Illustrated PRICE LIST of this and other Aneroid Barometers free by post on application to JOHN J. GRIFFIN & SONS, Ltd., NEGRETTI & ZAMBRA, 38 HOLBORN VIADUCT, LONDON, E.C. UNIVERSITY OF BIRMINGHAM. Mathematics Physics Chemistry Zoology Botany FACULTY OF SCIENCE. (Professor HEATH, Mr. PREECE, Mr. McLAREN and Mr. GRIFFITH. (Professor PoYNTING, Mr. SHAKESPEAR, Dr. BARLOW and Dr. DENNING. (Professor FRANKLAND, Dr. FINDLAY, Dr. MCCOMBIE, Dr. MURRAY and Mr. TINKLER. Professor BRIDGE and Mr. COLLINGE. Professor HILLHOUSE and Mr. WEST. (Professor LAPWORTH, Dr. GROOM and Mr. RAW. ¡Professor HAZEL, Mr. GILL and Mr. SINCLAIR. Professor DIXON, Mr. HUMMEL and Mr. BAIN. Professor KAPP, Dr. MORRIS, Mr. KIPPS and (vacant). BURSTALL, Mr. PORTER, Mr. Professor TURNER, Mr. HUDSON and Mr. Professor REDMAYNE, Mr. BORLASE and Mr. Brewing... and BROWN, Mr. POPE Mr. GUY'S HOSPITAL. PRELIM. SCIENTIFIC (M.B. London.). The next Course of Lectures and Practical Classes for this Examination will begin on October 1. Full particulars may be obtained on application REG. S. CLAY, D.Sc., Principal. ENGINEERING AND TECHNICAL OPTICS. NORTHAMPTON INSTITUTE, CLERKENWELL, LONDON, E.C. MECHANICAL AND ELECTRICAL ENGINEERING. Full Day Courses in the theory and practice of the above subjects will commence on Monday, October 1, 1906. Entrance Examination on Wednesday and Thursday, September 26 and 27. These Courses include periods spent in commercial workshops, and extend over four years. They also prepare for the degree of B.Sc. in Engineering at the University of London. Fees, £15 or £11 per annum. Three Entrance Scholarships of the value of £52 each will be offered for competition at the Entrance Examination in September next. ARMSTRONG COLLEGE, NEWCASTLE-UPON-TYNE, JOHNSTON CHEMICAL SCHOLARSHIP. This Scholarship (60), tenable for one year, together with a Prize in Books to the value of £5, will be awarded on the result of an Examination in Chemistry with Crystallography or Mineralogy, to be held during the week commencing October 1, 1906. Candidates, who must be Bachelors in Science of a British University of not more than three years' standing, are required to send in their names on or before September 20 to the undersigned. F. H. PRUEN, Secretary ARMSTRONG COLLEGE, NEWCASTLE-UPON-TYNE. (IN THE UNIVERSITY OF DURHAM.) The Council invite applications for the post of LECTURER MECHANICAL ENGINEERING. Stipend, 300 per annum. Candi dates must send in six copies of their application and testimonials not later than September 20, 1906, to the undersigned, from whom further particula may be obtaired, UNIVERSITY OF ST. ANDREWS. RECTOR ANDREW CARNEGIE, LL.D. UNITED COLLEGE. (Arts, Science, and Medicine.) This College will be formally opened on Friday, October 12, and the Winter Session will begin on Monday, October 15. The Preliminary Examinations, with which the competitions for Bursaries are combined, will commence on September 28. Schedules of application for admission will be supplied by the Secretary, and on being filled up may be received by him up to September 15. There are forty Bursaries vacant (four of which are open to second year students and two to fourth year students only), ranging in value from £40 to £10. Of these twenty-one are tenable by men only, fourteen (which are restricted to students who intend to enter the Medical Profession) by women only, and five (including two Spence Bursaries of the value of £30 each the first year of tenure and 40 the second year, a Malcolm Bursary, restricted to Medical Students, of the annual value of £25 for five years, a Stephen Williamson Bursary of the value of about £40 for one year, and a Smeaton Bursary of the value of about 20 for one year) by either men women. A number of Presentation and Preference Bursaries are also vacant. Grants not exceeding ao each may be assigned to students (men or wmen) during their fourth year who wish to take a Degree with Honours. In the course of the Session nine Scholarships will be competed for, five if which are open to men or women. They range in value from £80 to £50. ST. MARY'S COLLEGE. (Divinity.) This College will be opened on Monday, October 15. The Examinations for Bursaries will be held on October 12 and 13. Intimation of candidature i- not necessary. There are three competitive Bursaries vacant, ranging in value from £40 to 615. At the close of the Session one Scholarship of £, and one of £21, and one of £14, will be open to competition. The Classes are open to men or women Students, and include Latin, Greek, English, French, German, Hebrew, Aramaic and Syriac, Arabic, Assyrian, Logic and Metaphysics, Moral Philosophy, Political Philosophy, Political Economy, Education, Mathematics, Applied Mathematics, Natural Philosophy, Chemistry, Zoology, Botany, Geology, Agriculture and Rural Economy, History, Ancient History, Physiology, Anatomy, Military Subjects (Military History and Strategy, Tactics, Military Engineering, Military Topography and Reconnaissance, Military Law and Military Organisation), Systematic Theology, Biblical Criticism, and Church History. Specimen Examination Papers and full particulars respecting the Courses BROWNING'S PLATYSCOPIC LENS. WITH LARGer angles, increased field, and Engraved Real Size. AN ACHROMATIC COMBINATION, COMBINING THE DEFINITION OF A MICROSCOPE WITH THE PORTABILITY OF A POCKET LENS. "If you carry a small Platyscopic Pocket Lens (which every observer of Nature ought to do)."