MARcn 17, 1882.] 



KNOWLEDGE 



421 



that the perturbation of the planets could never transcend 

 certain narrow limits. The planes of the orbits could never 

 be mueli deranged, t}ie eccentricities of the orbits could 

 never be much altered. Tlie major axes of tliose orbits 

 could hartlly be changed at all. But all the great calcu- 

 lations of Lagrange involved one supposition, they all took 

 for granted that tlie earth and moon, the sun and the 

 planets, were rigid bodies. This we know is certainly not 

 the case with many of these Ijodies, it is probably not the 

 case with any one of them. Viewed with regard to the 

 present researches, we are tempted to ask whether the 

 absence of rigidity may aflect the truth of Lagrange's great 

 theorems. On the answer to this <iuestion depends the 

 stability of the solar system. There can be no doubt that 

 owing principally to their small sizes, and to the distances 

 at which they are separated, the planets behave nearly as 

 rigid bodies would so far as their mutual attractions are con- 

 cerned. Lagrange's theorems are therefore approximately 

 true, and they will remain substantially correct for 

 hundreds of thousands of years, Ijut for ail that the planets 

 are not rigid. Jupiter and Saturn do not act upon each 

 other merely as the two heavy particles which Lagrange's 

 theorj- would require. Jupiter and Saturn do, no doubt, 

 attract each other as Lixgrange supposed, but thej- also 

 raise tides in each other. These tides may be despised 

 when we are considering moderate periods of time, but the 

 tides are there nevertheless. It may be slowly, but it is 

 certainly surely, that these tides are doing their work, and 

 by their agency the solar system in course of time shall 

 become utterly transformed. Geometers know that when 

 a curve has to be drawn, the various parts of that curve 

 may be represented with all desirable accuracy by suitably 

 chosen arcs of circles. As we proceed from one part of the 

 curve to another, the radii and the centres of those circles 

 are changed so that each arc of the circle shall be substan- 

 tially coincident with the corresponding part of the curve. 

 As the arcs of the circles coincide with the curve, so do the 

 laws of Lagrange adapt themselves to the course of change 

 in the universe. At any moment Lagrange's laws are 

 practically true, but in immense periods of time the system 

 undergoes profound modification. The laws of gravitation 

 as ordinarily considered account for many of the ili'tuiln in 

 the present architecture of the heavens For the profounder 

 and gra'nder truths of the universe it seems not improbable 

 that we must interrogate the tides. 



Ekiuh. — In Part I. of "Photography for Amateurs" (Xo. 19, 

 p. 400), paragraph 1, for "improved" read "impressed." In 

 par 5, for " photoganic " rcad " photogenic " ; and in the last par, 

 read " J. Xicephore, Xiepee" ; and for " figures" read "pictmes." 

 In No. 17, p. 363, Letter 289, for "... this gas ; besides which, 

 coal-gas is harmless," read "... this gas, beside which coal-gas is 

 harmless." 



BiGHT.s OF AxiM.tLS. — Of the grotesque ideas which have imposed 

 on us in the solemn phraseologj' of divines and moralists, none 

 is more absurd than the doctrine that our moral obligations stop 

 short where the object of them does not liappen to know them ; 

 and assures us that, because the brutes cannot call us to account 

 for our transgressions, nothing that wc can do will constitute a 

 transgression. To absolve us from paying for a pair of boots 

 because our bootmaker's ledger had unluckily been burned, would 

 be altogether a pai-allel lesson in humanity. It is plain enough, 

 indeed, that the creature who is (as wo assume) without a con- 

 science or moral arbitrament, must always be exonerated from 

 guilt, no matter what it may do of hurt or evil ; and the judicial 

 proceedings against, and executions of, oxen and pigs in the 

 Middle .\gc3 for manslaughter were unspeakably absurd. But 

 •sot less absurd, on the other side, is it to exonerate men, who 



n-e consciences and free will, when they are guilty of cmolty to 

 lirutcs, on the plea — not that then — but the brutes, are immoral and 

 irresponsible. — Frances Power Cobbe, in the Cornhill Magazine. 



ILLUSIONS OF MOTION AND STROBIC 

 CIRCLES. 



By Thomas Foster. 



IT is a long time siace I last wTote about illusions. But 

 other subjects of more immediate interest have tilled 

 all the available space. 



The last illusion which I considered was a very singular 

 one, and I have been rather surprised to notice how few 

 among the readers of Knowledce have recognised its 

 interest and significance. It is one which admits of 

 various modifications, by which the real nature of the 

 illusion may be put to the test. It will be remembered 

 that in describing it, I noted that the paper held in the 

 reader's hand — Kxowledgk — might be used to illustrate 

 it. Rolling KxowLEDiiE into a tube an inch or so in 

 diameter, and looking through this with one eye, while 

 the hand not holding the tube is held touching 

 the tube, at about the distance for distinct vision, an 

 appearance is presented as though one were looking through 

 the hand. There seems to be a distinctly outlined aperture 

 through the palm of the hand, if the hand is held with the 

 palm open, or through the fist (and this has an even 

 stranger appearance) if the hand be clenched. Now, if the 

 experiment be modified by using tinted, or strongly 

 patterned paper for the tube, and by looking at variously 

 coloured surfaces, it will be found that the strength of the 

 illusion varies notably. (This may be tested by directing 

 the mind's attention specially to the hand, so as gradually 

 to overcome the absurd delusion by which one seems to 

 look through the palm or the fist.) I leave this as an 

 exercise to the student of illusions, noting that the result to 

 which my own experiments have led me is this, that in 

 ordinary vision what the left eye sees is referred by the 

 mind (unconsciouslj-, of course) to the right eye, and what 

 the right eye sees is referred to the left eye. By a series 

 of tests, such as those I have indicated, this peculiarity 

 may be recognised. I believe the eyes might be trained 

 to overcome illusions of this class. 



And now let us turn to some illusions of apparent 

 motion, which, like those we have already considered, can 

 be explained if carefully studied. 



Shading, and Motion. 



It may be remembered that in considering Fig. 1, in the 

 first number of Knowledge, I drew attention to the fact 

 that the lines AB, CD, EF, Ac, which are in reality 



