370 



♦ KNO\VLEDGE ♦ 



[Dec. 21, 1883. 



But the most remarkable pai-t of Kepler's speculations is 

 that in which he determines the dimensions of the sphere 

 of the fixed stars. It aftbrds a striking illustration of his 

 strange faith in numerical analogies ; a faith however 

 accompanied by that perfect desire to ascertain the truth 

 which had already caused him to abandon one after 

 another a series of many such i-elations, suggested by his 

 poetic imagination while he was dealing with the solar system. 



The radius of the concavity enclosing the sun was deter- 

 mined by a simple proportion. Saturn the outermost 

 planet travels at a distance from the sun equal to 2,000 

 times the sun's radius. Therefore by the harmony of re- 

 lations, the distance of the sphere of the fixed stars is 

 equal to 2,000 times the distance of Saturn from the sun. 

 This enormous distance in conjir/ned by the observations of 

 Tycho Brahe which shoir no annual displacement of the 

 stars as the earth sweeps round her widely-cctended orbit. 

 But the thickness of the crystalline shell can also be deter- 

 mined. All the matter of which the universe is formed is 

 divided into three equal parts. One third is included in 

 the body of the Sun. Another thii'd forms the substance 

 of the jilanets aud of the celestial Kther which fills up the 

 space within the sphere of the fixed stars. The remaining 

 third forms the Crystalline. Now since the aether fills a 

 space exceeding the sun's volume G4 trillions of times 

 [(4,000,000)'], its density must be proportionately small 

 compared with his. And the density of the crystalline 

 must needs be a mean between the sun's density and the 

 aether's. Thus the crystalline has a density 8,000 million 

 times less than the sun's ; and as its ma.ss is equal to the 

 sun's its volume is iS,000 million times greater. Hence it 

 is easy to calculate its thickness, which is found to be equal 

 to the 6,000th part of the sun's radius.^ So that according 

 to the modern determination of the sun's dimensions, 

 Kepler's theory assigns to the crystalline a thickness of 

 but about seventy miles ! 



Struve remarks very justly that these ideas of Kepler's, 

 fanciful though they are, yet merit attention, because they 

 contain the germ of modern views respecting the universe. 

 This remark relates specially, it would seem, to the passage 

 which is italicised, and to the admission presented as a 

 note. Struve adds that it would even seem as though 

 Kepler had sought only to accommodate the Copernican 

 theory with the ideas entertained in his day respecting 

 " the waters above the firmament," spoken of in the 

 Pentateuch. (To be continued.) 



Blackwood's diaries for 1884 are again before the 

 public, some . of them having been started twenty years 

 ago. [I have used the " Six Days' Diary " for twenty 

 years. — R. P.] They now number over thirty varieties, 

 so as to meet the wants of every person keeping a diary, 

 as every one should. Most of these diaries contain three 

 maps, an almanack with events and dates, and calendars 

 for 1884.5. All information is officially corrected; the 

 prices range from Id. to 12s. The sale is very large, in 

 one case 50,000 yearly. 



* Struve says 60,000, probably from his own calculation, as he 

 proceeds to__ employ the modern estimate of the sun's distance. 

 Bat the number should be 6,000. The calculation proceeds thus, — 

 The volume of the sun is equal to one-third of a cylinder having a 

 base equal to the sun's surface and a height equal to his radius ; 

 and the volume of the crystalline is equal to a cylinder having the 

 surface of the crystalline for base and the thickness of the crystal- 

 line for height. The surface of the crystalline exceeds the sun's 

 (according to Kepler) 16 billions of times — so that the volume of 

 the last named cylinder would be 48 billions of times larger than 

 the sun's if its height were equal to his radius. But its volume is 

 in reality but 8,000 million times larger than the sun's. Hence its 

 height must be the 6,000th part of the sun's radius — 48 billions 

 containing 8,000 millions 6,000 times. 



LADYBIRDS. 



By E. A. BuTLEE, B.A., B.Sc. 



LADYBIRDS are beetles; or, in other words, their 

 organisation and developmental history are of the 

 same type as those of the Stag Beetle, Dung Beetle, Colo- 

 rado Beetle, and a host of other similar creatures. They 

 have no connection with the fieet-footed and foul-smelling 

 household pests commonly though erroneously called 

 " Blackbeetles," and more correctly named "Cockroaches." 

 These are not beetles at all, but in consequence of great 

 differences both in structure and style of development, are 

 to be referred to quite a different order, that, namely, 

 which includes grasshoppers, crickets, ic. To satisfy 

 oneself as to the zoological position of ladybirds, a 

 specimen should be dissected, or at any rate so arranged 

 as to display all its external organs. Suppose now a good- 

 sized ladybird is before us, say one with seven large black 

 spots on its red arched back. We place the creature with 

 its flat side downwards and then observe that the upper 

 part is readily divisible into three areas, slightly movable 

 upon one another. The first, which is the smallest, is the 

 head ; besides the organs of the mouth, which will be 

 referred to further on, it carries two tiny, many-jointed 

 clubbed appendages, which are the antennae, and two 

 great masses of eyes, one on each side. Xo such thing as 

 a neck is visible, and the head seems sunk in the second 

 part of the body, the edge of which forms almost a con- 

 tinuous curve with that of the head. This second part, 

 the prothorax, is considerably wider than the head, and 

 much arched, like a long narrow shield thrown across the 

 body and excavated a little in front to receive the head. 

 Behind this comes the greater part of the insect, but here we 

 get to greater complexity ; we find that the arched back is 

 not solid ; we note a central longitudinal Une of division, 

 and on dexterously inserting a needle here discover that 

 we can raise and move somewhat aside each of the halves 

 at their outer extremity, but that at their other end they 

 are hinged to the body. They are now seen to be two 

 horny curved shields, stout and stiff, and capable of cover- 

 ing completely two more delicate membranous wings 

 which are folded up underneath them, one on each side. 

 These, on being unfolded, are found to be rather more than 

 twice as long as the space in which they lie, or as the shields 

 which protected them ; they are brownish in colour, and 

 flexible, and are folded transversely in the middle, and the 

 outer half is turned back underneath the basal part. They 

 are the true organs of flight, aud when the ladybird takes 

 to the wing, as it might be tempted to do in bright sun- 

 shine, the upper shields are merely raised to give free play to 

 the wings, and are not themselves vibrated. Underneath 

 the wings we come to the real body, which, when the 

 insect is not flying, is completely concealed above under 

 the great arching shields. 



Turning the creature over on its back, we see that the 

 underside is nearly flat, and is altogether differently 

 coloured from the upper part ; the six short legs are 

 capable of being folded up, joint upon joint, and packed 

 away so neatly in slight hollows excavated for their 

 reception that when thus closed they scarcely interrupt the 

 general level of the surface, and are rendered quite invisible 

 from above. 



The organs of the mouth are so small that they require 

 considerable care in their examination. A fine needle will 

 be found useful in opening them out, and a hand lens 

 in making out their form and arrangement. Beginning 

 from above we find, under a broad, overhanging kind of 

 lip, a pair of stout, broad, liorny jaws, or mandibles, each 