-GRANT ALLEN, in Knowledge. "I have long carried one of these instruments and found it invaluable."-JOHN T. CARRINGTON, Editor of Science Gossip. The Platyscopic Lens is invaluable to botanists, mineralogists, or entomologists, as it focuses about three times as far from the object as the Coddington Lens, and has a field unequalled for flatness, allowing opaque objects to be examined easily. It is made in four degrees of power, magnifying respectively 10, 15, 20, and 30 diams. ; the lowest power, having the largest field, is the best adapted for general use. Mounted in Tortoiseshell, magnifying 10, 15, 20, or 30 diameters, either power... ... In Nickelised German Silver, either power ILLUSTRATED DESCRIPTION SENT FREE. s. d. 15 O 17 6 27 6 32 6 Instruction, Fees, Examinations for Degrees, &c., will be found in the JOHN BROWNING, 78 STRAND, LONDON. OF THE published by Messrs. William Blackwood and Sons, 45 George Street, Edinburgh. Specimen Examination Papers for the Preliminary and Bursary Compe tition Examinations are published in separate booklets (Arts and Science Preliminary Examination and Bursary Competition, 1s.; Medical Preliminary Examination, 6ď.), and may be had from the Secretary, or from Messrs. Henderson, Books:llers, St. Andrews. A general Prospectus for the coming Winter Session, as well as detailed it formation regarding any Department of the University, may be obtained application to the Secretary. ANDREW BENNETT, Secretary. University of St. Andrews, August, 1906. THE DAVY-FARADAY RESEARCH LABORATORY OF THE ROYAL INSTITUTION. DIRECTOR: Professor Sir JAMES DEWAR, M.A., LL.D., D. Sc., F. R. S. SUPERINTENDENT OF THE LABORATORY: Da. ALEXANDER Scott, M.A., D.Sc., F.R.S. This Laboratory was founded by Dr. Ludwig Mond, F.R.S., as a Memorial of Davy and Faraday, for the purpose of promoting, by original research, the development and extension of Chemical and Physical Science. Michaelmas Term.-Monday, October 1, to Saturday, December 15 Full Information and Forms of Application can be had from the ASSISTANT SECRETARY, Royal Institution, Albemarle Street, W. To prevent delay Candidates ought to send in their applications for admission during the course of the Term preceding that in which they wish to enter. KING'S COLLEGE, LONDON. The Council invite applications for the post of ASSISTANT LEC TURER in PHYSICS. Salary, £150. Applications should be sent in iy September 1. For conditions apply to Send for Illd. Descriptive Pamphlet (including instructions for working) fost free from the Sole Agents for U.K. and Colonies. A. GALLENKAMP & CO., Ltd., 19 & 21 SUN STREET, FINSBURY SQUARE, LONDON, E.C. RADIUM ON HIRE. (Activity 1,800,000 units.) Fluorescent Screen, Electroscope, &'c., and Lantern Slides suitable for Lectures. Radium Pendant Microscope with Radium, 2/6 Scintilloscope, full size, 7,6 Self-Luminous Radium Screen, 5/Certificates of Radio-activity, 5/- each sample. Electroscopes for the Lantern, 7/6 Post free within United Kingdom. F. HARRISON GLEW, Patentee, 156 Clapham Road, WITH FOCAL PLANE SHUTTER. Fitted with ZEISS LENSES. SIZES:-6x9 and 9x12 cm., and 31-in. X4-in. and 5-in. X4-in. Also 9x 12 and 9x 18 cm. for Stereo and Panorama. SUITABLE FOR PLATES, PACK FILMS, ZEISS PACK-SLIDES AND ROLL FILMS. Illustrated Catalogue, "Pn," Post Free on application. THE NEW "DIAL" BAROGRAPH, It makes 20 or Self-Recording Barometer. This is a most useful instrument, and fills a long felt want. inte esting record of Barometric Variations, and at the same time readily shows (by means of the Dial) the present height of the Barometer. We guarantee the reliability of the readings obtained, both past and present. The Instrument is of the very best workmanship throughout, and is compensated for temperature. The Recording Arm and the Dial Hand, working by means of our Special Attachment off the same movement, a simultaneous action is thereby assured. Price, complete in handsome solid oak, walnut, or mahogany case, with one year's supply of Charts, Ink, and Instructions, £6 15s. THURSDAY, AUGUST 9, 1906. THE DETERMINATION OF ORBITS. Die Bahnbestimmung der Himmelskörper. By Julius Bauschinger. Pp. xv+653; mit 84 Figuren im Text. (Leipzig: Wilhelm Engelmann, 1906.) Die Gauss-Gibbssche Methode der Bahnbestimmung cines Himmelskörpers aus drei Beobachtungen. Mit einem Anhang zum Grundriss der theoretischen Astronomie." By Prof. Johannes Frischauf. Pp. 47. (Leipzig: Wilhelm Engelmann, 1905.) THE 'HE development of convenient and general methods for calculating the orbit of any body around the sun from a limited number of observations constitutes a classical problem in the annals of astronomy. Its history, which has yet to be adequately written, now covers a period of rather more than two centuries, and during that time it has attracted the attention of many famous mathematicians whose successes and failures are alike remarkable. At