400 



SCIENCE. 



[Vol. I., No. 14. 



omy. We onlj' wish the publisher had done 

 as well as the authors. The illustrations are 

 numerous, and probably sufl3cient to fulfil the 

 end of helping the student in his work ; but, 

 from an artistic point of view, they are, with 

 rare exceptions, simply atrocious. 



MINOR BOOK NOTICES. 



Guesses at purpose in nature, with especial reference 

 to plants. I5y W. Powell James, M.A. Lon- 

 don, 1883. 192 p. 12°. 

 This is a little book of ten chapters, which 

 has just reached us, and which we would notice 

 with a word or two in addition to an announce- 

 ment of its title. The author, we fancy, is a 

 clergyman and merely an amateur naturalist. 

 However that may be, his guesses are shrewd, 

 and the -w&y of putting them is taking. Con- 

 sidering the great number and variet}' of the 

 facts he has collected, — the greater part from 

 books, — he has fallen into few mistakes; so 

 that the volume has more scientific value than 

 is usual in such treatises. 



An outline of qualitative analysis for beginners. By 

 John T. Stoddard, Ph. I) , professor of chem- 

 istry in Smith college. Northampton, Gazette 

 printing company, ISSS. 4 + 54 p. 16°. 



The general plan of this work will doubtless 



be recognized as one which gives the best re- 

 sults in teaching qualitative analysis. To a 

 certain extent it is faulty in detail, both as 

 regards convenience of arrangement and the 

 selection of methods. Although this criticism 

 applies more especiallj' to the course of basic 

 analj'sis, if advantage were taken of differences 

 in solubilit}' of certain barium, calcium, and 

 silver salts of the acids, it would save the 

 student much time and labor in general analy- 

 sis. An appended list of the names and sym- 

 bols of the more common reagents wiU be 

 found useful. 



A short course on quantitative analysis. By John 

 Howard Appleton, A.M., Brown university. 

 Philadelphia, Cowperthwait §• Co., 1881. 183 p., 

 cuts. 12°. 

 , The course of analj-sis presented in this 

 work consists, with few exceptions, of a judi- 

 cious selection of methods and determinations. 

 The descriptions of processes and apparatus 

 will undoubtedly' be of much service in the 

 laboratory, although considerable descriptive 

 chemistry' is introduced with which the student 

 is supposed to be familiar before undertaking 

 quantitative analj'sis. An exception will proba- 

 bly be taken to the completeness of the notes 

 and explanations, which leave little opportunity 

 for thought or study on the part of the student. 



WEEKLY SUMMARY OF THE PROaRESS OF SOIENOE. 



MATHEMATICS. 



Alignment curves on the ellipsoid. — Mr. C. H. 

 Kummell describes several curves tliat represent the 

 straiglit line, all of which, on the sphere, reduce to 

 the great circle. The vertical section is traced by the 

 surveyor at one end, who fixes points in range with 

 the other end. The proorthode (irpo, dpdog, 6d6c) results, 

 if the alignment at each point is determined at a 

 point previously fixed, the distance between the two 

 being infinitesimal. It is followed in chaining, or 

 more roughly by the pedestrian in moving toward an 

 object. In these two curves no back-sight is taken : 

 they are differently related to the two ends, and do 

 not return upon themselves. The dlorikode ((5m) is 

 the locus of all points at which the vertical plane 

 through one terminal point also includes the other. 

 It is used in laying out primary base-lines, the points 

 of which are determined by making fore-sights and 

 back-sights differ always by 180°. This curve has 

 been confounded with the preceding by Dr. Bremiker 

 {Studien ilber hohere (jeoddsie, 1SG9) and others; but 

 the proiJrthode is everywhere tangent to the vertical 

 plane passing through one terminal point, while the 

 diorthode, except at the ends, is not. The curve of 

 shortest distance between two points, often called 

 the ' geodetic line,' would more properly be called the 

 brachislhode (/3pii,t£CTrof). These names were sug- 

 gested by Mr. VV. R. Gait of Norfolk, Va. 



Mr. Kummell shows the diorthode to be the inter- 



section of the ellipsoid with a hyperboloid of one 

 sheet. In the case of an ellipsoid of revolution, this 

 is the parabolic hyperboloid. Taking the three prin- 

 cipal axes, a, b, c, as axes of x, y, and z, he i-epresents 

 the points where the chord connecting the two ter- 

 mini of the proposed alignment pierces the planes 

 xy, xz, yz, by (a-j, yz, 0), (xy, 0, Zy), and (0, y^, Zx), 

 respectively, and introduces quantities, — 



b'' 



a=2 = 1 — 



and so, by cyclic permutation of letters, Pc"^ and /3a^, 

 ya^ and yt^; where the ratio of each of his first set of 

 auxiliary quantities to one of his last gives one of the 

 co-ordinates of position of those generatrices of the 

 hyperboloid which are perpendicular to the co-ordi- 

 nate planes. The equation of the hyperboloid is, — 



(- 3) (»-S) ('-*)■ 



and it passes though the centre of the ellipsoid. 



The diorthode cannot be traced practically, be- 

 cause of the curvature of the earth. Mr. Kummell 

 has investigated the locus of all points through which 

 one taogent line meets the normals drawn at the two 

 extremities, and finds its intersecthig surface to be of 



