GIFT OF 
 
Professor Montgomery's Discoveries 
 in Celestial Mechanics 
 
 BY 
 
 L. A. REDMAN 
 
 Pernau-Walsh Printing Co. 
 
 753 Market Street 
 
 San Francisco 
 
Copyright, 1919 
 
 by 
 L. A. REDMAN 
 
 Qift of 
 
 -ere e - 
 
"Thus the Seer, 
 With vision clear, 
 Sees forms appear and disappear, 
 In the perpetual round of strange, 
 Mysterious change 
 
 From birth to death, from death to birth, 
 From earth to heaven, from heaven to earth; 
 Till glimpses more sublime 
 Of things, unseen before, 
 Unto his wondering eyes reveal 
 The Universe as an immeasurable wheel 
 Turning for evermore 
 In the rapid and rushing river of Time." 
 
 Longfellow. 
 
The views herein set forth were made known to me in the year 
 1886 by the late John J. Montgomery, afterwards a professor in 
 Santa Clara College, and at that time the model referred to in the 
 text was exhibited to me and it is now in my possession. On sev- 
 eral occasions thereafter I urged him to publish his discovery, the 
 last time in the year 1909, about two years before his death. He 
 did not do so however, and on my pressing him for an explana- 
 tion on the last occasion, he said that his failure to publish was 
 not because of any doubt as to the soundness of his views, but 
 that the discovery made by him was connected with or inci- 
 dental to certain underlying principles, and that in due time he 
 would reveal it in its relation to such principles. I do not 
 know what he had in mind. Possibly principles of molecular 
 action, or it may be that he saw and intended presently to 
 explain how the progressive changes which he proved were 
 mechanically necessitated were incidents of the dissipation of 
 energy in the solar system. This (to a limited extent) was per- 
 ceived by Professor Percival Lowell, and was expounded in his 
 "The Evolution of Worlds", which was published at about the 
 time I last saw Montgomery. Professor Lowell says that Sir Robert 
 Ball was the first to suggest the "argument" which he employed 
 (p. 145). I do not recall that Montgomery ever mentioned to me 
 this phase of the subject. I first became acquainted with this 
 principle on reading Lowell last year when I began my investiga- 
 tion. Montgomery met with a sudden death by the fall of an air- 
 plane with which he was experimenting. During his lifetime (in 
 1905) there appeared in the newspapers an article, telegraphed 
 from Cambridge, Massachusetts, setting forth that Professor Wil- 
 liam H. Pickering had discovered that the planets were "keeling 
 over", and thereupon, without Montgomery's knowledge, I sent to 
 the San Francisco "Bulletin" the following communication which 
 it published: 
 
 "CALIFORNIA ENTERTAINING A GENIUS UNAWARES. 
 
 San Francisco, March 27, 1905. 
 Editor Bulletin: 
 
 Referring to the dispatches in The Bulletin of the 15th inst. 
 from Cambridge, Massachusetts, and the Lick Observatory, 
 relating to Professor Pickering's theory that 'all the planets 
 have keeled over or are keeling over', I feel impelled to make 
 public the fact that this discovery was made by Mr. John J. 
 
Montgomery, now a professor in Santa Clara College, more 
 than twenty years ago. It was disclosed by him to me in 1886 
 or 1887. With him it was more than a theory. By means of 
 a mechanical device a sort of orrery he physically demon- 
 strated that spheres having a retrograde rotation being in 
 unstable equilibrium, will necessarily 'keel over'. The parts 
 nearest the sun of a planet having a retrograde rotation move 
 with relation to the sun more rapidly than those parts on its 
 remote side ; hence the former tend to move away from the 
 sun while the latter have a tendency to move toward it. The 
 result is that the planet turns over and establishes a condition 
 of stable equilibrium one in which the inner parts tend to 
 move towards the sun and the outer parts away from it. I 
 have not sufficient knowledge of the subject to set forth accu- 
 rately all the remarkable implications of this great discovery 
 some of which I believe are still occupying Mr. Montgom- 
 ery's attention. I may say, however, that it accounts for the 
 precession of the equinoxes, the tides, the transfixed position 
 of the moons of Jupiter and the earth and of Venus ( ? ) , the 
 half-tilted over condition of Uranus, the retrograde rotation 
 of Neptune and the retrograde translatory motion of Saturn's 
 ninth moon. 
 
 In my judgment this brilliant revelation eclipses any dis- 
 covery made in astronomical science since the days of Kepler 
 and Newton. In unassuming John Montgomery, whose recent 
 experiments in wireless telegraphy and aerial navigation have 
 been attracting public attention, California has these many 
 years been ' entertaining an angel unawares.' His self-abnega- 
 tion is so extreme that unless some one else drew attention to 
 his claims the merit of the discovery referred to would nat- 
 urally be bestowed wholly upon Professor Pickering. I do not 
 question the latter 's claim to originality, nor do I know when 
 the discovery was made by him, but I do know that it was 
 made many years ago by Mr. Montgomery. 
 
 Respectfully yours, 
 
 L. A. REDMAN." 
 
 I learned upon investigating the subject last year that Professor 
 Pickering had first advanced his theory in 1893. But the reading 
 of his articles disclosed that, while he contended that polar 
 inversion, where the rotation is retrograde, must ensue, his explan- 
 ation of the cause thereof is totally different from that of 
 Montgomery and is, as I think I have clearly shown, erroneous. 
 
 Montgomery was a firm believer in the nebular hypothesis. He 
 also believed, as Kirkwood did, ("The American Journal of 
 Science", Vol. 36, p. 1), and as Professor Pickering and others do, 
 that the planets formed from detached parts of the nebula as it 
 
contracted would have retrograde rotations. I have not however 
 dealt with this feature of the problem. Postulating this, I 
 have set forth the argument showing how the planets are inverted, 
 and then how forward rotation (which inversion involves) is 
 retarded until the rotation and revolution periods coincide; and 
 finally how the planets and their satellites will be drawn into 
 the sun. I have also shown the harmony between Montgomery's 
 discovery and the proposition that energy will be dissipated until 
 it is reduced to the least quantity consistent with the original 
 and unchanging moment of momentum of the system. And I 
 have pointed out (what Ball and Lowell did not see) that their 
 " argument" involves the proposition that by dissipation of energy 
 the matter composing the nebula will ultimately be concentrated 
 in a cold rotating body. 
 
 There is one feature of the process which I have merely indi- 
 cated without going into it in detail, namely, the inversion of 
 the orbits of the satellites. The planets do not "carry over" 
 their moons, but the orbits of the moons are "carried over" 
 by the sun. And where the differential attraction of a satellite is 
 greater than that of the sun it controls the inversion of its prim- 
 ary. In the case of the few very remote satellites which still have a 
 retrograde revolution, the inversion force has been so feeble that 
 little progress has been made. And in this connection it is to be 
 noted that while Mercury and Venus (which have no moons) turn 
 always the same face to the sun, the earth will not do so until 
 after it has absorbed the moon. It is the moon and not the sun 
 which controls the earth's inversion, and it will also control the 
 earth's rotation as its differential attraction is greater than that of 
 the sun. Hence, the earth's rotation will only be retarded until 
 the day and month are the same. The earth and moon will finally 
 rotate and revolve as if united by a bar. Thereupon the moon will 
 spiral inward upon the earth; and finally the earth-moon will 
 spiral into the sun. 
 
