458 



♦ KNOWLEDGE ♦ 



[Dec. 



1884. 



as at La M 6, so that LcM its horizontal diameter meets 

 A Q D, D P A in L and M. Then the circle ahaMh is 

 equal to the figure A P D L. I join A D (passing, 

 obviously, through c). Then A P D Q is divided into two 

 equal parts, each equal to a semicircle FAG or F i G. 

 The spaces A K L, M N I), are equal ; and each is obviously 

 equal to either of the equal spaces K a M, L 6 N. Again, 

 any space like A P Q is equal to the corresponding segment 



a qp, — Q qP p being parallel to A i>, B D. Also A K ^ Q 

 is equal to aTLT p ; and Q 9 L is equal to P ^ M. What 

 a number of odd relations, each one of which seems un- 

 provable directly, seem to come in ! 



M. You would find each one of these relations readily 

 demonstrable, independently of the general result. Con- 

 sidering such corollaries one often recognises simpler proofs 

 of the main proposition. You wUl find several examples 

 of this in my " Geometry of Cycloids." 



A. I see that, reverting to Fig. 2, the area A P D J 

 must be equal to the semicircle A p B. Can this be proved 

 directly 1 



M. It can ; bat I will leave this to you as an exercise. 

 Begin thus, — From P, R, draw P h, R i perp. to A b. Then, 

 noting that by a property of the cycloid the tangent at 

 P or R has ultimately (when these points come near 

 enough together) a direction parallel to A^, show that the 

 rectangle P i is equal to the rectangle hp. This you will 

 find easy by making a rectangle corresponding to P i, in all 

 respects, as shown at pi' : this rectangle and Lp are com- 

 plementary, and therefore equal. The rest should be easy. 

 But, should you fail, note that the next example, which will 

 relate to the area of a parabolic segment, will show the 

 method fully. 



(To be continued.') 



SUN-SPOTS, TEMPERATURE, AND THE 

 AFTERGLOW. 



IN an excerpt from his " Memoirs of Life and Work," 

 Dr. C. J. B. Williams, F.R.S., has published an 

 account of a series of observations made at Cannes which 

 possess sufficient interest to render some notice of them 

 desirable. After speaking of the beginning of 1883 as a 

 period of sun-spot maximum, he goes on to say : — " But on 

 Feb. 28, 1883, I was surprised to find the sun without a 

 spot. On March 3 I observed again, and still found no 

 spot. The next day began a fall of temperature of 6° Fahi-., 

 with a high wind from the north-east, which continued till 

 Maif^h 7, when there came on a heavy snowstorm, covering 

 the ground to the depth of eight inches, and causing great 

 destruction in my garden, bearing down and breaking many 

 valuable trees and shrubs. This was followed by a fall of 

 temperature to five, six, and seven degrees below freezing, 

 even in my sheltered situation : in more exposed places it 

 fell four and five degrees lower. Such cold had not visited 

 Cannes before for sixcy years ; and it was the more remark- 



able as the previous part of the winter had been quite 

 mild, only two or three times reaching the freezing-point 

 This severe weather lasted till the middle of March, when 

 the sun-spoti began to re-appear, and the average tempera- 

 ture to rise in proportion." A similar fall in temperature, 

 we may note, occurred in the month of December, at a 

 time when the solar disc was free from signs of disturbance. 



In order, however, to prove that this quiescence of the 

 sun's surface, and a merely local fall in terrestrial tem- 

 perature, stood in the relation of cause and effect, it would 

 be very desirable, if po.ssible, to collect data as to the 

 meteorological conditions at Cannes during the years 1870 

 (maximum period), 1878 (minimum), and so on ; and to 

 ascertain how far temperature was simultaneously affected 

 elsewhere. 



Another statement of Dr. Williams's will certainly 

 possess the charm of novelty. We refer to his announce- 

 ment that Mr. J. F. Campbell, of Islay, has invented 

 what he calls a " Pictorial Thermometer, which marks 

 degrees of heat by certain changes of colour in Prussian 

 blue, Scheele's green, and other pigments." Assuming (in 

 the absence of any description) the indications of this in- 

 strument to be trustworthy, it is interesting to read : — 

 " 1. That an area in a solar image, focussed on a sensitive 

 screen, in the proportion of ^, is much hotter thsin the 

 rest', as proved by colours which record temperatures. 

 2. It was clearly proved that sun-spots, while within the 

 hot area, radiate much more heat than the rest of the area. 

 Spots were seen to draw hot traces repeatedly. 3. The 

 same spot, when outside of that hotter area, radiates less 

 heat than the rest of the visible sun. Mr. Campbell 

 further informs me that he actually measured the heat of 

 the sun on the spotless day, December .5, which I have 

 recorded, and that it did not rise higher than 1100° Fahr. ; 

 while on many previous days, with many spots, it reached 

 1600° and upwards." 



Here again, however, some check on or control of the 

 observations recorded would seem desirable. Dr. Williams' 

 observations of the afterglow diflfer in no material respect 

 from those of hundreds of others which have been made 

 all over the world. In opposition, however, to what he 

 excellently describes as the "sensational expansion of Mr. 

 Meldrum's hypothesis of volcanic dust," which appeared 

 in the Titties at the beginning of last December, he makes 

 the infinitely more rational and scientific suggestion that 

 it is icedust in the higher regions of the atmosphere whieh 

 has been the chief operative agent in the production of the 

 exquisite phenomena with which we are now familiar. It 

 is needless to point out that this, if accepted as a vera 

 causa, would explain the apparition of the afterglow at 

 the beginning of 1883, six months before the Krakatoa 

 eruj)tion ever took place at all ! ( Vide Knowledge, Vol. 

 v., p. 418.) 



THE ENTOMOLOGY OF A POND. 



By E. A. Butler. 



ABOVE THE SUEFACE {continued). 



THE transition from the obscure, sluggish, and inoffen- 

 sive stone-flies and alder-flies to the brilliant, active, 

 and rapacious dragon-flies, which are the most highly pre- 

 daceous of all the insect denizens of the air, is, indeed, a 

 passage from one extreme to the other, so far as habits are 

 concerned, and well illustrates the heterogeneous composi- 

 tion of the order Neuroptera, of which the dragon-flies are 

 usually regarded as forming the section Odonata. We 

 have already seen how these creatures comport themselves 



