258 



♦ KNOWLEDGE ♦ 



[September 1, 1888. 



Atlantic, availed themselves of the opportunity to kill some 

 seala that were basking upon it. 



Bergs have been seen in the North Atlantic laden with 

 lumps'of rock, sand, and soil. The banks of Newfoundland 

 would ajipear to have been formed iu this way. Arctic 

 lands sufler denudation by the inland ice as it creeps along 

 towards the sea, and the berijs, separated from their parent 

 glaciers, deposit the fragments at the bottom of the old 

 ocean, there to harden into rocks and help in moulding the 

 surface of the coast. Nothing is lost, nothing is new. In 

 August 1827 a berg was observed stranded in eighty-five 

 fathoms in 46. V N. 45 W. Much earth and rock were em- 

 bedded in its fissured sides. Polar bears and other Arctic 

 animals were .seen on the bergs of 1883. An abandoned 

 ship was passed high and dry on a huge ice island in 1794. 

 and a ship with her crew was seen similarly situated in 

 1845 ; but no help could be afforded. On April 21, 18.51, 

 the brig Renovrition passed an immense ice island, about 

 ninety miles to the eastward of St. John's, Newfoundland. 

 Two dismantled ships lay snugly upon it, but there was no 

 sign of life. Captain Ommanney, E.N., was deputed to 

 investigate this report, and took great pains to arrive at its 

 truth, as it was inferred that these ships were the Erebus 

 •and Terror, of Sir John Franklin's ill-fated expedition. 

 Some people are still of the same way of thinking. The 

 crew of the German discovery ship Uansa were compelled 

 to abandon their vessel, crushed by ice, and took refuge on 

 an immense floating mass of ice, where they remained for 

 eight months. Their floating ice island was seven miles in 

 circumference, and drifted south, until the poor fellows were 

 able to m.ake their escape. During this time they had lived 

 in a hut constructed from the co.al saved from their ship. 

 H.M.S. Resolute was abandoned embedded in the ice, but 

 was picked up after a long drift to the southward. This ice- 

 bearing current tends to make the American coast very 

 cold, and, as wo write, Sydney, C.B., is not yet open to navi- 

 gation, although it is 7 degrees further south than Liver- 

 pool. The warmer water of the Gulf Stream, on the other 

 hand, enables the whalers to get far to the northward, on 

 this side of the Atlantic, and makes the mean temperature 

 of Ireland in 52 degrees N. as high as that of American 

 coast ports in 38 degrees N., 14 degrees nearer to the 

 equator. 



Many losses and casualties were caused by the ice in the 

 North Atlantic last .season. Masters should take frequent 

 observations of the temperature of the sea, although it must 

 not be relied upon as a specific indication. Warning may 

 often be obtained by means of the echo given oft' from a 

 berg when a steam whistle is sounded. No precaution must 

 be neglected by those who navig.ite our floating palaces and 

 ocean tramps, but the safest plan is to adopt a southerly 

 route clear of bergs. The Etrurla has followed this course 

 in her fastest passages. Our Admiralty charts show the 

 seasonal limits of bergs, and the United States Hydro- 

 graphical Office issues charts every month giving the exact 

 position of each berg up to the moment of going to press. 

 Notices of bergs passed at sea should be forwarded to 

 Washington immediately on arrival, and every berg reported 

 to us will receive due publicity in our columns. 



Dollond'3 New (Patented) Tabulated Dark Slide.— 

 This invention will be found of the greatest service to those who go 

 scientifically into the details of the photographic art. The centre 

 panel of each slide is rcade of specially prepared vulcanite, and is 

 tabulated so that every particular maybe at once written on it with 

 lead pencil, thus doing away with the hitherto indispensable note- 

 book. All details, such as the subject taken, time of exposure, 

 stop employed, maker of dry plate, state of weather, ice, may be 

 readily registered. This invention will, or should, entirely prevent 

 the frequent mistake of exposing the same plate twice. 



EASY 



PROBLEMS IN THE 

 CALCULUS. 



DIFFERENTIAL 



o5— -. ;- ea\y 

 the diflerential 



N" Knowledge for July I suggested 

 exercises, to be dealt with by 

 calculus, .and then geometrically to show the 

 superior genertility of the former method, these 

 two : — 



To determine (i.) the cijUnder of greatest 

 volume; nn'i (ii.) tlie cylinder of greatest sur- 

 face, ivhich can be enclosed in a given sphere. 



Let P Q R S be a cylinder enclosed within the sphere 

 A C B D, M O K being Ihe axis of the cylinder. 



Let the angle P B bi^ taken as our variable, and put 

 <P0 B = 6. The con.struction of the figure (omitting for the 

 present? the dotted lines) and its lettering needs no explana- 

 tion. Then, if r is the radius of the sphere, 

 PL^j'sin^; OL=rcos6; and 

 (i.) Vol. of cylinder P R=7r ?- cos^ d.2rsm0 

 = 2 7rr3cob2esine, 

 and the differential coelficient of this expression with respect 

 to 6 gives us the equation 



cos^e--2cos.0sm'^6=0, 

 or cos6=;0 ; 

 and cos- 0='2 sin- 6 ; or cot ^= »/2. 

 Wherefore for a maximum L should exceel P L, as v2 

 exceeds 1, or as a diagonal of a square exceeds a sides 

 [cos 6=0 obviously gives a minimum value], 

 (ii.) Area of cylinder PN, 



= 2 TT r- cos- + '2irr cos 6 . 2rsin0 

 =2 IT r^ (cos'- 9 + 2 cos 6 sin 6), 

 and for a maximum we must have 



— 2 cos e sin ^ - 2 sin2 61 -t- 2 cos^ 6^= 0, 

 that is, 2 cos 2 (9=sin 2 0; or tan 2 6=0. 

 So that if we draw the tangent C E^i B, and join OE, 

 P must bisect the angle E O B. 



To solve the same problems geometrically, complete the 



pqr6 



dotted construction representing ]) grs, ti cylinder coaxial 



with P Q R S, and having very nearly the same dimensions. 



Then, first, if PQRS has the maximum volume, the 



increment and the decrement in passing to the cylinder 



s are ultimately equal. Hence 



27rOL . LZ. 2nL=2 77(MP)2. Pn, 



or 2 L; . wL=M P . Pn=0 L . Pn. 



T -DT u \ 2PL Pn P« OL 

 (since n L=P L, ulty.), ---^= -p = — =iJr' 



or f'^-^y==:2; and 0L=v"2 P L as before. 