 In December, 1917, I asked Professor Campbell, Director of the 
 Lick Observatory, if the views of Montgomery were known to and 
 accepted by astronomers as correct, and was informed by him that 
 the theory of Professor Pickering was well known, but that it was 
 not generally accepted. I thereupon made an investigation and 
 was amazed to find that not only was there a want of agreement 
 amongst those who had given the matter consideration, but that 
 the arguments made in support of the propositions advanced by 
 the various writers on the subject were of the loosest character, 
 
and that some of the positions taken were manifestly untenable. 
 Everywhere I found confusion and contradiction, and nowhere 
 any recognition of the controlling factor detected by Montgomery. 
 I found Professors Pickering and Moulton differing upon what the 
 former denominated an ' ' elementary ' ' mechanical proposition ; and 
 I also found that men eminent in mathematical research had 
 reached conclusions which, however profound the mathematical 
 reasoning by which they were deduced, were obviously erroneous. 
 
 In a recent number of "Popular Astronomy" Mr. Cordeiro 
 says that the mention of Sir George Darwin as an "authority" 
 makes him "shudder". Mr. Cordeiro, however, falls into the 
 same error as Professor Pickering. He attributes inversion to 
 tidal action which he says is always "positive". It is not 
 positive when the rotation is forward. 
 
 Another remarkable thing is that no one seems to have perceived 
 that there are no "couples" in celestial mechanics. Bodies in space 
 caused to rotate by attraction do not turn on fixed axes, but every 
 particle of an attracted body, notwithstanding such rotation, moves 
 towards the attracting body. The failure to note this accounts 
 for the error into which Professor Newcomb fell in his analysis 
 of the cause of the identity of the periods of the moon's revolution 
 and rotation. It probably also accounts for Professor Moulton 's 
 admitted inability to understand the reason for such identity 
 ("An Introduction to Astronomy", 1916, p. 458). 
 
 This strange condition of affairs presents an interesting 
 subject for study. It is probably due to a habit of mind 
 produced by a too exclusive mathematical discipline. It has 
 been observed that mathematicians are prone to accept as 
 indisputably correct conclusions deduced mathematically but 
 resting upon erroneous or inaccurate data, notwithstanding 
 that they are manifestly unsound. "The mathematician", says 
 Herbert Spencer, "in dealing with contingent matters does not go 
 wrong in reasoning from his premises ; he goes wrong in his choice 
 of premises. He continually assumes that these are simple when 
 they are really complex omits some of the factors. His habit of 
 thought is that of dealing with few and quite definite data and he 
 carries that habit of thought into regions where the data are many 
 and indefinite, and proceeds to treat a few of them as though they 
 were all, and regards them as definite." And it may be further 
 observed that even where the premises or "starting points" are 
 correct the mathematician is apt to overlook changes in some of 
 the factors produced by subsequent occurrences. But whatever 
 
 8 
 
the explanation may be, the extraordinary situation is presented 
 of mathematicians studying for generations the mechanical prob- 
 lems herein considered without solving them, and profoundly con- 
 fusing the subject by applying to them mathematical principles 
 and formulae applicable to ideal but not real conditions. Astro- 
 nomical growth has been stunted by the procrustean assumptions 
 of the mathematicians. 
 
 Aside from Montgomery, Ball and Lowell came nearest to solv- 
 ing the problems in question by applying, as I have said, the 
 principle of the dissipation of energy. But, as above stated, 
 neither of them saw the most important implication of this 
 doctrine the absorption by the sun of the planets and their satel- 
 lites and neither of them mastered the subject as a mechanical 
 problem, and consequently both fell into serious errors. No one 
 but Montgomery perceived the pregnant proposition that the retro- 
 grade-rotating parts of a planet are virtually nearer the point of 
 attraction than the relatively more rapidly moving forward parts. 
 Hence a retrograde-rotating planet is in unstable equilibrium and 
 will invert under the influence of attraction. It is of course true, 
 as Lowell observes, that there is more "superfluous energy" in a 
 retrograde than in a forward-rotating body, and that by dissipa- 
 tion of energy, inversion (which converts retrograde into forward 
 rotation) will ensue (p. 145). But he did not see how this was 
 mechanically brought about. He erroneously asserts that "tidal 
 action" will "accomplish the end". He strangely, however, does 
 not refer to the ' ' annual tide ' ' theory of Professor Pickering. Nor 
 does he allude to Professor Moulton's attempted refutation of the 
 tidal theory. Professor Lowell is also in error in asserting that 
 tidal friction acts as a "brake" on rotation; and further in 
 error in contending that the tidal bulges "carry over" the 
 orbits of the planets' satellites. He did not see that where the 
 differential attraction of a moon is greater than that of the sun, 
 the inversion and rotation of the planet will be controlled by the 
 moon and not by the sun. In such case, as I have already indi- 
 cated, the sun will invert the orbit of the moon and the moon's 
 attraction, assisted by that of the sun, will invert the planet. 
 
 Professor Moulton's attack on Professor Pickering's "annual 
 tide" theory is as ill-based as the theory itself. He fell into the 
 error of applying to a spheroid with tides, principles applicable 
 only to rigid spheres. He impliedly denied precessional motion. 
 
He said that a planet would not tilt, but that the axis (in a 
 spheroid) would shift! 
 
 Ball and Lowell contend that the obliquity of the earth's axis is 
 decreasing and that it will continue to decrease until it is perpen- 
 dicular to the orbital plane; but Ball failed to explain how this 
 was mechanically caused, and Lowell, as I have said, erroneously 
 attributed the result to "tidal action" (which Darwin says is 
 causing increasing obliquity). And they both impliedly denied 
 the true cause, namely the attraction of the moon and sun on the 
 earth's equatorial protuberance. They assert that such attrac- 
 tion causes precession exclusively, whereas precession would not 
 occur unless the axis were tilted. Rotation does not prevent tilt- 
 ing, but tilting proceeds accompanied by precession. The two 
 motions compounded cause the poles to move in spirals. 
 
 On completing my investigation I sent to Professor Camp- 
 bell (last July) a communication wherein I set forth as the 
 result of refreshed and cleared-up recollection of Montgomery's 
 views and my own study of the subject, the principles which 
 govern the motions of the planets and their satellites; and from 
 time to time thereafter sent him additional communications in 
 which various aspects of the subject were dealt with and the con- 
 tentions and arguments of Pickering, Moulton, Darwin, and 
 others, reviewed. These are reproduced here together with two 
 previous letters wherein I stated Montgomery's views in a 
 general way. 
 
