3o6 



SCIENCE. 



[Vol. XX. No. 512 



posely patted and praised it while tbe dog's eyes kindled omi- 

 nously at the pretended neglect of himself. Suddenly the kitten 

 jumped from my arms to the iloor, and before I could interfere 

 the dog had seized and shaken its little life out of it. I mention 

 this as simply an instance. I believe that even birds show jeal- 

 ousy and sulk if too much notice is given a mate or a rival. 



L. L. H. 



BOOK-REVIEWS. 



A Treatise on Plane and Spherical Trigonometry. By Edwaed 

 A. Bowser, LL.D. Boston, D. C. Heath & Co., 1892. 



The different treatises in Dr. Bowser's series of text-books are 

 all charactei'ized by an abundance of well-selected exercises. For 

 class-room use this is a commendable feature. The accompanying 

 texts, however, are often open to some criticism; they partake 

 too much of the nature of compilations. It can be asserted that 

 all such works are compilations to a greater of less extent, but 

 such a claim is not always just. An author may go over the 

 whole ground, making himself thoroughly familiar with his sub- 

 ject, then condense his materials, classify carefully, present in a 

 comprehensive manner, allowing himself to be governed in all 

 this work by well known pedagogical principles. Against a text- 

 book prepared in this way this charge could not, in justice, be 

 brought. In a prospectus issued along with the trigonometry, 

 his publishers state that Dr. Bowser is accustomed to bring out, 

 on the average, one new volume a year. Whether such a feat is 

 a matter of pride on the part of the publisher or the author does 

 not appear. At any rate, it furnishes an explanation of the weak- 

 ness as well as the strength of the series. 



As a general rule, a presentation of a science which varies 

 greatly from tbe historic development is likely to be more difficult 

 to master than one which does not. Some authors of trigonome- 

 tries actually reverse the natural order. If the student could 

 commence just where Hipparchus commenced, with the relation 



between arcs and chords, and be shown the advantage in the use- 

 of a table of chords, and then led from that to a table of sines and 

 thence to the other functions, the subject would be learned in its 

 true bearing from the start. It is true trigonometry was for cen- 

 turies regarded merely as an introduction to astronomy, the result 

 being that the spherical part was developed abnormally. But 

 from the days of Regiomontanus (Cantor, II., p. 242) it was studied 

 as an independent science and grew accordingly. As topics in a 

 natural treatment of plane trigonometry we might have : Arcs and 

 chords; chords and sines; sines and the other functions; these 

 functions in the solution of right triangles, exercises; solution of 

 oblique triangles by dropping perpendiculars, exercises. Princi- 

 ple of continuity ; angles and functions in other quadrants ; funda- 

 mental relations between the functions; derived relations. Ad- 

 dition and subtraction formulse, including all formulas which are 

 easy consequences. Cases in the solution of oblique triaugles, 

 with exercises, deriving appropriate formulse as needed. Loga- 

 rithms; solution of triangles by logarithms, model arrangements, 

 exercises. Solution of trigonometrical equations, De Moivre's 

 theorem, and such other topics as it may be thought best to in- 

 sert. It is a grave pedagogical mistake not to use the natural 

 tables first, and until the student is made to feel the need of some- 

 labor-saving system. The use of the functions and the use of the 

 logarithms are entirely distinct, and should be well separated 

 from each other in the mind of the beginner. The natural tables 

 were calculated to fifteen decimal places the century before Napier 

 invented his logarithms. To sum up in one sentence, there should 

 be more of historical evolution in the presentation of trigonome- 

 try. 



Let us test the plane portion of the present work by the princi- 

 ples suggested. After giving the ratio definitions of the functions 

 first, the student is plunged into the generalized conception of 

 arcs and functions. Next the addition formulae are given and all 

 their corollaries, which means a considerable part of theoretica^ 

 trigonometry. Next, logarithms and the log-function tables are- 



CALENDAR OF SOCIETIES. 



Chemical Society, Washington. 



Nov. 10.— F. P. Dewey, Crystallized Sul- 

 phite of Zinc; W. D. Bigelow, On the Vis- 

 cosity of Sorghum Juices. Mr. Dewey's 

 paper first reviewed the literatures of sul- 

 phite of zinc from Berthollet (1789) to De- 

 niges (1892)> showing that most of the early 

 investigations were occupied with the com- 

 plex action of SOg on metals, in which the 

 production and examination of sulphite of 

 zinc was merely an incident, and while 

 some had produced the sulphite by the direct 

 union of ZnO and SO^, only a few had pro- 

 duced it by double decomposition. Two 

 formulse have been announced. The first 

 ZnSOg SHjO was proposed by both Mus 

 pratt and Forclos and Gelis in 1843, upon 

 meagre analytical data, followed, in 1844, 

 by Dr. Koene with quite satisfactory results. 

