I30 



NATURE 



{Dec. 12, 1878 



limit, I dx = the element of area described. In passing 



over a finite area this will equal / Id x = I x, where x 



is the whole distance recorded by the roller. If now the 

 roller be mounted at a distance r from the centre of the 

 line, in traversing the element of area as before, it will 

 first record Id x in its motion parallel to itself, and then, 

 as the line turns about its centre, it will either add or 

 subtract from that reading an amount corresponding 

 to the arc of the circle of radius r, through which 

 it turns; the roller will thus show Id x ± rdO, 

 where dO is the small angle turned through. In 

 traversing a finite area this will record I x ±. r 6 

 where 6 is the angle between the initial and final positions 

 of the line. It is now obvious that if the initial and final 

 positions of the line are parallel or coincident, the area 

 passed over by the line will be equal to the area recorded 

 by the roller, even though it were not mounted on the 

 centre of the line, as the second term in the expression 

 just given vanishes. Returning now to the illustration, 

 we see the line represented by the rod carrying the roller, 

 its two extremities being the tracer and the axis of the 

 pivot. Assume that the tracer is placed at the extreme 

 right of the area to be measured : by moving it to the 

 extreme left the roller is made to record an area dif- 

 fering by ± r ^ from the whole area between the initial 

 and final positions of the rod, and bounded by the portion 

 of the circle described by the further extremity of the 

 rod and by that portion of the boundary of the area tra- 

 versed, rand 6 having the meanings previously assigned to 

 them. Let the tracer be now carried round the boundary 

 back to its starting point on the other side of the area ; the 

 roller will now revolve the reverse way, and will subtract 

 from its previous reading an area differing by + r5 

 from the area contained between the two positions of the 

 rod, the arc described by the pivot and the portion of 

 boundary traversed. It is now apparent that the reading 

 of the roller gives the difference of these areas, which is 

 that of the figure required (Fig. 4).^ A different form of the 

 polar planimeter is shown in the second illustration, and 

 is provided with an adjustment for varying the effective 

 length of the arm carrying the tracer, by which means 

 the dial and the graduations on the roller are made to 

 show the area to different scales. Mr. F. J. Bramwell 

 was, we believe, the first to publish an intelligible de- 

 ■scription of the planimeter. This the author refers to, 

 but has rendered it incomplete and far from lucid by 

 condensing it ; we would, however, refer him to a short 

 -account of the instrument published by Mr. F. P. Purvis 

 in the Philosophical Magazine for July, 1874. 



With this sketch of two of the most important instru- 

 ments described by Mr. Stanley, we must conclude our 

 notice of his book. We hope the publication of the new 

 •edition may lead to a more extended employment at 

 .least of these, and that the favour now shown throughout 

 India and the Colonies, as well as England, for the in- 

 struments manufactured by the author's firm may be 

 sufficient inducement to keep them up to their present 

 high standard. 



NOTES 



The announcement that Dr. W. B. Carpenter is about to 

 r tire from the post of Registrar of the University of London 

 will be received with general regret. He has filled the office 

 for twenty-three years. 



Prof. Marey has been elected to fill the place of the late 

 Claude Bernard in the Section of Medicine in the Paris Academy 

 of Sciences. 



The tenth annual report of the U.S. Geological and Geogra- 

 phical Survey of the Territories, in charge of Prof. Hayden, will 

 be ready for distribution in a few weeks. The report has been 



' It is here assumed for simplicity sake that the po'.nts at which the 

 motloa of the roller is reversed are at the extreme right and left of the figure. 



in type nearly a year, but has been delayed on account of the 

 engraving of the plates. These are now comple.ed and the 

 report will be issued at once. It contains 546 closely printed 

 pages octavo, with eighty plates, sections, maps, &c. Fifty of 

 the plates illustrate the remarkable cliff dwellers in Southern 

 Colorado and Northern New Mexico. This is the last annual 

 report pertaining to Colorado and contains a very interesting 

 series of chapters on the geology of that remarkable country. 

 On the whole this report will prove one of great popular interest 

 and ought to have been published in great numbers. Only 4,500 

 copies have as yet been ordered. About 250 pages of the 

 eleventh annual report of the field work for 1877 are in type at 

 the Public Printing Office. This will contain a detailed descrip- 

 tion of the geological and geographical features of Southern 

 Wyoming and Idaho. The reports of Sir Joseph D. Hooker 

 and Dr. Asa Gray will give this volume a high character as well 

 as great popular interest. 10,000 copies have been ordered by 

 Congress. There will be very extended geological reports by 

 Messrs, Endlich, White, St. John, and Peale, and geographical 

 reports by Messrs. Gannett and Wilson, and special reports by 

 Leidy, &c., &c. 



Various items on electric lighting are to hand. It is tele- 

 graphed from Washington, December 7, that Mr. Edison's 

 application for a patent for his electric light has been favour- 

 ably passed by the Patent Office, and that the letters patent 

 were to be issued on Tuesday. The Journal of the Society of 

 Arts for December 6 contains a useful rhume of the practical 

 application of electricity to lighting purposes, by Mr. J. N. 

 Shoolbred. A new system of electric lamp has been invented 

 in Paris and will be experimented on shortly in public. The 

 carbon rods are four in number, as in the Rapieff system, but 

 instead of crossing at an angle they are arranged in two parallel 

 lines. The consumption of carbon for electric lighting is in- 

 creasing so rapidly that M. Carre, the well-known Paris maker, 

 is extending his works. He is manufacturing now at the rate 

 of 2,000 meters a day. The electric light illumination has been 

 prolonged, by a vote of the Municipal Council of Paris, up to 

 January 19, for the Avenue de _rOpera and the front of the 

 Legislative Palace. The city engineers have received orders to 

 prepare, during the interval, a report on the several systems 

 which are now in operation or may be proposed. 



The New York papers report that Mr. Edison has stated that 

 he has made an improved receiver for his telephone by means of 

 which persons standing 15 feet from the instrument can hear a 

 whisper uttered miles away. 



After the masterly works of Tscbudi on " Animal Life in the 

 Alps," and of Heer on the " History of Vegetation in Switzer- 

 land," another work likely to be of high value is announced, — H. 

 Christ on the plants of that country — " Das Pflanzenleben in der 

 Schweiz." The interest of the work is all the greater that 

 Switzerland contains on its narrow area nearly all the diversity 

 of plants which grow in middle and northern Europe. Many 

 years' research of the author in the field, his previous works on 

 separate parts of the Alps, as well as his connection with the 

 botanists of Europe, have enabled Dr. Christ to pubUsh a work 

 which may be expected to range with those above-mentioned. 

 It will appear in four fascicules, with many illustrations, and 

 four maps of vegetable zones, one of which, the distribution of ■ 

 grapes and of several plants of the Fohn and lake regions, will ' 

 appear this month. The whole work will be finished about' 

 the spring of 1879, the first half fascicule having just appeared. 



A NEW Botanical Society has just been formed at Munich, j 

 the president is Prof. Robert Hartig, and the vice-president 

 Dr. Arnold, an eminent lichenologist. 



Herr Albert Kuppers, an eminent sculptor at Bonn, hasj 



