November, 1903. 



KNOWLEDGE, 



251 



uniform in width, so regular in their intersections, so 

 synuuetrical, with dark spots so inevitably marking their 

 intersections, must be accounted, as he accounts them, 

 artificial ; the handiwork of intelligent beiags. But if 

 actual details of perfectly irregular and unsymmetrical 

 character, details having no sign of artificiality about them, 

 can present exactly the appearance, and make just the 

 impression which the network of the canal system does, 

 the argument for the existence of inhabitants on Mars has 

 vanished. We are freed, too, from the necessity of 

 considering such Ijizarre theories as would make out the 

 planet to have been scored into its jtresent form by 

 grazing meteorites, or to have assumed it through 

 crystallization. To have been set free from the grotesque 

 in oliservation is to have been freed also from the 

 grotesque in speculation. 



This service I think the drawings of the Hospital School 

 boys have effectually rendered to us. They have shown 

 that perfectly unbiased observers will see and draw the 

 Schiaparellian canals when the actual markings presented 

 to them are as little regular and artificial as any which our 

 own earth might jjresent to an outside spectator. 



I do not think we need claim more for these experiments 

 than this ; a complete explanation of the canal system 

 would proliably involve other factors than those indicated 

 above. Thus a most able letter by M. Antoniadi, which 

 appeared in the Enylish Mechanic for July 31st, 1903, 

 sums up the canal-imjjressiou uuder five heads : — 



" {a) Entirely physiological niarkiiios, like those seen by Mr. 

 Lowell ou other planets, by myself ou Mars, and by Mr. Lane on 

 his artificial tlises. 



" (A) Subjective lines, generated by the topographical details. 



" (c) Edges of physiological half-tones, begotten by contrast. 



" {d) Edges of objective half-tones, arising from the same 

 reason. And 



" (e) Ineontestably real canals, which, were we to see Mars 

 betfer, would resolve themselves into groups of knotted or unevenly 

 shaded areas." 



This classification cannot be mucii bettered with our 

 present knowledge. I should myself give the first place to b 

 as the most fruitful source of canals, and the next to d, 

 these two classes being those with which our Greenwich 

 experiments were concerned. The two physiological classes, 

 (/ and c, were not inchided in our work. But I ain inclined 

 to think that they are intimately combined with the others 

 in producing the canal system as we know it ; and that its 

 geometrical appearance is largely due to them. In the last 

 class e, I should myself prefer to withhold the name 

 "canal" from features which, like Nasmyth Inlet and 

 Hugguis Inlet, were well known long before the canal 

 system as such had its commencement. I well remember 

 that my first disposition to be sceptical of Schiaparelli's 

 discoveries arose from the fact that he drew so many canals 

 which I could not see at all as bi'ing e(|u;illy distinct with 

 Nasmyth Inlet which I had seen con.^pifiMusly. That may 

 have liei'n a bit of personal bias, but 1 think it is clear that 

 whilst the canal system as a whole must be considered as 

 subjective ouly, same markings which have been included 

 in it have been too thoroughly well defined to be anything 

 but roil. At the present moment the most interesting 

 feature with regard to the entire discussion is the tendency 

 of the ablest and most favourably circumstanced observers 

 to see the chief canals no longer as straight uniform lines, 

 but as close sequences of spots, as if an approach had been 

 made to their complete resolution. It is now a quarter of 

 a century since the canals as such were first introduced to 

 us. It may well be that the next quarter of a century may 

 see such an advance that ere its close we may have detected 

 the actual lomponent details of what we now consider as 

 str.iijdit hues, and that therefore the canals — as such — 

 may have entirely disappeared 



MODERN COSMOGONIES. 



By Agnes M. Clerke. 



v.— THE FISSION OF ROTATING GLOBES. 



Few people need to be told that a rotating fluid mass is 

 shaped very much like an orange. It assumes the form of 

 a compressed sphere. And the reason for its compression 

 is obvious. It is that the power of gravity, being partially 

 neutralised by the centrifugal tendency due to axial speed, 

 gains progressively from the poles, where that speed has 

 a zero value, to the equator, where it attains a maximum. 

 Here, then, the materials of the rotating body are virtually 

 lighter than elsewhere, and consequently retreat furthest 

 from the centre. The " figure of equilibrium " thus 

 constituted is a spheroid, a body with two unequal axes. 

 In other words, its meridional contour — that passing 

 through the poles — is an ellipse ; while its equator is 

 circular. 



Now we know familiarly, not only that a spinning sphere 

 becomes a spheroid, but that the spheroid grows more 

 oblate the faster it spins. The flattened disc of .Jupiter, 

 for instance, compared with the round face of Mars, at 

 once suggests a disparity in the rate of gyration. But 

 there must bo a limit to the advance of bulging, or the 

 spheroid, accelerated (xcZ i)ifiintiim,v!ould a.i last cease to 

 exist in three dimensions ! Clearly this unthinkable 

 outcome must be anticipated ; at some given point the 

 process of deformation must be interrupted. A breach of 

 continuity intervenes ; the train is shunted on to a branch 

 line. Nor is it diflicult to divine, in a general way, how 

 this conies to pass. Equilibrium, beyond doubt, breaks 

 down when rotation attains a certain critical velocity, 

 varying according to circumstances, and the spheroid 

 either alters fundamentally in shape, or goes to pieces. 



So much plain common sense teaches ; yet the precise 

 determination of the course of events is one of the most 

 arduous tasks ever grappled with by mathematicians. 

 M. Poincarc essayed it in 1885* ; it was independently 

 undertaken a little later by Professor Darwiuf ; and the 

 subject has now been prosecuted for eighteen years, chiefly 

 by these two eminent men, with a highly interesting 

 alternation of achievement, one jiicking up the thread 

 dropped by the other, and each in turn penetrating some- 

 wdiat further into the labyrinth. The results, nevertheless, 

 are still to some extent inconclusive ; they indicate, rather 

 than indite, the genetic history of systems. A strong 

 light is, indeed, "thrown upon it ; but in following its 

 guidance, the limitations of the enquiry have to be borne 

 in mind. The chief of these are, first, that the assumed 

 spheroid is liquid; secondly, that it is homogeneous. 

 Neither of these conditions, however, is really prevalent in 

 nature, so that inferences based upon them can only be 

 accepted under reserve. They were adopted, not by choice, 

 but through the necessities of the case. There was no 

 possibility of dealing mathematically with bodies in any 

 other than the liquid state. The equilibrium of gaseous 

 globes defies treatment, except under arbitrary restrictions.* 

 Nor is it possible to copj with the intricacies of calcula- 

 tion introduced by variations of interior density. Cosmical 

 masses, as they actually exist, are n^>vertheless strongly 

 heterogeneous, so that, at the utmost, only an approxima- 

 tion to the genuine course of their evolution can be arrived 

 at by the most skilful analysis. Yet even an approximate 



• " Acta Mathematical" Vol. VII., Stockholm, 1886. 

 t Proc. Itoiial Soeieii,; Vols. XLII., LXXI. ; Phil. Trnus., Vols. 

 C.XCVIII., C'XCIX., Series A. 

 I J. H. Joans, Phil. Trans., Vol. CXCIX., A., p. I. 