 In 1845, Rammelsburg announced the for- 

 mula as 2 ZnSO, 5 HjO, which was sup- 

 ported by Marignac, in 1857, in an elaborate 

 and complete examination. Finally, in 

 1892, Deniges somewhat arbitrarily an- 

 nounced that the formula must be 3 ZnSO^ 

 5H,0. Mr. Dewey's first results, which 

 were all obtained by dissolving ZnO in 

 SO, water, clearly and unmistakably sup- 

 ported the earlier (1-3) formula, but, on re- 

 peating Denige's work, the later formula 

 (2-5) was obtamed. Finally, from the same 

 solution of ZnO in SO^ water, both salts 

 were obtained. By allowing the SO3 to go 

 ofiE slowly, a crop of small, powdery crystals 

 was obtained, showing the 3-5 formula. 



The mother-liquor from this salt was heated 

 to drive off SOg quickly, when quite large 

 and distinct crystals were obtained, which 

 gave the 1-3 formula, thus showing that the 

 salt crystallizes with two proportions of 

 water, and that both formulas are correct. 

 It was also found that sulphite of zinc heated 

 with free access of air is completely decom- 

 posed and yields an oxide carrying less than 

 O.Ol per cent of sulphur. W. D. Bigelow 

 read a paper on the Viscosity of Sorghum 

 Juices. About one hundred juices of dif- 

 ferent specific gravity were taken and tbe 

 amount delivered by a 50 cubic centimeter 

 pipette was carefully weighed. This was 

 deducted fr-om the true weight of 50 cubic 

 centimeters of the juice and tbe result taken 

 as loss due to viscosity. From this it was 

 estimated that a 50-cubic centimeter pipette 

 would deliver from 49.5 to 49.9 cubic centi- 

 meters of the juice. It was also noticed 

 that the most varying results were obtained 

 from different juices of the same specific 

 gravity. 



Biological Society, Washington. 

 Nov. 19. — Theobald Smith, On Certain 

 Minute (Parasitic ?) Bodies within the Red 

 Blood Corpuscles; C. W. Stiles, The Topo- 

 graphical Relations of the Excretory Canals 

 of Cestodes; David White, A Walchia from 

 New Mexico; F. M. Webster, Some Entom 

 ological Factors in the Problem of Country 

 Fences ; F. V. Coville, Comparative Value of 

 Plants in Determining Floral Zones. 



Appalachian Mountain Club, Boston. 



Nov. 9. — John Ritchie. Jr., The State 

 Park on Temple Mountain, N.H. ; John Cole- 

 man Adams, The Brook Path up Chocorua. 



Reading Matter Notices. 

 Ripans Tabules : best liver tonic. 

 Eipan.s Tabules cure jaundice. 



RACES AND PEOPLES. 



By DANIEL G. BRINTON, M.D. 



"The book is good, thoroughly good, and will long 

 remain the best accessible elementary ethnography 

 in our language." — The Christian Union. 



"We strongly recommend Dr. Brinton's 'Races- 

 and Peoples' to both beginners and scholars. We 

 are not aw^re of any other recent work on the 

 science of which it treats in the English language.'* 

 —Asiatic Quarterly. 



"His book is an excellent one, and we can heartily 

 recommend it as an introductory manual of ethnol- 

 ogy," — The Monist. 



"A useful and really interesting work, which de- 

 serves to be widely read and studied both in Europe 

 and America."— Bri^7iio?i (Eng.) Herald. 



"This volume is most stimulating. It is written 

 with great clearness, so that anybody can under- 

 stand, and while in some ways, perforce, superficial,. 

 grasps very well tbe complete field of humanity." — 

 The New York Times. 



"Dr. Brinton invests his scientific illustrations and 

 measurements with an indescribable charm of nar- 

 ration, so that 'Races and Peoples.'' avowedly a rec- 

 ord of discovered facts, is in reality a strong stim- 

 ulant to the imagination." — Philadelphia T*ublic 

 Ledger. 



" The work is indispensable to tbe student who re- 

 quires an intelligent guide to a course of ethno- 

 graphic reading." — Philadelphia Times. 



Price, postpaid, $1.75. 



N. D. C. HODGES, 874 Broadway, H. Y. 



■Iiurnil P Cabinet SpecimeDs, Collections, and 

 llllilllnALui material by the pound, for miner- 

 alosists. C'llectors. colleges, schools, and chemists. 

 Send for 100-page catalogue, paper bound, 15 cents; 

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Kindly mention "Science" in 

 tvriting to Advetiisers. 