 As excuses for such an informal presentation of a matter of so 
 great importance, I plead want of time and equipment to develop 
 and present a better organized and complete discussion of the 
 subject, as well as a rather sharp desire to give the discovery wide 
 publicity without further delay. I have no doubt as to the verdict 
 that will be rendered. The name of John J. Montgomery will be 
 written high up in the hall of scientific fame beside that of New- 
 ton, Charles Darwin, and other great and original thinkers. 
 
 San Francisco, May 6, 1919. 
 
 10 
 
Letters to Professor Campbell of December 21, 1917, and 
 
 January 23, 1918, Setting Forth the Views 
 
 of Professor Montgomery. 
 
 Many years ago the late Professor John J. Montgomery of 
 Santa Clara College informed me that the reason why the moon 
 rotated on its axis in the same period that it takes to go 
 round the earth is that such a position is one of stable equilibrium 
 one into which the moon would necessarily pass no matter how 
 rapidly or in what direction it was rotated. If, for instance, it was, 
 given a retrograde rotation it would in course of time turn over, 
 thereby assuming a forward rotation, and that its rotary motion 
 would be gradually retarded until it finally reached its present 
 state of stable equilibrium. He showed me the reason for this 
 and proved it by a model which he still had when I last saw him, 
 about two years before his death. Professor Montgomery informed 
 me that in his opinion the planets originally all had retrograde 
 rotations and that they have all, or nearly all, been capsized by 
 attraction. Their ultimate state, he said, would correspond to that 
 of our moon, namely, each of them having a rotation period equal 
 to its revolution period. 
 
 I have for a long time been curious to know whether or not 
 these views are known to astronomers, and if so, to what extent, 
 if any, they have been accepted. Evidently Professor Larkin either 
 never heard of them or takes no stock in them, as the enclosed 
 clipping shows. [Referring to a statement that the period of the 
 moon's revolution and rotation has been the same ever since the 
 moon "fell into its orbit as it now stands".] But clearly the 
 chances are infinity to one against an accidental exact correspond- 
 ence between the time of the moon's rotation on its axis and the 
 time of its revolution round the earth. I understand that the same 
 thing is true of Jupiter's moons, and if so, it passes comprehension 
 how any one can believe that such a thing could have resulted 
 otherwise than from some common cause. 
 
 As heretofore stated, Professor Montgomery contended that a 
 central body will necessarily bring a rotating body circling round 
 it into the relation which the moon bears to the earth. If the 
 planet or satellite have a retrograde rotation, the central attracting 
 
 11 
 
force will first capsize it which movement is along the line of 
 least resistance and then slow down its axial speed until it makes 
 but one rotation in its course round the central body; and further 
 that if such planet or satellite have no rotation, the central 
 force will initiate such rotation and gradually increase its speed 
 until axial and annual correspondence is attained. The parts 
 of a planet which has no rotation will not move in a circle 
 a condition which the central force will not tolerate. A correc- 
 tion of it results in turning the planet on its axis until such 
 an axial speed is attained that all of its parts move round the 
 central body in a circle; that is to say, with the same side always 
 towards the center. And if the rotation be greater (as in the 
 case of the earth) the parts, instead of moving in circles, will 
 move in wave lines another unstable condition which the central 
 attracting force will correct. 
 
 As above stated, Professor Montgomery contended that a planet 
 with a retrograde rotation will gradually capsize, the reason being 
 that the inner parts move, in relation to the central ~body, faster 
 than the outer parts. If, for instance, the rotation were equal to 
 the speed of the planet through space, the outer parts, in rela- 
 tion to the central body, would be motionless, and if detached from 
 the planet of which they form a part, would fly straight to the 
 central body (assuming, of course, the removal of the other parts 
 of the planet). The inner parts, on the other hand, if detached, 
 would move away from the central body in a larger orbit than that 
 of the planet as a whole. The effect of these two opposing forces 
 is to turn the planet over gradually. And Professor Montgomery 
 proved this by the device to which I referred in my former letter. 
 Of course, the natural and artificial conditions are not precisely 
 the same, but their points of difference are immaterial. The 
 attractive force upon all of the parts is simply concentrated at 
 the center of the wheel. The effect of the tug at the center 
 is the same as the force of attraction distributed throughout 
 the entire body. The outer parts having a slower motion with 
 respect to the central force, due to retrograde rotation, will be 
 more affected thereby than the relatively rapidly moving inner 
 parts. They will tend to go further towards the central body in a 
 given time than the inner parts. The situation is the same as if 
 the inner and outer parts were disconnected. Place two rifles one 
 above the other and fire them, the lower one discharging its bullet 
 with greater force than the upper one. Gravity will cause the 
 upper bullet to cross the course taken by the more rapidly moving 
 
 12 
 
lower one. And if they be connected as in the case of a planet 
 a capsizing movement will result. And the capsizing will continue 
 until the body rotates on an axis at right angles to the plane of 
 its orbit. It is still, however, in unstable equilibrium, which, as 
 above stated, consists in the parts moving in wave lines instead 
 of in smooth circles round the central body. 
 
 Professor Montgomery believed that all of the planets orig- 
 inally had retrograde rotations and he informed me that this 
 belief was confirmed by experiments made by him. He said that 
 they are all in course of inversion except Venus and Mercury, 
 where the process has been completed. The force which produces 
 this result is proportional to the times of revolution thereby ac- 
 counting for the condition of the innermost planets and for the 
 fact that Uranus is but half turned over and that Neptune 
 still has a retrograde rotation. 
 
 I realize that I am writing in a more confident tone than my 
 knowledge or capacity in such matters justifies, but I cannot help 
 being deeply impressed by the apparent truth of these theories 
 of Professor Montgomery, which I am anxious to have confirmed 
 and made known if sound, or if unsound, to see refuted. 
 
 Letter of July 24, 1918, After 
 Investigating the Subject. 
 
 Professor Montgomery dissented from the views of those who 
 say that in the absence of tides there will be no inversion or 
 retardation of rotation. He contended that there would neces- 
 sarily be inversion and retardation in the case of any real 
 body, regardless of tides. A spheroid would invert, he claimed, 
 if it rotated retrograde-wise, and ultimately would be brought 
 into a condition where the rotation and revolution periods 
 would be the same. The same thing is true with respect to any 
 body except a perfect (ideal) sphere. An iron bar rotating in 
 space will finally point one end towards the central attracting 
 body as it rotates and revolves around it, and a non-rotating bar 
 will be caused to rotate by attraction. 
 
 While Kirkwood (in 1864) contended, as did Montgomery, that 
 the planets originally had retrograde rotations, the process by 
 which forward rotation was brought about, as described by him, 
 is essentially different from that asserted by Montgomery. Kirk- 
 wood's contention was that tidal friction retarded retrograde 
 
 13 
 
rotation until the day and year corresponded, and that thereupon 
 forward rotation was initiated. He failed to note the fact that, as 
 contended by Montgomery, attraction will invert a retrograde- 
 rotating planet. As I stated to you in a previous letter, Montgom- 
 ery in 1886 first informed me regarding his views and experiments, 
 and he also said that in respect to the capsizing and retarding 
 processes they were original. 
 
