Oct. 14, 18 So] 



NATURE 



557 



without this." Some time ago the present writer honestly- 

 endeavoured to understand Mr. Lunn's " Philosophy of 

 Voice," and utterly failed in his attempts. He cannot 

 find any assistance towards understanding it in the 

 present little tract (pp. 88) of loose writing, wonderful 

 reasoning, and jumping exposition. Let us hope that 

 Mr. Lunn's teaching is better than his preaching. His 

 axioms are however rather startling, especially the second 

 (p. 7), "All voices are naturally beautiful. All ugliness 

 in vocal tone is the result of transferred habits acquired 

 by the artificial use of voice in speech." If this use is 

 "artificial," what use is "natural"? But attempts to 

 understand and criticism are all thrown away. Notwith- 

 standing Mr. Lunn's initial confession that he is a mere 

 follower of Galen, he declares in his introduction (p. i) : "It 

 is z. fait accompli. I have founded a New Profession stand- 

 ing midway between the Musical and the Medical worlds, 

 with Art on its one side. Science on the other ; firm and 

 irrefutable." In this state of suspension, like Mahomet's 

 coffin, "midway between" two "worlds," and belonging 

 to neither Science nor Art, which seems fitly to describe 

 the nature of the book, we are content to leave it to the 

 happy conviction of the author that what he says (of 

 course when others can find out what it is) is " firm and 

 irrefutable." 



Practical Plane Geometry and Projection for Science 

 Classes, Schools, and Colleges. By Henry Angel. 

 Vol. I., Text; Vol. II., Plates. Collins's Advanced 

 Science Series. (London and Glasgow, 1880.) 

 A VERY practical and useful book by an experienced 

 teacher : it is designed to meet the requirements of 

 students at the Royal School of Mines, at the Royal 

 Military Academy, at Cooper's Hill, and elsewhere, and 

 embraces great part of the two higher stages of the 

 Science and Art Department syllabus. There is no 

 great scope for absolute novelty' in such a work, and our 

 author acknowledges his indebtedness to the works of 

 many, if not most, of his well-known predecessors, but 

 the arrangement appears to be judicious, and the 

 constructions good and clearly enunciated. In the 

 Practical Geometry (six chapters) the student is taught 

 the use and construction of scales, of triangles 

 and polygons, and there are numerous problems on 

 areas, on circles in contact, and on other plane curves 

 with their tangents and normals. The orthographical 

 portion treats of the projection of the five regular solids, 

 of other simple solids, of flat and curved surfaces, inter- 

 sected by cutting planes, and of solids inscribed in, or 

 circumscribed to, the surfaces of other solids ; of the 

 interpenetration of soUds, of the projection of shadows, 

 on isometric projection, on the solution of the spherical 

 triangle, and on horizontal projection — a very extensive 

 and varied bill of fare. In addition there are numerous 

 questions for practice, many of which are taken from 

 examination papers, and the text is illustrated by several 

 clearly-drawn figures. Part ii. contains eighty-one large- 

 page plates to further illustrate the constructions. The 

 two parts together ought to enable any painstaking 

 student to take a creditable place in his examination and 

 to acquire a solid acquaintance with the subject. 



Teonca delle Forze Newtoniane e sui applicazio}ii all' 

 Elettrostattica e at Magnetismo del Prof. Enrico Betti. 

 365 pp. (Pisa, 1879.) 

 In the session 1863-64 Prof. Betti delivered at Pisa a 

 course of lectures, subsequently (1865) printed in the 

 Nttovo Cimento under the title " La Teorica delle Forze 

 che agiscono secondo la legge di Newton e sua appli- 

 cazione alia elettricita statica"; the volume before us is 

 what may be looked upon as its greatly enlarged second 

 edition. It consists of an introduction and three chapters. 

