KNOWLEDGE 



iglo is 



hat side when the 



My necessary. 



■ectly to the determination of 



'■' - 'i--^. .! V i'ltiii the enter 



I ■ : 1 i li, I ,. i.lu-re itself, liy 



■ 11 the spheres 



triangle, (and can only be e_q 



A. The problem leads of cc 

 the volume of the sphere, fn 

 surface. 



M. Yes ; because the pol; 

 sphere ABED, Fig. 4, diflVrf 

 a Tolume less than that of tli 

 A B E D and F C, H K ; and t 

 please by making the radius of the inner sphere as nearly equal as 

 we please to the radius of the outer. 



-4. Euclid, then, might have determined the solid content of the 



M. Not quite. For he has nowhere shown, nor with his methods 

 is it possible to show, either that the surface of the sphere is equal 

 to the curved snrface of the enclosing cylinder, or that the area of 

 an enclosed polyhedron may be made to differ as little as we please 

 from that of the circumscribing sphere. For the last point it would 

 be necessary to show that the area of a plane triangle as ah c 

 Fig. 4, may bo made to differ from the area of the spherical triangle 

 a h c, by a quantity which vanishes in the limit compared with either 

 area, by making the sides of the triangle small enough compared 

 with the radius of the sphere. No one really doubts this ; no one 

 for instance, imagines that an equilateral triangle with one-inch 

 sides on a globe as large as our earth differs appreciably from an 

 equilateral plane triangle with one-inch sides. But it is impossible 

 to ]prove this. 



A. What do we take next ? 



M. I think it now may be interesting to determine the areas and 

 volumes of spindles. 



A. I should have thought that would require the higher mathe- 



M. No ; they can be dealt with geometrically, and by a method 

 applicable to so many problems abont curved areas, volumes, &c., 

 that it is well worth studying for its own sake. 

 (To be continued.) 



ilflisrellanfa. 



Obituaet. — Mr. W. J. Thorns, the originator and editor np to 

 1872 of Notes and Queries, died at his residence, St. George's- 

 square, Belgravia, on Saturday last. He was in his eighty-second 



The necessary arrangements are being made at Chatham Dock- 

 yard for lighting the workshops and factories with the electric 

 light, the results of the trial in those of the workshops already 

 lighted by electricity having been found to be satisfactory. 



Dlsco^•EKY OF Mica.— A recent discovery of mica at Tallnlah, 

 Ga., is reckoned the richest in the world. It is said that blocks a 

 foot square can be taken out, and that the supply is declared in- 

 exhaustible. There is such a demand for the mineral in stove 

 making that it has been growing scarce and dear for several years. 



The Sf.vekx Tunnel. — Considerable progress has been made 

 with the works of the Severn Tunnel. The brickwork in the 

 tunnel is practically finished ; the western face of the tunnel is 

 built, and the eastern face has been commenced, the ballasting is 

 nearly completed, and the greater part of the permanent way has 

 been laid. About 48,000 cubic yards of excavation still remain 

 to be done in the English cutting, and about 5,000 yards on the 

 Welsh side. Arrangements for the permanent pumping and ven- 

 tilation are being practically carried out. 



The Pacific Mills, situate at Lawrence, Massachusetts, are re- 

 ported to be the largest textile manufacturing corporation in the 

 world, covering forty-three acres ; there are four steam-engines of 

 3,500 horse-power, forty-two small steam-engines, and fifty boilers 

 and eleven turbines of 5,000 horse-power. The annual consump- 

 tion of cotton is 15,000 bales; of wool, 4,000,0001b., the product of 

 750,000 sheep. The annual capacity is, in cottons, printed and 

 dyed, 65,000,000 yards; worsted goods, 35,000,000 yards, or a total 

 of 100,000,000 yards ; 3,600 females and 1,900 males are employed. 

 The roll pay for the year ending May, 1884, amounted to 

 1,790,000 dols. 



A EAILTV.4T JorRNET THRorGH A Bt-'RxixG FoREST. — During the 

 recent hot weather a curious, but somewhat alarming, incident 

 occurred on a railway in Finland. On approaching the town of 

 Eaipios the driver of a train saw that the forest on both sides of 

 the line was burning furiously, enveloping it entirely in smoke and 

 flames. Afraid of proceeding, he despatched a messenger to the 

 town, and after waiting for three-quarters of an hour, during 



i bo 8 



veil 



quarter of an hour, the heat being lurrilic. 