 At first (June, 1893) Professor Pickering advanced the theory 
 that inversion of a retrograde-rotating body would be caused by 
 "annual tides" produced by attraction. He said that a planet 
 with a retrograde rotation was in unstable equilibrium and that 
 such tides would upset it. A few months later, however, after 
 acknowledging the inadequacy of his tidal theory (September, 
 1893, "Astronomy and Astro-physics", Vol. 12, p. 692), he said 
 that "a second cause of inversion has recently been found which 
 in its action is probably still more important than that of the 
 tides", and argued that a rigid body, such as a wheel for ex- 
 ample, would be upset by gyroscopic action. But this "second 
 cause" is as inadequate as the "annual tide". When the rotation 
 of the wheel becomes forward and the rear rim is nearer the 
 point of attraction than the front rim, the axis, on Professor 
 Pickering's theory, would be precessionally tilted into greater 
 obliquity. Perhaps his perception of this accounts for the fact 
 that he has not in any of his subsequent articles referred to 
 this "second cause". Apparently for this reason he has aban- 
 doned it, but he has not, so far as I am aware, expressly 
 withdrawn his admission of inadequacy with respect to 
 his "annual tide" theory. It is plain that he does not 
 understand how inversion is brought about. He fails to 
 note the pivotal fact which I think no one but Montgom- 
 ery perceived, that the retrograde, and therefore, relatively to the 
 attracting body, slowly moving outer parts, are drawn inward by 
 attraction, and the inner parts, moving with relatively increased 
 velocity, tend to go outward. In the case of Uranus, for example, 
 attraction directly draws the retrograde-moving rim inward. This 
 causes precessional motion which turns the rear rim inward, and 
 the combined motions bring about inversion, as shown by the 
 Montgomery model. The wheel therein, with three freedoms, is 
 supported by gimbals at one end of a horizontal bar and is bal- 
 anced by a weight at the other end. The revolution of the bar 
 round a central support causes the retrograde-rotating wheel to 
 invert its poles, which move in spirals as the wheel turns over. 
 
 14 
 
This motion represents the action of the planets as inversion 
 proceeds, and it is not explained by the theory of Professor Picker- 
 ing. It does not occur when the stand of a gyroscope is turned 
 against the rotation of the wheel while resting on the same spot. 
 In such case inversion takes place but in a different manner, due 
 to the application of a couple to a stationary body an artificial 
 condition which does not obtain in the case of the planets. Their 
 situation and action are correctly represented by the rotating and 
 revolving wheel in the model. 
 
 The wheel and the planets invert with a reeling motion. 
 The apparent circles made by the poles of the earth in twenty- 
 five thousand years, for instance, are really spirals and accord- 
 ingly not re-entrant. In the case of a planet, each particle of 
 matter is pulled by attraction, and in the case of the model, the 
 pulling force is exerted upon the center of the wheel with pre- 
 cisely the same result. In each case it is as if there were a 
 contactual pull at the center. The retrograde and relatively 
 slowly moving particles are pulled further inward in a given 
 period than the forward and relatively rapidly moving particles. 
 
 And when the wheel in the model has turned over and settled 
 down in a horizontal position it remains in this position as it 
 rotates and revolves, because then the inner parts tend to move 
 towards the center of revolution and the outer parts away from it. 
 
 But attraction is not satisfied until forward rotation of a planet 
 is stopped relatively to the central body. This stoppage is due 
 to the unequal effects of attraction on all the particles which com- 
 pose the planet, including the water on its surface, and in the 
 model is represented by friction on the wheel corresponding in 
 the case of a planet to the "friction" to which it is subjected by 
 attraction. But such "friction" is not dependent upon the 
 substance of the planet; attraction will retard the rotation of a 
 tideless body. The rotation of a bar as well as a viscous or elastic 
 planet will be affected by attraction. And if rotation were stopped 
 (absolutely) attraction would start it whether the body was a bar 
 or any other real body, regardless of tides. But the rotation 
 would never exceed the revolution. Professor Newcomb 
 ("Popular Astronomy", p. 315) says that we have "every 
 reason to believe" that if the rotation of the moon were consid- 
 erably increased it would never stop. But I submit that he is 
 either in error regarding this or he is in error in his statement 
 that if the rotation were only slightly increased the moon would 
 be drawn into line by attraction. His fly-wheel on an axle would 
 
 15 
 
not stop in the absence of friction but would continue to oscillate. 
 But his illustration was faulty because while it is true ..that when 
 the near end of a rotating bar in space is moving towards the 
 attracting body, rotation will be accelerated and when it is moving 
 away from the attracting body, rotation will be retarded, yet the 
 latter force is longer in operation than the former. It is not as if 
 the bar were turning on a fixed axle. The difference between these 
 forces is the measure of the retardation of rotation. The tideless 
 moon, no matter how much its rotation was increased or decreased, 
 would be brought back by attraction to its present attitude. Where 
 there are tides, however, there is a steady pull in the same direc- 
 tion which continuously retards rotation. 
 
 Let me add that Professor Montgomery asserted that the attrac- 
 tion of the sun had inverted the orbit of the moon. The retro- 
 grade revolution of a satellite is unstable for the same reason 
 that the retrograde rotation of a planet is. In the case of retro- 
 grade revolution or rotation by reason of the cancellation, meas- 
 urably, of forward motion, the outer body or part is, as it were, 
 nearer the attracting body. If the backward movement exactly 
 equals the forward movement, the body or part will be (in rela- 
 tion to the point of attraction) motionless, and if free to do so, 
 will move directly towards it. Herein lies the solution of the 
 problem. 
 
 I should appreciate the privilege of submitting to you here- 
 after, by way of additional argument in support of Professor 
 Montgomery's views, some criticisms of the writings of Mr. Dar- 
 win, Professor Moulton, and others who have dealt with this most 
 interesting subject. 
 
 In re Pickering. 
 
 In "Astronomy and Astro-physics" for June, 1893, Professor 
 William H. Pickering advanced the theory that a retrograde rotat- 
 ing planet would be inverted by the action of "annual tides". In 
 September, 1893, however, in the same journal, referring to this 
 theory, Professor Pickering said: 
 
 "It does not, however, fully explain the case of rapidly 
 rotating bodies like the planets, since in their case the inver- 
 sion could not proceed much further than to make the axis 
 coincide with the plane of the orbit." 
 