the time of Newton long records had made the principal features of the orbits of the known planets familiar, and no addition to their number was made within the next hundred years. Hence in the eighteenth century efforts were mainly directed to the determination of the parabolic orbits of comets. the completely satisfactory solution was deferred until 1797, Whea Olbers's celebrated work appeared. Why Olbers succeded when far greater mathematicians, such as Euler and Lagrange, had m.t with comparative failure is an interesting question. The fact is that the determination of orbits is an art demanding as such a sense of arithmetical technique and not merely an insight into the mathematical principles involved. Yet presentment. The well-known treatise of Watson we owe to America. Of other works, by far the most notable is that of Oppolzer. Unfortunately, the second volume of this book is now out of print and has be come scarce. In these circumstances a warm welcome must be extended to Dr. Bauschinger's treatise. His position as Director of the Recheninstitut in Berlin, the prominent feature of the work of which is the surveillance of the rapidly accumulating multitude of minor planets, leads us to expect an eminently practical treatment, and we are not disappointed. No great originality will be found, nor was it to be looked for, so far as regards the fundamental methods themselves. The aim of the author has evidently been to follow the path which has been proved by experience, and any originality must be sought in the modes of presentation, which are always elegant, concise, and lucid. A most important feature of a work of this kind is the choice of illustrative examples of actual computations. In both the liberal selection and the arrangement of these Dr. Bauschinger has done well. The diagrams are neat and clear. The style of printing, a matter of which the importance in the case of a mathematical work can hardly be exaggerated, will bear comparison with the best English examples of a similar class. It is impossible that all errors should have been detected in the course of proof-reading, but though two or three have certainly escaped notice, it is unlikely that there will be any necessity for a list of corrections such as that inserted in Oppolzer's second volume. Some time ago Dr. Bauschinger published a very useful collection of astronomical tables. Frequent reference is made to these in the present work, which is thus relieved of a large amount of additional matter, while the tables themselves are available in a handier form than as an appendix to a bulky volume. As it is, the author has covered the same ground as Oppolzer's In the nineteenth century, on the other hand, the discovery of minor planets, which are now being found at the average rate of on a week, has required" Bahnbestimmung," and even included some addigeneral methods of dealing with planetary orbits. The deduction of an orbit from the n.cessary three observations has ben based mainly on the methods of Grauss's "Theoria Motus." Even in matters of detail the variations which have been added have been for the most part slight and unimportant. In a less degree use has been made of the earlier method of Laplace, which has been generally regarded as inferior in practice. In reality the two solutions are essentially equivalent as regards their mathematical foundation, a remarkable theorem due to Lambert standing as the formal connecting link. Again the difference is a matter of technique rather than of principle. The determination of orbits, considered in a wide sense, forms a subject so complicated and so closely dependent on other branches of astronomy that comprehensive treatises serving to bring together what experience has shown to be the most practical methods have rendered indispensable service. In England, owing, perhaps, to the too exclusive predominance of one school of thought, little has been contributed to the development of the theory and nothing to its connected tions within the limits of a single volume. But it is of necessity a large one, and can scarcely fail to suggest the question whether its size could not be reduced by omissions or compression without prejudice to its utility. At first sight this would certainly seem to be the case. The first part, containing a discussion of astronomical coordinates, is occupied with matter which ought to be accessible in general treatises on practical astronomy. The chapter on the method of least squares might be replaced by simple references to some work devoted to that subject, and what is given in the chapter on mechanical integration ought to be found in treatises on the calculus of finite differences. But apart from the fact that this supposes the existence of ideal books which have not yet been written, it is a distinct advantage to be saved the trouble of consulting a number of separate works, even when these are at hand. The fuller treatment must be justified by a severely concise and practical discussion of all subordinate topics, and in this respect little fault will be found with Dr. Bauschinger's handling of his material. It is difficult to believe, |