Makcu 17, 1882.] 



KNOWLEDGE • 



423 



parallel, appear to converge towards AG, BD, CE, itc. 

 Later (in No. 4), I called attention to the fact that this 

 figure illustrates an illusion of motion. If the eve lie run 

 up and down the parallels, these appear to move. When 

 the eye is at rest, they seem alternately convergent, 

 especially if the figure is viewed a little askew, lieing 

 neither held with the parallels vertical nor horizontal. But 

 if the eye runs along two parallels which before had seemed 

 to converge, they are found not to converge, and the effect 

 produced is as tJiough they had moved from each other at 

 the end towanls which they had seemed to converge. 

 Another effect, also, is noticed. The level surface on which 

 are the zigzag sets of lines, appears to be ridged, this 

 being apparen;ly due to the fact that the alternate sets of 

 close parallelsare viewed in different aspects. Thus, sup 

 pose the papei held so that B, Fig. 1, is lowest, then the 

 parallels in s?ctions CD, GH, MN, OR, appear farther 

 apart than thjse in the other, or alternate sections. Now, 

 if the Hgure is rotated in its own plane, so that first HL, 

 then R come lowest, there is a change from the a])pear- 

 anoe just desiribed to its reverse, the parallels in sections 

 l'|), CiH, MT, OR, appearing now closer instead of farther 

 iyurt than t'.e others. Accompanying this change will be 

 •Mid certaiily singular and rather complicated appear- 

 ■s of moion, the ridges sinking, then rising again, the 



^ of close parallels drawing apart or closer (and, if the 



tion is coitinued, closing up again, and drawing apart 

 J liii respecively), and the other sets of parallels (vertical 

 .1 the picure) seeming to bend and grow straight 

 •Alternately. 



Leaving he reader to study these changes and to note 

 that they ccrespond with what we should anticipate, we 

 proceed to nore familiar instances of apparent motion, 

 which find their explanation, I believe, in what we have 

 learned froi Fig. 1.* 



Consider -figs. 2 and 3, first at rest, and then as each 

 appears wbn a slow circling movement is given to it (as 

 when a sau^r is so moved as to set a small quantity of 

 ■ uid in it ircling round near the edge), and then as each 



; '-ars wh'i swayed through a short distance from side to 



ii\ or froi and towards you, in its own plane. 



When loking at either picture, held perfectly at rest, 

 the eye, if k|)t still, is presently affected by appearances of 



ivering n tion, apparently affecting the entire picture. If 

 eye mo\s backwards and forwards across the picture, 



irregular) over it, the sets of concentric circles appear 

 undergo jrtial rotations, — in alternate directions in one 

 ■, irreguir in the other. When the pictures are made 



lircle intheir own plane, all the sets of concentric 

 les seen to tui-n round in the direction of the 



■ ling motin given to the picture. Lastly, when the 

 |'i;tures are lifted back and forward in their own plane, 

 finm side to ide, each set of concentric circles is blurred 

 at the sides, • rather in the side quadrants, distinct in the 

 upper and lo9r quadrants, regarding the sets as divided 

 into quadran by diameters situated thus x . When the 

 motion is froi and towards the observer, the upper and 

 lower quadras of the sets of circles are blurred, the side 

 •quadrants disnct. 



To produceiie rotatory motion, it is necessary to give a 

 tolerably rap circling motion to either picture. The 

 experiment sioeeds better if the picture is mounted on 

 card, and the rcling motion is communicated by a suitable 

 crank, so as t be more uniform than any motion which 

 can be given \\h the hand. 



* At the mang of the British Association in 1877 (at 

 nymouth), Profior Sylvanus Thompson exhibited these singular 

 illusions. 



When Fig. 4 is swayed like the others, by a circling 

 motion in its own plane, the small black discs seem to be 

 carried round in a tlirection contrary to that of the circling. 

 It will be noticed that if the circle in which this figure 

 is swayed is somewhat larger than is necessary to produce 

 the deceptive appearance of motion, a regular pattern 

 seems to be formed, by the persistence of the visual images 

 of the small black discs in the picture. 



NEWCOMB'S POPULAR ASTRONOMY. 



"ITfE turn now to the less pleasant task of pointing 

 \ * out defects which might mislead those who rely on 

 Professor Newcomb's well-deserved eminence as a mathe- 

 matician and an astronomer. 



We should have been disappointed if such subjects as 

 the tides, the precession of the equino.xes, &c., had been 

 simply left unexplained in a work of this character. Few 

 subjects are less satisfactorily explained in most works on 

 astronomy than the tides, for instance. We are supplied 

 over and over again with the statement that the water im- 

 mediately under the moon is drawn from the (!arth, while 

 the earth is drawn from the water at the opposite 

 side, a statement true enough (when properly limited) 

 in itself, and a necessary preliminary to aii}- explana- 

 tion of the tides. But there the usual (Explanation 

 comes to an end, the student being simply told that 

 but for friction there would be high water in the 

 region under the moon and at the antipodes of that 

 region. Now, what would be thought of an explanation 

 of the motion of a reeling top which only showed that an 

 inclined top tends to tumble over t The reader would 

 assuredly say, " What I want to know is why the top 

 when spinning does not tumble over, but reels round." 

 The common explanation of the tides is open to precisely 

 such an objection. In the actual case of the rotating 

 earth there would be low water instead of high in the 

 regions under the moon, and opposite, were there no 

 friction ; and the effect of friction is not to throw back 

 the place of high water about half a quadrant, but about 

 three half quadrants. These are the relations which have 

 to be explained ; whereas the ordinaiy explanation deals 

 with relations which have no existence, not even a theoretical 

 existence, in nature. Now, it would have been very 

 useful if Professor Newcomb had given an original 

 and effective explanation of the true theory of 

 the tides. Sir G. Airy has given one, but it is not in 

 the books ; Sir Edmund Beckett has given another, in his 

 fine work, " Astronomy without Mathematics " ; but the 

 conditions he imposed on himself prevented him from 

 giving the best explanation, though he has avoided mathe- 

 matical reasoning. We should, then, have been disappointed 

 if we had merely found that Professor Newcomb had left 

 the tides entirely unexplained, or if he had simply repeated 

 the usual incomplete explanation. Unfortunately, he has 

 done worse than this. He has given an explanation 

 which is entirely incorrect. He describes the earth, and 

 truly, as circling once in a month around the common 

 centre of gravity of the earth and moon ; but he attri- 

 butes to different parts of the earth as she thus moves 

 different degrees of centrifugal force, according to 

 the distance of each part from the centre of gravity 

 just mentioned. If these different degrees of centri- 

 fugal force (or rather tendency) in reality existed, 

 the tides would be far more important phenomena than 

 they really are. A calculation which Professor New- 

 comb might have made on liis thumli-nail as he wrote the 



