.t sentence, indeed, supplies the clue: "The treatment of elementary trigonometry here presented depends fur such completeness and generality as il achieves on the precise, use of certain

mathematical terms." These are tonus in common use, "but usage," says Professor I'ieken, "has not "iixed their meaning with siidieiont- deliniteness to permit (ho assumption that they will convoy what it is intended that they should, without some preliminary statement." It is his ell'ort at precision that, niakes the author obscure. i''or example, whore the standard text-books assumed in students a common-sense that made elaborate definitions of "quantity' , or "magi'.itudo" unnecessary, Professor Pieken insists on saying thai "the word 'quantity' is to he use , .] as the ■ concrete substantive that corrcf,pnm!s to the abstract substitutive 'magnitude.' " Now, it is not in the least necessary to tell a student iluit "three magnitudes of the same kind" are "throe quantities of the same kind"; the student mentally translates magnitude into "size," or "amount,' , or "quantity." When he meets at r.ho gateway a confused insistence- o'n abstract and concrete characters in termii that would be clear whether theywere abstract or concrete, he is apt to. bo puzzled and uneasy, and ultimately,' if he follows the professor with perfect trust, to bo haunted evermore in his mathematical studies by ■ the ghosts pi uncertainty and insecurity. The main argument of at any rate the lirst chapter is found in the supposed distinction between (he abstract and concrete senses of common terms, and, since that distinction is.for the purposes of trigonometrical beginnings nonexistent, the result is very confusing, and the student is put to much labour in thinking without any counterbalancing gain in an understanding of the elements of trigonometrical methods. The style, too, is not strong and limpid as it.ought to bo in an elementary treatise, but occasionally there is a point well made. The definition of a variable, for instance, is extremely good, and meets a difficulty that besets most beginners. We think wo have indicated Professor l.'ieken's method, which is the result of his causeless -]istrust of, not the common use of common tonus, but the eonimon-senso understanding of them. To find a terminology that is complete in itself and that, owes nothing to the general usage of language is an impossible business, and such a terminology would be no gain could jt be devised. How keenly the professor hankers after this terminology is interestingly illustrated by his complaint about the "unfortunate" want of a better name for an angle of 360 degrees than "the angle of one revolution'." In his treatment" oil orthogonal. projection, too, lie goea to infinite trouble to mako a distinction between lines that aro parallel and lines that have "one and the same direction." lie .'also holds to the phrase "the. angle between two given directions," making in a footnoto a distinction between this phrase and the phrase in which "straight line" replaces "direction." It is surely an obscuring of the universality of general trigonometrical facts to use the term "direction" at all.- Upon the whole we are afraid .that the little book will be puzzling to beginners. "Wrack." By Maurice Drake. Duckworth's Colonial Library. 2s. 6d. "Wrack" is nearly, as good a study of life at sea as '"I'ho Nigger of the | Narcissus," but it is by no means all sea.and nothing else. The. work'of the salvage gang is finely pictured: it is impossible to step on the deck of the "iileclra," where men aro toiling with ferocious energy and sleill in the roar of pumps and crashing machinery, and remain quite unmoved. But these fine studies of the working of the mercantile marino aro only part of tho excellence of Mr. Drake's book. He knows as much about men as. about ships— about nnii in their un-marine aspecte—and tho hanging and roaring and swishing of iron, steam and water aro only a fine accompaniment to a very dramatic story. The hero, a naval student, becomes the chief engineer of tho salvage ship, and a strong and efficient fellow. He leaves his crowning contract at-'the call of a woman, and a storm that sinks the rich prize he is salving leaves him ruined. Having married his artistgirl, he takes a berth on a tramp steamer, and. is very .unhappy, torn between remorse at the ruin of his career and longing for his wife. Incidentally he writes a book, which is left with his wife for publication. It is a huge success, and leads to tho passage of an Act providing for a seamen's representative in the House of Commons. He returns to. find himsolf and his book the topics of tho hour, and is elected to Parliament. In the moment of his triumph he finds that his .wife has been unfaithful. "He knew that of all the influences in his life—tho work, the play, the love, the careless hope of power —ho had anchored his hopes to one alone. . And his love, weak, not rock hut windtossed wreckage, had drifted to perdition." There is some fine characterdrawing in this powerful and gloomy novel, which is shot through with that imagiiiHtion born of the real memories and feelings and of .tho romantic dreams of youth, without which art cannot make its appeal to tho spirit.

"Kowa, the Mysterious." By Charles Foley. London: George Bell ami Sons. 2s. 6d. and 3s. 6d. (Whitcombe and Tombs.)

~ Beneath the stately city of Minneapolis art lingo subterranean caverns, and, for the matter of that, if the truth were only known, the lower foundations of London are probably very odd and draughty. The author of "Kowa, the Mysterious," takes as tlie scene of his Kowa, an enormous American city, built over vast caverns, where the Chinese inhabitants fashion for themselves a secret city, crowded, elaborate, and disreputable, which becomes the refuge of all Chinese criminals and the living grave of their enemies. Now, here the author has got hold of a distinctly new and valuable ill an, and lie works it out well with many excitements and sensational events, from the day when first Carl Stone, the financial prince of Kowa, makes r.n enemy of Tao, the most influential of all the Chinese residents. Tao vows that he will lie revenged, and he ac3Mii|)lishe.s hie cud when his servants seize Car! Stone's beautiful wife Krclyn in ,, a passage of her own house, convey her secretly to a disused quarry, and thence by winding secret paths to the centre of the suhteri'iiiiean city, where she becomes the slave of a degrade:! Chinaman. Her faithful friend Ninette tracks h'er (.i the quarry, and is there seized and hurried to tin same mysterious citv, while-:i clever young scholar who lovl's Ninette devises n scheme by which Tno is forced to admit him secretly to the heart of the huge cavern. At this point the story becomes very exciting, and the judicious reader will 'skip one or two pages, where tin.- stray words glanced at seem to indicate: that iho brai'o adventurer witnessed scenes of torture. The end of the tale is cataclysmic, overwhelming, and the last chapter, while comparatively mild, is not the weakest in the book. As a tale of pure adventure and sensation, "Kowa, the Mysterious," is to be recommended.

