oO 



KNOWLEDGE 



[Nov. 1», 1**1. 



Wr get in Miig way a ]inriibolic nnd a hyperbolic arc (tlio rllipso 

 i'niinut bo roprcHcnti'd ut nil in tliis way by tlic Biniplu uso of 

 |ianillol HtruiKlit linvii), but wo linvo no mcaiia of drawing a pnra- 

 bulu or by|iorbola of K>^'''n Hizu, liuvinK a given fuciiH and directrix, 

 or in tlic case of tlio liyiierbola, having a given centre and given 

 niivni|iti>t<'i!. I am aware that there are mechanical means, eunic of 

 which seem i<in>|iIo enough, for drawing all the conic sections, but 

 they do not suit my |iur|iOse. I want to be able at any time, with 

 the instruments ftjund in an ordinary box of instruments, to draw a 

 parabola, hyperbola, or ellipse of determinate size, position, and 

 shape. Can you help mo to meet this difficulty ? 



Geometeicl'.s. 



[I will take an early opportunity to describe some simple methods 

 of drawing the conic sections in the way required by Geomctricus. 

 The methods described in his letter are correct j but in practice it 

 is well to have methods which give a scries of enveloping lines, 

 gniding the liand in sweeping out the curves after such points as 

 p, q, r, s, and ( have been obtained ; or the curve may be struck out 

 in that way without obtaining determinate points as above. To 

 illustrate my meaning, let Geomctricus join C 3 in Fig. 1, which line 

 will be trisected where crossed by ^ 5 and s -4. Join these points of 

 triscction with the points 2 and 1 (on A B) respectively; then the 

 two straight lines thus drawn and C 3 will touch the parabolic arc 

 at C, s, and q respectively. With A 13 there will bo four tangents. 

 If A 3 and C 3 (3 on A 15) be divided into six equal jiarts, and the 

 successive points of division along C 3, be joined with the succes- 

 sive points of division along 3 A, there will bo obtained seven 

 tangents touching the arc AC at A, p, q, r, .«, t, and C. 

 Tangents for the curve A, q, s, Fig. 2, may be obtained in 

 another way, which I will describe, as also methods for draw- 

 ing ellipses, either by obtaining any number of points along 

 the curve, or by getting a series of tangents enclosing it. In the 

 meantime, I note that A is the vertex, AD the axis of the parabolic 

 arc AC in Fig. 1 ; neither its focus nor its directrix is given directly 

 by that method, but by taking BC bearing a definite ratio to AB, 

 the position of the point which is at the extremity of the latus 

 rectum (or focal chord perpendicular to the axis) can be determined 

 at once, and thence the position of the focus and directrix. In 

 Fig. 2, A q, is part of one branch of a rectangle hyperbola, of which 

 Ois the centre, and OD, OE are a.svmptotes. The point A is not a 

 determinate point on the curve ^unless the rectangle OA is also a 

 square, in which case A is the vertex of the branch. By making 

 OA a rhomboid, a hyperbolic arc having its asymptotes inclined at 

 any angle, can be obtained ; and if the rhomboid is also a rhombus, 

 the vertex of the arc so described will be at that angle of the 

 rhombus which lies farthest from O. — Ed.] 



CAX ICE-YACHTS SAIL FASTER THAN THE WIND ? 



[17] — "Upsilon" (letter 3, p. 16) is one of the many and intel- 

 ligent men who have been perplexed by this apparently simple 

 question. I think the following considerations appeal to the judg- 

 ment, perhaps, more forcibly than those you append to"Upsilon's" 

 letter : — 



H a ship is sailing before the wind, a pressure is manifestly 

 exerted on its sails, and i»«!consequence, the velocity increases until 

 the ship has the same velocity as the impelling fluid (the air). This 

 is the theoretical limit, for then the ])ressm'e ceases. 



But if, on the other hand, a ship is sailing with the wind abeam, 

 no matter how great the velocity, the moving air exerts a pressure 

 on the sails. The component of this pressure resohod in the direc- 

 tion of the ship's motion tends to increase that motion, and since 

 the wind pressure is constant in action nnd direction, the ship may 

 be considered to be moving under a uniformly accelerating force. 

 Hence, if there be ne drifting to leeward (of course, a theoretical 

 consideration), there is no theoretical limit to the velocity which the 

 ship may attain. In the case of ice-yachts, the drifting and friction 

 are at a practical minimum, and the speed they attain may bo very 

 much greater than that of the wind. 



Cri'sader. 



[The reply we gave last week takes the lino which "Cmsader" 

 suggests. Ho will see, however, that the accelerating force is not 

 nniform, but diminishes as the velocity of tho ship increases. It 

 would be a pretty problem to determine, with certain necessary 

 assumptions as to .sails, frictionni resistance, ic, the maximum, 

 velocity uttuinuble with a given wind. — En.] 



IS THE SUN HOT? (Abstract.) 