Some interesting statistics in the coal trado have just been 

 pubUshed, showing the character of the Welsh trade. The best 

 customer Cardiff has is Port Said, which took 00,000 tons in July, 

 and the least important amongst the principal Buenos Ayres, which 

 took only 12,000 tons. Newport's principal customer is Genoa, 

 which in July took 15,000 tons ; Malta only 5,000 tons. Swansea's 

 best customers were the French, Russian, and Genoese ports. 

 During last month Cardiff sent away to foreign destinations, in 

 round numbers, 588,000 tons of coals; Newport, 169,000 tons; 

 and Swansea, 69.000. In the same period Cardiff sent away 13,000 

 tons of iron and steel ; Newport, 7,000 tons of iron and steel ; and 

 Swansea, 1,000 tons. Cardiff, 18,000 tons of patent fuel ; Swansea, 



Timber Growth on the Pacific Coast of the U.nitkd States. 

 — The timber forests of the north-western portion of Washington 

 Territory, U.S., contain a wealth of forest growth which is not 

 met with elsewhere on the globe ; 20,000,000 acres of forest growth 

 are environed around the inland waterways of Paget Sound, with 

 a coast line of 1,800 miles, indented with numerous harbours 

 admirably suited to the manufacture of timber into merchant 

 shapes, and loading on vessels. This timber belt, lying between 

 the 47th and 49th parallels of latitude, will average 25,000 feet of 

 lumber to the acre, most of which is fir, but also abounding in 

 cedar, alder, and maple. The value of the twenty-four saw-milla 



Exhibition at South Kensington. The awards in the Music 

 Division will be published in October. There have been distri- 

 buted 235 gold medals, 438 silver medals, 515 bronze medals, 

 and 24 diplomas of honour. The following gold medals have 

 been awarded by the Society of Arts on the recommendation of 

 the Juries:— Sir Henry Bessemer, F.R.S., for the invention of 

 Bessemer steel ; Percy Gilchrist, for the Thomas-Gilchrist basic 

 process of steel-making ; Hathorn, Davey, & Co., for their 

 domestic motor; Samson Fox, for the invention of corrugated 

 iron flues for steam boilers; Crossley Brothers, for the "Otto" 

 gas-engine ; Ralph Tweddell, for his system of appljnng hydraulic 

 power to the working of machine-tools and for the rivetting and 

 other machines which he has invented in connection with that 

 system ; Badisehe Anilin and Soda Fabrik, for their improve- 

 ments in the manufacture of colouring matters and intermediate 

 products from coal-tar; William Crookes, F.R.S. , for his im- 



for his invention of the radiometer. 



The Government Astronomer of Hong Kong has published a 

 notice with regard to typhoons, from which it appears that the 

 earliest signs of these phenomena in the China seas are clouds of 

 the cirrus type looking like fine hair, feathers, or small white tufts 

 of wool travelling from east to north, a slight rise in the barometer, 

 clear and dry but hot weather, and light winds. These aro 

 followed by a falling barometer, while the temperature rises still 

 further. The air becomes oppressive from increasing dampness, 

 and the sky presents a vaporous and threatening appearance. A 

 ,, and also phosphorescence of the w 



gloric 



B other 



signs 



useful I 



the I 





linted with the usual conditions in the locality. When the 

 typhoon is approaching, the sky becomes overcast, the temperature 

 in consequence decreases, the dampness increases, and the baro- 

 meter falls more rapidly, while the wind increases in force. 

 Nearer the centre the wind blows so that no canvas can withstand 

 it, and the rain pours down in torrents, but there is no thunder 

 and lightning. Still nearer the centre there is less wind and rain, 

 and the sky is partly clear, but the sea is tremendous. This is 

 therefore the most dangerous position. Typhoons may be encoun- 

 tered in any season of the year, but are most frequent in August 

 and September. They appear to originate south-east of the 

 Philippine Islands. In August and September they frequently 

 pass east of Formosa, or travel towards north-west up through the 

 Formosa Channel, or strike the coast of China. Afterwards they 

 usually recurve towards north-east and pass over Japan or across 

 the sea north of Japan, but not with the violence that is charac- 

 teristic of tropical storms. During the remainder of the year they 

 most frequently cross the China Sea from east to west. 