 But in all subsequent articles, the last appearing in the October, 
 1917, number of "Popular Astronomy", he ignores this objection 
 
 16 
 
which he himself urged against his theory, and insists that 
 "annual tides" will completely invert a retrograde-rotating planet. 
 While he did not state the reason why "annual tides" could not 
 cause inversion to "proceed much further than to make the axis 
 coincide with the plane of the orbit", it seems probable that what 
 he had in mind was this: he assumed that when the rotation 
 changed from retrograde to forward the tidal bulge would shift. 
 According to this view when the rotation was retrograde the bulge 
 would be carried forward by rotation and be pulled back by attrac- 
 tion, and when the rotation was forward the bulge would be car- 
 ried back and be pulled forward. The backward pull would 
 precessionally tilt the axis one way and the forward pull would 
 tilt it the opposite way. Hence the "annual tide" would not 
 invert the planet beyond the point where the axis was brought 
 into coincidence with the orbital plane. Assume, for instance, 
 that the equator of Uranus, from some cause, was tilted over to- 
 wards the sun beyond 90. Then the tidal bulge would shift to the 
 other side and attraction of it would precessionally tilt the equator 
 back to 90. But notwithstanding this obvious objection to his 
 theory, which Professor Pickering himself presumably saw, he has 
 strangely ignored it and has continued to assert that the effect 
 of the "annual tide" would be to make the "process continue 
 without intermission until the two planes coincide". But if 
 "tidal friction" were the controlling force, then it is manifest, as 
 Mr. Darwin says, that obliquity in the case of the earth is, 
 and for a long time has been, increasing ("The Tides", p. 310). 
 Clearly if the axis of the earth were being precessionally tilted 
 by "tidal friction", it would now be inclining into greater 
 obliquity since the tidal pull is against the rotation. But Darwin, 
 as well as Pickering, was in error because "tidal friction" is not 
 in control. The axis is not precessionally tilted by "tidal fric- 
 tion", but directly tilted by attraction on the equatorial bulge of 
 the planet. Hence where, as in the case of the earth, the rotation 
 is forward, obliquity must decrease. And where the rotation is 
 retrograde, the far side of the planet (assuming adequate rotation) 
 is virtually nearer than the near side. The outer retrograde- 
 rotating parts move, relatively to the attracting 'body, slower than 
 the inner forward-moving parts. They therefore are drawn 
 further inward in a given time than the relatively more 
 rapidly moving inner parts. If the retrograde rotation were 
 sufficient to cancel the forward motion of the planet, the retro- 
 grade-moving parts would be at a standstill, relatively to the 
 
 17 
 
attracting body, and if free to do so would move directly towards 
 it. The planet would therefore turn over. But as it is rotating, the 
 tilting is accompanied by precessional motion; the poles move in 
 spirals and will continue to do so until the planet has been com- 
 pletely inverted and rotates in a forward direction on an axis 
 perpendicular to the orbital plane. Professor Pickering's conclu- 
 sion was correct, but he assigned the wrong cause. It is true, as 
 he contends, that if a rotating planet without revolution assum- 
 ing an ideal case for illustration were turned against its rotation, 
 its axis would tilt 90. And it is also true that if the planet were 
 thereafter subjected to the same force, it would turn completely 
 over, as is proved by rotating the stand of a gyroscope in a direc- 
 tion, at first opposite to the spin of the wheel, and when the spin 
 is reversed, with it. But as above pointed out (and as Professor 
 Pickering himself saw in September, 1893) " tidal friction", in 
 the case of a rapidly rotating planet, does not work in this fashion. 
 It does not tend to cause rotation in the same direction through- 
 out. Assuming, as Professor Pickering contends, that when the 
 rotation is retrograde it tends to turn the planet against such 
 rotation, yet when the rotation becomes forward, it tends to turn 
 the planet in the opposite direction. 
 
 Nor does the action of the gyroscope give any support to 
 Professor Pickering's theory. On the contrary it demonstrates 
 it to be erroneous. If the wheel in the Montgomery model is 
 placed in the position of Uranus with the axis pointing towards 
 the central support and be given a retrograde rotation, the retro- 
 grade-rotating rim tilts inward when the wheel is revolved and the 
 rear rim precesses inward, which proves conclusively that the tilt- 
 ing of the axis is not a precessional effect of the "annual tide", as. 
 Prbfessor Pickering supposes, but that it is the cause of a preces- 
 sional movement opposite to the direct movement which the 
 "annual tide" would cause if it were controlling. The inward tilt- 
 ing of the retrograde-rotating rim is caused directly by the pull at 
 the center of the wheel which produces precisely the same effect 
 as attraction on all the parts of a retrograde-rotating planet. In 
 both cases the retrograde (and therefore relatively slowly) moving 
 parts yield to a greater degree to the pull, applied in the one 
 case at the center and in the other upon the parts, than the rela- 
 tively rapidly moving forward parts. The planet and the wheel 
 turn over (the poles moving in spirals) until they spin in a 
 forward direction on perpendicular axes and continue so to rotate. 
 
 18 
 
In the foregoing the expression "tidal friction" has been 
 employed merely as a convenient term. As I have elsewhere 
 shown, the friction of the tides is a false quantity. Retardation of 
 rotation is due not to friction (which accompanies acceleration 
 as well as retardation of rotation) but to attraction on a 
 rotating elongated body with or without tides. 
 
 In re Moulton. 
 
 In his reply to Professor Pickering ("The Astrophysical 
 Journal", Vol. 22, p. 355) Professor Moulton says that "the 
 question is to determine the effects on the rotation of a 
 planet of the attraction of the sun for the tides which it has 
 raised on the planet". He confines the issue to the effect on 
 a rotating but not revolving planet of a "couple" around 
 the perpendicular or Z axis of the planet. And he contends 
 that such a couple is incapable of inverting or even tilting 
 the planet. He says that the "first principle of the dynamics 
 of rigid bodies is that all the forces which act upon a body 
 may be resolved into three rectangular components applied 
 to its center of gravity and three couples about three rectangular 
 axes". He disregards the "three rectangular components" as not 
 involved in the problem, and then proceeds to consider the effect 
 of one of the couples that around the Z axis. He justifies this 
 course because, he says, this couple is the one which Professor 
 Pickering claims causes inversion. He then proceeds to demon- 
 strate that such couple can only retard or cause rotation around 
 the Z axis that it can neither retard nor cause rotation around 
 any other axis. And he reaches the conclusion accordingly that 
 the planet under such an influence will not invert. 
 