[18] — Tlic sun is regarded as the fountain head of all terrestrial 

 energy. Tho gravitation of tho central mass of the sun causes 

 tremendous compression, giving birtli to the forces that are trans- 



mitted to as. Now the forces that wc arc most gt'nsiblo to arc 

 heat and light, but there is another force that we a>v not so sensible 

 to, i.e., chemical force. Did " Anti-Gucbre," wlnxi ho drew near to 

 his fire, ask himself tho following question : Where did the heat 

 originate ? Tlie answer is : Tho sun. For tN sun transmitted his 

 energy (by the medium of the lethcr) to 'fto earth, tho force was 

 utilised by plants, plants in course of timo changed into coal. 



Now, as regards tho "mountain pro/>osition." It is u well-known 

 fact that the "rays" of the sun pass Ihrowjh the atmosphere 

 without materially altering its frnperature, and are absorbed by 

 the earth, which gives out again the heat which it has absorbed to 

 the surrounding atmosphere. Now, on a mountain or in a balloon, wo 

 are further from the actoaJ source of heat, and the air, being thin 

 and rarefied, does not absorb heat like the denser and nearer-to- 

 the-<'arth atmosphere. 



Tho explanation of the mountains, Ac, will also apply to the 

 ciri-us clouds. — Yours, 4c. .Sf.N. 



[19] — With regard to Mr. Newton Crosland's letter (No. 5, p. 35) 

 on this subject, which is after all mere supposition, surely it is 

 more natural to suppose that a body which produces all the phe- 

 nomena of heat is in itself hot — at all events, till we find more 

 evidence to the contrary than N. C. can furnish. He says the 

 inflammatory action may be merely the chemical conversion of 

 substance into force. I should like to know what is combustion but 

 this ? Your correspondent " Tyro " seems under the impression 

 that light is visible ; perhaps when he hears it is not, he will be able 

 to account for the non-appearance of the broad flood of effulgence. — 

 Yonrs, Ac, C. J. Shaw. 



[20] — I may, perhaps, be permitted to say a word in opposition 

 to " Anti-Guebre's " views. 



Before discussing any point, I shall at once state that I take the 

 " conception of a medium filling space, and fitted mechanically for 

 the transmission of vibrations of light and heat " — in other words, 

 Ute himiitiferoiis (cther, an the foundation of my remarks. "Anti- 

 Guebre" leaves the subject of radiation and absorption untouched, 

 and here I think we have the explanation of his observations. 



The conception of the a?ther filling space may now fairly be said 

 to be inductively proved. Prof. Tj-ndall's exiieriment, in which he 

 allows heat waves from a radiant body to pass through a glass tube, 

 taking the temperature by the thenno-electric pile, shows, beyond a 

 doubt, that air is incapable of absorbing heat. 



He says " oxygen, hydrogen, nitrogen, and the mixtnre, atmos- 

 pheric air, prove to be practical vacua to the rays of heat." Waves 

 of heat, then, travel from the sun to us without having been ab- 

 sorbed ; but directly they impinge upon the earth, and upon absorb- 

 ing and radiating bodies, they produce heat, and cause a brisk 

 radiation. Taking the accepted scientific definition of heat as " a 

 brisk agitation of the parts of an object," we can easily understand 

 that when the atoms of the a;ther "swing" with the atoms 

 of tho bodies upon which they impinge, a quicker movement 

 takes place, and consequent!}' heat is generated. Absorption, 

 then, is a source of heat, and heat so generated is radiated 

 into the air and turned to account. The power of the atmospheric 

 aqueous vapour to absorb heat radiated from the earth is immense, 

 and it is calculated that 10 to 15 per cent, of heat from the earth 

 is absorbed within 10 or 20 feet of the earth's surface. It has been 

 observed that where the air is dry, and remarkably free from 

 aqueous vapour, as in Australia, the temperature of the night is 

 50° to GO' below that of the day, because thero is no check to 

 radiation. Anti-Guebre's, 'and all observations fall in with these 

 explanations, and jirove them. The fm-ther we go from the earth's 

 radiation, the colder we get. It is a remarkable fact, proved by 

 experiment, that aqueous vaiiour has the power to absorb rays of 

 heat coming from the earth, but is incompetent to absorb rays from 

 the nun. 



Bj' this remarkable adjustment the earth is rendered habitable. 



G. F. P. DvBR. 



1, Queen-square, Bath. 



WASTE OF SOLAU HE.VT. 



[21] — The letter in your present issue touches on a point in which 

 it has long appeared to me that scientific language is erroneous. 

 We talk of "Heat " coming from the Sun ; and under that impres- 

 sion, "Anti-Guebre's" complaint of tho "loss of Heat" has some 

 plausibility. But it appeal^s to me that the energy radiated by the 

 Sun is only one factor of the result called Heat. 



Energy 4 or x Something = Heat 



Energy -h or x Something else = Light. 

 Energy -t- or x Something else = Electricity, 

 and Heaven knows how many other yet unknown powers. There- 