"Tim House of Tenor." By GeraM Hiss. Growing's Colonial Library. 2s. Gil. and 3s. fyl. (Whiicombe and Tombs.) A certain ancient Hn«lish house ;mSscsEPS a drp'!iif;;l hereditary secret, which is never known b.v more than two living people, tho rar! and his lioir, who learns it when ho ponies of aj.;e. A recent marriage in the family has tcvived the memory of this weird fact, and it has served as foniidalion for more than one newly-published tale. "The House of Terror" is the story of a mansion that holds such a secret, but ihp theiuo is weakly worked out. The

brother ami heir of an curl takes advantage of a legend of horror, and shuts tho t>ll rl up in tho haunted wing of tho castle, while making it appear that ho has been drowned. At the end of fifteen years the imprisoned carl's daughter, Lady Elizabeth, is brought to her old home, and an attempt is made to force her to marrv her cousin, the son' of tho villain. But the son is Incredibly brutish, and not at all nice, and there is another quite charming cousin who acts us agent on the estate who helps Lady Elizabeth to solve the mystery hidden in the haunted wing. They open the secret rooms and discover the lost earl, a handsome man who, in -pite of his dishevelled appearance and very scanty attire, has the manners of a grand seigneur and tells his history in stately language., without waiting for a moment'to array himself. The story ends happily with the drowning of tho villain, and the death of the son in a motor accident, when he is ''smashed out of recognition" says the author complacently.

"The Diary of an English Girl." Duckworth's Colonial Library. An intense curiosity as to why '.his book was ever published fills the mind of the reader when the last page is turned. It is simply the diary of a girl, which apparently is commenced upon her eighteenth birthday, and in which she writes down at length ner thoughts and feelings, tho small evervday incidents of her homo life, and vhe gradual growth of her lovo for a man who.does not return her affection. She lias a. great desire, to plunge into literary life, and is always sending away to various editors MSS. which have taken her only a few minutes to write, and which, it is hardly surprising to note, are in most cases returned to her. Several of her verses appear on tho pages of the book, and arc about as uninteresting as :ier journal. There ire no characters 'A any interest; the incidents are very trivial; nor does the manner of writing redeem the book in any way. Even the love theme, and the way in which it is mado plain to the girl that- the man sho loves does not love her are distasteful. The author is unknown.

"Lady Susan and the Cardinal. ' By Lucas Cleevc. London: George Bell , and Sons. 2s. 6d. (Whitcombo and Tombs.)

Lucas Clcevo.is a writer who :ias gained for herself a largo circle of readers who are always on tho watch for tho latest books from her pen. The latest ono she has written, "Lady Susan and tho Cardinal," leaves ono with a distinct feeling of disappoint, luent when one remembers some of those that have appeared in past years. Tho characters in it do not appeal to ouo; their actions appear unreal or forced, and the situations unconvincing and ineffective. The opening events of the story take place in Switzerland and Italy, and include many people dl various stations in life, from a cardinal to a pet poodle. Lady _ Susan (the storm child) whom tho story centres, is a wayward, impulsive, inconsequent woman who is meant to be a very living llesh and blcod personality, but who. somehow leaves one unconvinced of her reality, and, to say *:he least of it, exceedingly impatient with her. She manages to fall in love with a cardinal who happens to bo nor guardian, and is supposed to sow a plentiful crop of wild oats, mysteriously alluded to now. and again, and from which she reaps tho whirlwind, as well as other people entirely innocent of such proceedings. Tho cardinal, although he does figure in the title of the booic, does not play a very important part in events, beyond the fact that he repulsrr. L:::ly Susan's love when she confei.:;:: it to him, and is tho cause of her running away from everyone through humiliation. Kinaldo, Due d'Ostia, who happens to have.tho misfortune to be Lady Susan's husband, is a shadowy personage, and soon Jisappears from tho scene of events. The second part of the book describes Lady Susan's life in England, wjth her second husband, Lord Sledinere, peaceful; simple, and home-loving, till sho is taken to London, where the society life brings back her old lovo of sensation and excitement. The storm child onco more, wakes up, and troubles ensue, as well as the reaping of her wild oats. Lucas Cleeve has written far better books than this ouo.

Tho principal article in the Juno issue of tho "Lono Hand" is ' by J. H. M' Abbott, who writes of "What Kitchener dicl not say." Mr. Abbott's object is a very praiseworthy • one— the pouring of cold water upon , the idea that Australians arc exempt from the necessity of other peoples to prepare ceaselessly for defence. He is brutally frank in his advocacy of humility and determination. It is suggested that a hostile raid would do Australia good. Tho commerce of Australia is dealt with in an interesting article illustrated by diagrams Amongst the short stories, which are well up v to tho standard, arc "The Treasure Seekers," by C. A. Jeffries; and "For the Land he Dishonoured," by "G. B. Lancaster." Tho usual budget of verse is iMs "time although Ella il'Fayden's "House of Dreams" is full of tenderness and genuine feeling, iilr. Roosevelt's contribution tells of his assault upon t.lie African eliphants. Of special interest is the first instalment of Edmund Fisher's account of Australian actors and actresses. The contribution of Australia to the stage, one is astonished to find, has been' simply huge. It is a pity .that "The Judicious " Thief" section has been dropped, but the general articles that take its place are interesting and wellchosen. . The price is sixpence.