 But Professor Moulton 's remarks apply only to the case of a 
 rigid perfect sphere. If such a sphere be rotating around the 
 Z axis and an attempt be made to rotate it around the X or Y 
 axis it will not rotate around either, but around a new axis. 
 The axis of rotation will shift in the sphere. But this it not 
 true of a spheroid. In such case if the rotation be not around 
 the Z axis, a couple around such axis has the effect, not 
 of shifting the axis in the body, but of tilting the body itself. 
 For example, take a rotating planet whose axis lies in the plane 
 of its orbit and points somewhat to one side of the sun. It is 
 clear (eliminating the factor of translation), that attraction will 
 tend to turn the planet on the Z axis. The effect thereof will not 
 be to change the axis of rotation in the planet, but to tilt the 
 
 19 
 
planet itself. Its upper rim will move inward or outward, depend- 
 ing upon which way the planet is rotating. Precession will ensue. 
 The gyroscope furnishes a familiar illustration of the effect of 
 such a force. Hence Professor Moulton's reasoning and con- 
 clusions, true only in the case of rigid perfect spheres, have 
 no application to the case of planets as they are. It is sur- 
 prising that he should have sought to apply to the planets which 
 are not rigid spheres, principles of mechanics inapplicable to 
 them. After saying that the question is what effect tidal action 
 has on rotation, he proceeds to lay down principles relating to 
 " rigid" bodies, which of course have no tides. If a body were 
 perfectly rigid and spherical, attraction would not affect its 
 rotation at all. And if it had no rotation, attraction would not 
 start rotation. Hence, even in the narrow way in which he 
 viewed the problem, Professor Moulton was in error. He was 
 also in error in eliminating the factor of translation. 
 As I have shown, in this lies the explanation of the inversion 
 of the planets. In considering the effect of attraction on a 
 particle of a planet, we should take into account not only its 
 rotation motion but its translation motion as well. It is the motion 
 of a particle in relation to the attracting body which we 
 have to consider. This proposition was overlooked by 
 Professor Pickering also. The inward tilting of the retrograde- 
 rotating rim of Uranus is not precessional as he supposes not an 
 effect of attempted rotation around the Z axis. It is primary. 
 It is not caused by "annual tides" but directly by attraction. 
 This primary motion causes precessional motion of the rear rim 
 of the planet which accordingly turns inward as the retrograde- 
 rotating rim tilts inward. This is proved by the Montgomery 
 model. 
 
 In "Popular Astronomy" for February, 1918, Professor Moul- 
 ton says: "It is sometimes supposed that a planet may have orig- 
 inally rotated in one direction and that tides may have caused 
 it to rotate in the opposite. * * * This can have been brought 
 about only by forces having a moment about an axis perpendic- 
 ular to the plane of the orbit of the planet." Such a force or 
 couple would of course first stop the rotation and then start 
 it in the opposite direction if it were absolutely opposite to the 
 rotation, but otherwise it would invert the planet. Proof of this 
 is furnished by the gyroscope. If the wheel be spun in one direc- 
 tion and the stand be rotated in the opposite direction (approxi- 
 mately) the wheel will be inverted. The reason for this is plain. 
 
 20 
 
The two rotations are not absolutely opposed and hence the body 
 moves along the line of least resistance* it turns over. But as I 
 have pointed out, attraction does not work like an artificial 
 couple. 
 
 Professor Moulton was not happy in his exposition of the 
 mechanics of rotation. While from a purely theoretical point of 
 view it may be unobjectionable to say, as he does, that "any rota- 
 tion may be resolved into rotations around three axes", yet this 
 is a practical impossibility. While it is true, of course, that a 
 force which causes rotation, may be resolved into three forces 
 which taken separately, will cause three different rotations and 
 when combined but one the rotation around the so-called "in- 
 stantaneous" axis yet such single rotation is the only real rota- 
 tion. While in a mathematical sense it may be regarded as the 
 "sum" of three rotations, such rotations cannot actually co-exist 
 in the same sphere. Nor will the axis of rotation shift in the case 
 of any real body. Assuming that there may be a real "perfect 
 sphere" yet the application of a force which causes rotation will 
 convert it into a spheroid; and hence when an attempt is made to 
 rotate it on a right-angular axis instead of the axis shifting in 
 the body, the body will tilt and thereby cause precession. Professor 
 Moulton 's failure to note this accounts for the errors into which 
 he fell. 
 
 In re Darwin. 
 
 In "The Tides" and in his article in the Encyclopedia Bri- 
 tannica, Mr. Darwin says that tidal friction is increasing the 
 earth's obliquity. He says ("The Tides", p. 311) that it is 
 "certain that a planet rotating primitively without obliquity 
 would gradually become inclined to its orbit although probably 
 not to so great an extent as we find in the case of the earth". 
 And (p. 310) that "at present and for a long time in the 
 past", the earth's obliquity has been increasing. If Professor Mont- 
 gomery's views are correct, Mr. Darwin has here fallen into error. 
 His error arises from ignoring the orbital motion of the earth. 
 With him there is no "forward" or "retrograde" rotation. The 
 earth is rotating but not revolving. "Tidal friction" under such 
 conditions would, as he says, precessionally cause a tilting of the 
 axis unless it was absolutely perpendicular to the tidal force 
 obliquity would increase. But orbital motion brings in a factor 
 which renders Mr. Darwin's deductions erroneous. Where there 
 
 21 
 
is orbital motion rotation is either "forward" or "retrograde". 
 If forward, obliquity, as in the case of the earth, will decrease; 
 and if retrograde, the planet will invert, thereby changing 
 retrograde into forward rotation, and thereupon obliquity will 
 decrease until the planet rotates on an axis perpendicular to 
 the plane of the orbit. 
 
 But obliquity would not increase, Mr. Darwin says, if there 
 were less than two days in the month in such case instability 
 would not exist. He does not explain the reason for this distinc- 
 tion, but it cannot be well-founded. The rapidly moving outer 
 parts and the slowly moving inner parts (relatively to the 
 attracting forces) will bring the axis of the earth (the poles mov- 
 ing in spirals) to a position at right angles to the orbital plane 
 and keep it there. Hence, regardless of the number of days in 
 the month, the obliquity of the earth's axis will decrease and not 
 increase, as Mr. Darwin contends. 
 
 On page 309 Mr. Darwin says that "the attraction of the moon 
 and sun on the equatorial protuberance of the earth causes the 
 earth's axis to move slowly and continuously with reference to 
 the fixed stars"; and that "throughout this precessional move- 
 ment the obliquity of the equator to the ecliptic remains con- 
 stant". But I submit that such precessional motion would 
 be impossible if the obliquity remained "constant". It occurs 
 because attraction tilts the axis. The near and more slowly moving 
 inner parts are more strongly attracted than the far and more 
 rapidly moving outer parts. Hence the axis tilts and the tilting 
 causes precession. The compounding of the two motions results 
 in a. spiral motion of the poles. As this spiral motion pro- 
 ceeds, obliquity decreases. If the effect of "tidal friction" 
 were to precessionally increase obliquity, precession would be at 
 right angles to actual precession. The earth could not precess 
 as it does and also precess in a right-angular direction. If its 
 "precession" is really precessional, it must be due to a tilting of 
 the axis in a direction to decrease obliquity. If, on the other 
 hand, the "precession" of the earth is not really precessional, but 
 a primary motion caused by "tidal friction", then such motion 
 would precessionally tilt the axis into greater obliquity as it 
 proceeded. And this would be the case if the earth had no orbital 
 motion. This is shown by turning the stand of a stationary 
 gyroscope against the rotation of the wheel. Mr. Darwin's con- 
 tention is based on this proposition. (See Ency. Brit., p. 377.) 
 
