2GG 



KNOWLEDGE ♦ 



[May 4, 1883. 



interior is nearly 5,000 feet high ; and from this a straight 

 dark lino, or " rill," will bo seen to extend in a south- 

 easterly direction to the wall. These rills, as they have 

 been called, are very numerous on the moon ; but few are 

 so conspicuous as the one of which we are speaking. They 

 appear to bo exceedingly deep ravines, clefts, or cracks ; but 

 they are, undoubtedly, the most inexplicable of all lunar 

 objects. Sometimes they pass through wall and plain in- 

 dilFerently ; at others, they seem to stop short at an object, 

 ijut to reappear on the other side of it. Moreover, they 

 occasionally intersect. We shall have more to say of them 

 as we proceed. Before concluding to-night's work, the 

 attention of the young observer may be directed to one or 

 two points of the Leibnitz Mountains (259), just coming 

 into sunlight, and shining like stars close to the southern 

 cusp of the moon. 



In rebuilding the Pittsburgh and Western Railway as a 

 standard-gauge road an extensive change was made at the 

 Summit tunnel. The Railroad Gazette says : — " Its bed 

 was lowered 9 ft. without stopping a train. The work was 

 accomplished by the excavation of the bed of the tunnel 

 while the track was kept up by trestle work. A row of 

 blasts would be fixed ready for firing, and as soon as a 

 train had passed through they would be touched off and 

 the debris cleared up before the next train arrived. The 

 track for the broad gauge was laid 9 ft. below the narrow 

 gauge, and when all was ready cars were run in on the 

 lower tracks and the trestle for the narrow gauge knocked 

 down and dragged out." A similar operation was carried 

 out some years ago with the tunnel near Blackburn, when 

 Pulman cars first began to run in this country. 



M. G. TissANDiER has described to the Paris Academy 

 of Science his new electrical motor for balloons. It con- 

 sists of a screw propeller with two heliooidal blades nearly 

 10 ft. in diameter, a Siemens dynamo-electrical machine of 

 new design, and a light bichromate of potash battery. It 

 is intended to propel an elongated balloon of about 1,000 

 cubic yards capacity. The frame of the screw propeller 

 weighs \b\ lb., is stretched with silk varnished with 

 india-rubber lacquer, and kept taut by steel wire 

 stretchers. The dynamo-electric machine has four electro 

 magnets in the circuit, and frame parts are of cast steel, 

 so as to bring the weight down to 121 lb. It drives 

 the screw by gear, which reduces the speed in the propor- 

 tion of 10 to 1 ; thus, if the coil makes 1,200 revolutions 

 a minute, the screw makes 120. It gives out 220 foot- 

 pounds per second with a useful effect of 5.5 per cent. The 

 bichromate battery gives a better yield than accumulators 

 of the same weight. It consists of an element divided 

 into four series and arranged in tension. The element 

 consists of an ebonite cell holding four litres — or 0'S8 

 gallon — and containing ten plates of zinc and eleven cakes 

 of retort carbon, arranged alternately. The immersed 

 surface of the zinc is one-third that of the carbons. This 

 battery, charged with a highly-concentrated and very acid 

 solution, is constant for two hours. The liquid becomes 

 heated as it is impoverished, and the duration of activity 

 may be prolonged by the addition of chromic acid. 



Errata. — " EnKlisli Seaside Health Resorts " (Knowledge, No. 

 78). — Pago 217, third lino from the bottom, read instead of 20° —20°. 

 Second line from the bottom, instead of -10° and 10°, read —10' and 

 — 10°. Pago 218, line 20 from the top, read "barometer follows," 

 instead of " barometer falling." Lino 11 from the bottom, instead 

 of " TallusoUs," read " Tatteraall's." 



Jlfbi'thjss. 



PRACTICAL GEOMETRY.* 



PROFICIENCY in practical geometry may be obtained 

 without much (or, indeed, any) knowledge of mathe- 

 matics, properly so-called ; and, vice versa, many excellent 

 mathematicians are very unskilful in practical geometry. 

 We have sometimes thought that the two subjects might 

 be brought into closer connection, in a treatise presenting 

 mathematical truths and reasoning, in company with con- 

 structions depending thereon. In this way, we believe, 

 practical geometry and mathematical geometry would both 

 be made much more interesting and instructive. But, 

 hitherto they have been kept very carefully apart. The 

 present work is on the old lines. The constructions are 

 given, and are meant to be learned, not proved, or even 

 inquired into. Constructions which are only approximately 

 correct are not distinguished from those which arc geome- 

 trically exact. Trial methods are mixed up with strict 

 constructional rules. The student is, in fine, kept closely 

 to practical rules, and though encouraged in the preface to 

 read Euclid, is not very likely either to do so or to have 

 his progress in practical geometry much advanced by such 

 reading. Albeit, as a work on practical geometry, this 

 little treatise is as good as most, and better than many, 

 works on the same lines. 



The student of geometry would find it useful to take the 

 propositions of this volume and prove them mathemati- 

 cally in the order in which they stand, showing in the case 

 of those which are not exact the degree of approximation 

 here attained. To do this thoroughly, however, will re- 

 quire more than a knowledge of Euclidean Geometry. The 

 property on which Problem III., Part IV., is based, is a 

 singular instance of close approximation obtained by a 

 simple construction for all regular polygons from the 

 pentagon to the dodecagon. It may be thus indicated as 

 a formula : — 



Let a be the side of a polygon of n sides, n being not 

 less than 5 nor greater than 12. Then, if r is the radius 

 of circle circumscribing the polygon, and we put 



— (n - 6)n-=a 

 36 ^ _ 



r-=o-(I -I- 2 y3 sin a -f- 4 sin-a). 



A Melbourne correspondent writes to the Mining 

 Journal that already two gold mines are lighted by 

 electricity, and that others are introducing the electric light 



The Academy of Painting and Sculpture at Berlin has 

 been lighted by 200 Edison lamps. The dynamo is driven 

 by a Ruston-Proctor engine of 16-horse power. 



The Telepuone in Boston. — An increase of 27,210 

 subscribers to the telephone in Boston is reported during 

 the past year. 



At a recent meeting of the Glasgow Town Council it 

 was stated that the Bazaar Committee " had twice visited 

 the eighteen electric clocks in the City, and on each occa- 

 sion had found them all correct. The nineteen turret 

 clocks under the charge of the Committee had also been 

 visited, and ten were found correct, eight being slightly 

 wrong and one standing." 



* " The Art Student's Second Grade Pr.actical Geometry." By 

 John Lowres. Revised to date and partly written by George Brown, 

 of the Blackheath School of Art. (London : Moffat & Paige.) 