 The first chapter, in twenty-three sections, treats of 

 Potential Functions and of Potentials (§ 1 1 gives Green's 



theorem and some others due to Gauss; § 12 Stokes's 

 theorem for transforming a double integral into a simple 

 integral, and the properties of a surface which has on 

 one face a stratum of attracting, and on the opposite face 

 an equal stratum of repulsive, matter ; the other sections 

 appear to contain nearly all the known properties of 

 these functions). Chapter II., on Electrostatics, in six- 

 teen sections, discusses several cases of electrostatical 

 distribution, the method of images (Sir W. Thomson's 

 theory) and condensers; Chapter III., on Magnetism, is 

 divided into ten sections (on p. 304 Prof. Betti announces 

 the theorem, " Se la superficie di un corpo e semplicemente 

 connessa ed ha un numero finito di poli, questo numero 

 sarh. sempre pari," an advance upon Gauss, w-ho has 

 shown that if there be three poles there must also be a 

 fourth). 



Kalkiil der Abzdhlenden Geojnetrie. Von Dr. Hermann 



Schubert. (Leipzig : Teubner, 1879.) 

 Dr. Schubert in this work gives us, in the form of a 

 treatise of 359 pages, the principal results as yet arrived 

 at in the " Numerical Geometry," a branch of mathe- 

 matics originated by AL Chasles and subsequently 

 studied by Zeuthen, Sturm, Halphen, Klein, and in this 

 country by Dr. Hirst (" On the Correlation of Two 

 Planes," vol, v. ; " Correlation in Space," vol. vi. ; " Note 

 on the Correlation of Tw-o Planes," vol. viii. ; London 

 Math. Soc. Proceedings). The book closes with a full 

 historical and bibliographical list in the form of notes to 

 the several chapters. 



LETTERS TO THE EDITOR 



[The Editor does not hold himself responsible for of inions expressed 

 by his corresfondints. N'eithcr can he undertake to return, or 

 to correspond with the writers of, rejected manuscripts. No 

 notice is taken of anonymous communications.'\ 



[The Editor urgently requests cori-esfondents to keep their letters as 

 short as fossible. The pressure on his space is so great that it 

 is impossible otherwise to ensure the appearance even op com- 

 munications containing interesting and nai'el facts. 'X 



The Spectrum of Hartwig's Comet 

 The .spectrum of this comet was examined here on the evening 

 of October 7 with a spectroscope having a .single prism of 45°, 

 and was found to consist of three bright bands and a continuous 

 spectrum correrponding to the nucleus. The middle and brightest 

 band was compared with the band at W.L. 519S in the spectrum 

 of a vacuum tube containing alcohol vapour, and three micro- 

 meter measures gave the position of the less refrangible edge of 

 the comet band at W.L. 5184, 5215, and 5204 tenth metres 

 respectively. The breadth of the band was about 40 tenth 

 metres. These measures would indicate that the principal 

 comet-band is coincident with the band at W.L. 519S of the 

 vacuum-tube spectrum of carbon-compounds, and not with that 

 of the Bunsen-flame at W.L. 5165. The observations however 

 were made under unfavourable circumstances, the comet being 

 low, and involved in haze and cloud. The positions of the other 

 two bands were not determined. W. H. M. Christie 



Royal Observatory, Greenwich, October n 



Wire Torsion 



I HOPE you will allow me to seek information, tlirough yoiu: 

 aid, on a subject which is perplexing me a good deal at present. 

 I am engaged in studying a gravimeter de-igned by the late 

 J. Allan Broun, in which gravity is balanced by the torsion of a 

 single w ire ; or is intended to be so. As the function of the 

 instrument depends largely on the law of torsion in wires, I have 

 been making experiments to satisfy myself on some points. It 

 is in the results of one of these tliat I have met with ray diffi- 

 culty. I was using thin brass wire (diam '02), and after stretching 

 it till it broke, twice, I supposed it to be at or near its maximum 

 elasticity, and proceeded to use it in the intended way. At each 

 end of a 6-foot plank I inserted into the edge a 2-inch screw. 

 The w ire was fastened upon these so as to get a strain by turning 

 them. The wire was in two pieces, attached to opposite sides of 

 a ring in the middle. By turning this ring the two wires w ere 