 22 
 
But attraction on the rotating and revolving earth produces no 
 such effect. It is true that in such case also rotation is re- 
 tarded but greater obliquity does not ensue because the backward 
 and relatively slowly moving inner parts tend to go inward and 
 the relatively rapidly moving outer parts tend to go outward. 
 The planet is elongated towards and away from the central 
 attracting body. This prevents increase of obliquity. With or 
 without tides .attraction will cause decrease of obliquity. If 
 there were no oceans on the earth, rotation would still be re- 
 tarded, but at the same time obliquity would continue to decrease 
 until the planet spun on a perpendicular axis. 
 
 Mr. Darwin's views find no support in the actual conditions. 
 Inversion is proportional to the times of rotation and revolution. 
 Mercury and Venus have probably made the greatest number of 
 revolutions and inversion in them is complete. Jupiter has the 
 most rapid rotation and inversion is almost complete. The least 
 number of revolutions has probably been made by Neptune and 
 Uranus and their rotations are still retrograde. Mr. Darwin 
 says (Ency. Brit., p. 379), referring to Jupiter and its small 
 obliquity, that its system is "obviously far less advanced 
 than our own," but that the "high obliquity" of Saturn indicates 
 a later stage of development. This is begging the question. On 
 the other hand the progressive change of inclination from Neptune 
 to Jupiter tends strongly to confirm the views of Professor Mont- 
 gomery. Nor is the obliquity of Mars and the earth inconsistent 
 with his views. This is due to their slow rotation. And the 
 absence of satellites in the case of Mercury and Venus is signi- 
 ficant. "Development" is most advanced in the case of these 
 planets and it seems not improbable that their moons have been 
 wound up. 
 
 In re Newcomb. 
 
 In my letter to you of last July, I disputed Professor New- 
 comb's statement ("Popular Astronomy", p. 315) that we have 
 "every reason to believe" that if the moon were rapidly rotated on 
 its axis the earth's attraction would not retard such rotation, and 
 asserted on the contrary that however great the moon's rotation 
 might be, the earth's attraction would retard it until it coincided 
 with its period of revolution. I also asserted that if it had no 
 rotation at all, the earth's attraction would start rotation and 
 increase it until the period thereof equalled the period of its 
 
revolution. But I did not therein elaborate the reasons for these 
 conclusions. I will now do so. 
 
 Consider first the case where the moon has no rotation. It is 
 clear that the effect on the moon's rotation of the earth's attrac- 
 tion is the same as if the earth revolved around the moon instead 
 of the moon revolving around the earth. Let the moon be repre- 
 sented by a bar without rotation (a-b) and the earth, (c) as 
 revolving around the moon, thus : 
 
 The attraction of c on b is greater than on a, and hence as c 
 revolves around a-b it will start a-b rotating. Assume that c has 
 revolved and a-b rotated until their positions are as follows : 
 
 Thereafter c will more strongly attract a than b the 
 rotation of a-b will be retarded. But the period of retardation 
 will be less than the period of acceleration, a-b does not, as 
 Newcomb erroneously assumed, rotate on a fixed axle, a as well 
 as b is attracted by c. There is no "couple". Hence, although 
 a-b rotates, a at all times is moving towards c. And as a con- 
 sequence when c reaches a, a-b will still be rotating; and on the 
 next acceleration period will rotate further than on the preceding 
 acceleration period. The acceleration will increase until a-b 
 rotates in the same period that c revolves. 
 
 24 
 
Consider now the case where the rotation of a-b is more rapid 
 than the revolution of c. Assume that a-b will have rotated and 
 c revolved until their positions are as follows: 
 
 Thereafter c will attract a more strongly than 6, thereby accel- 
 erating the rotation of a-b. But, as above explained, the period 
 of acceleration will be shorter than the period of retarda- 
 tion. Hence when a reaches c the rotation of a-b will be slower 
 than at the start. Thus alternately the rotation of a-b will be 
 retarded and accelerated, but the periods of retardation will be 
 longer than the periods of acceleration, thereby decreasing the 
 rotation of a-b until it coincides with the revolution of c. 
 
 Hence the question of " tides" in the moon is immaterial. Tides 
 or no tides, attraction will increase or decrease the period of the 
 moon's rotation until it corresponds with the period of its revolu- 
 tion. Where however there are tides, the retardation or accelera- 
 tion is continuous, but where there are no tides, rotation is alter- 
 nately retarded and accelerated, but the periods thereof are dif- 
 ferent. Where the moon has no rotation, the periods of accelera- 
 tion will be longer, and where it has excessive rotation they will 
 be shorter. It is also clear that the attraction of the sun on the 
 moon cannot prevent the consequences due to the earth's attrac- 
 tion, which is greater than that of the sun. 
 
 Hence Newcomb was in error in his statement that the moon's 
 rotation would not be retarded if it were several times greater 
 than it is; and Ball erred in saying that when the tides in the 
 moon shall have subsided, the periods of rotation and revolution 
 will no longer coincide; and Moulton erred in saying that the 
 identity of the periods of rotation and revolution was due to some 
 unconsidered influence; and Darwin erred in saying that if 
 there were "oceans" on the moon, solar tides would retard its 
 rotation. 
 
 The foregoing demonstration also disproves Mr. Darwin's con- 
 tention that the attraction of the earth is retarding the moon's 
 orbital velocity. Let a-b represent the earth and c the moon. As 
 
 25 
 
we have seen, when the rotation of a-b is more rapid than c's 
 revolution, c's orbital velocity will alternately be accelerated and 
 retarded, but the periods of acceleration will be longer than the 
 periods of retardation. And where there are tides on or in the 
 central body, the orbital velocity of the revolving body will be 
 continuously accelerated. Hence while the moon is retarding the 
 earth's rotation, the earth is accelerating the moon's revolution; 
 and such retardation and acceleration will continue (in diminish- 
 ing degrees) until the period of the earth's rotation is the same as 
 the period of the moon's revolution. 
 
 Letter of January 27, 1919, Accompanying 
 "The Burial of a World." 
 
 Professor Montgomery informed me that the planets and 
 their satellites would finally be drawn by attraction into the sun. 
 He did not however state the reasons which led him to this con- 
 clusion. I have recently been considering this subject, and in 
 another paper enclosed herewith I advance grounds which I 
 think sustain this proposition. 
 
 In his "The Evolution of Worlds", Professor Lowell has a chap- 
 ter entitled "The Death of a World". My paper, which I have 
 entitled "The Burial of a World" fittingly supplements it. Per- 
 haps "Cremation of a World" would be a better title. He 
 contends, just as Montgomery did, that a retrograde-rotating 
 planet is in unstable equilibrium (p. 140, et seq.), and that 
 forward rotation will be acquired by inversion, and that such 
 rotation will be retarded until the periods of rotation and revolu- 
 tion coincide. 
 
 Professor Lowell did not, however, comprehend the operation 
 of the forces by which these effects are brought about. He asserts 
 that the tides "necessarily act as brakes upon the planet's spin". 
 This is not so. The water on the earth is not external to it but a 
 part of it. The reduction of rotation would be the same if the 
 water were frictionless, or if friction were increased to the point 
 of rigidity. It is due to the shape of the earth. Mr. Darwin's 
 contention that the earth's rotation would not be retarded if it 
 was composed of an elastic and frictionless substance is, I submit, 
 clearly erroneous. In such case the retardation of the whole 
 planet would be more uniform. Tidal friction does not retard 
 rotation. It decreases the retardation of the water (part of the 
 earth) and increases the retardation of the underlying core. 
 
 26 
 
Energy is lost by tidal friction, but it is not the cause of the 
 reduction of the rotational momentum of the whole body. "Fric- 
 tion" is a false quantity. If the rotation of the earth were slower 
 than the moon's revolution, it would be accelerated by the moon's 
 attraction and such acceleration would be accompanied by tidal 
 friction. Retardation of rotational momentum of a planet is 
 caused by a power which also causes friction between its parts, 
 but such friction does not reduce the rotational momentum. It 
 merely dissipates energy. The retardation of some parts by con- 
 tact with other parts is offset by the reduction of the retardation 
 of such other parts. The rate of retardation (or acceleration) of 
 the whole planet is the same regardless of the incidental friction 
 between the parts. As the period of rotation expands to the 
 period of revolution, with or without tidal friction, energy declines 
 because when the periods of rotation and revolution are the same, 
 the parts of the planet instead of traveling around the sun in 
 wave lines, move in approximate circles. This was not perceived 
 by Professor Lowell, although it is necessarily involved in the 
 general principle which he expounded. It is true, of course, that 
 tidal friction generates heat, and that the radiation of such heat 
 reduces energy, but in the case of a body without tides heat will 
 also be generated by the strains and distortions to which it is 
 subjected by attraction. In both cases the generated and dissipated 
 heat measures the loss of energy resulting from the change to cir- 
 cularity of the orbits of the parts of the planet. And where 
 rotation is caused by attraction heat will be generated either by 
 tidal friction or distortions dependent upon the character of the 
 body; and energy in such cases will be dissipated by radiation 
 of the heat. In both instances, the one where rotation is retarded 
 and the other where it is initiated and accelerated, energy will 
 be lost as the orbits of the parts of the planet become circular. 
 
 Assuming that the cause of retardation of rotation is tidal 
 friction, then in a case where tidal friction ceases before its work 
 is accomplished, ''superfluous energy", which excessive rotation 
 involves, would never be "dispensed with". If it be true, as 
 Professor Lowell asserts, that Nature is ridding itself of "super- 
 fluous energy ' ' in the solar system, then clearly it must be employ- 
 ing some agent other than tidal friction to produce this result. 
 
 Professor Lowell is also in error in saying, as he does, that 
 inversion is caused by "tidal action", as I have shown in my 
 analysis of Professor Pickering's "annual tide" theory. 
 
 27 
 
He is further in error in asserting (p. 147) that a planet's 
 "tidal bulges" tend to "carry over" its satellites. Con- 
 sider the case of the earth, for instance. The orbit of the moon 
 was not inverted by the earth, but by the sun. The inversion of 
 the earth is not the cause of the "carrying over" of the 
 moon, but the effect (chiefly) of the moon's influence as it 
 was "carried over" by the sun, the differential attraction, of the 
 moon being greater than that of the sun. The fact that the 
 earth's inversion has lagged behind the inversion of the moon's 
 orbit, conclusively disproves Professor Lowell's theory. His 
 "distrust" on this point was well founded. 
 
 Professor Lowell says that Sir Robert Ball was the first to sug- 
 gest the "argument" he makes (p. 145). Ball's views are set forth 
 in "The Earth's Beginning", and in "The Story of the Heavens", 
 but that he did not comprehend the nature and operation of the 
 forces which were bringing about the results which he said were 
 impending is disclosed by his statement in the latter work that 
 retardation is caused by tidal friction, and by his further statement 
 that when the tides in the moon shall have subsided, "there would 
 then be no longer any necessary identity between the period of 
 rotation and that of revolution ' ' ; and hence that it is possible 
 that future generations may see the other side of the moon. This 
 is not so, as I have shown. Gravity would keep the long diameter 
 of the moon pointing towards the earth, if the moon were 
 as rigid as it is possible for any real body to be. And if its 
 period of rotation were increased, gravity would decrease it until 
 it coincided with its period of revolution. 
 
 There is a remarkable divergence in the views on this subject of 
 Ball, Darwin, and Moulton. Ball says (see chapter on the tides 
 in "The Story of the Heavens") that when the tides in the moon 
 subside, the earth 's control will cease ; Darwin says that the earth 's 
 control would cease now, owing to the sun's influence, if there 
 were tides on it; and Moulton says that the situation is inexplic- 
 able and implies the presence of some unconsidered influence! 
 
 It is strange that Professor Lowell, whose "The Evolution of 
 Worlds" was published in 19:09, makes no reference to either 
 Pickering or Moulton. Of course, if Lowell and Ball are right in 
 their conclusions, Moulton is in error, for in his controversy with 
 Pickering, he contended that attraction will not invert a retro- 
 grade-rotating orb. It is no less remarkable that Moulton in his 
 "An Introduction to Astronomy" (1916) makes no reference to 
 Lowell or Ball. 
 
 28 
 
The Burial of a World. 
 
 In "The Evolution of Worlds" (p. 140, et seq.), Professor 
 Percival Lowell contends that a retrograde-rotating planet is in 
 unstable equilibrium and that stable equilibrium will be attained 
 only after it has been inverted and its consequent forward rotation 
 retarded until the period thereof coincides with its period of 
 revolution. He attributes this result to the dissipation by 
 "Nature" of "superfluous energy" in the solar system, and its 
 reduction to the smallest quantity consistent with the fixed amount 
 of moment of momentum. 
 
 But "superfluous energy" would exist under the conditions 
 depicted by Lowell in his chapter entitled "The Death of a 
 World". If, as he argues, Nature "abhors" superfluous energy, 
 it may dispense with some of it by contracting the orbits of the 
 planets until they are drawn into the sun. It may, I think, be 
 demonstrated that the forces which cause rotation and revolution 
 will bring about this result, as well as inversion of retrograde 
 rotation and retardation of forward rotation, as I have already 
 shown. 
 
 Consider a planet as not rotating or revolving, and as being 
 subjected only to the attraction of the sun. Eliminating for the 
 moment the motion of the planet towards the sun, the effect of 
 such attraction will be elongation of the planet to the point of 
 balance between the force tending to elongate it and the forces 
 which tend to maintain a spherical shape. Now give full effect 
 to the force of gravity exerted by the sun on the planet, and at the 
 same time apply to the system such tangential and rotatory forces 
 that the planet will rotate and revolve in the same period and 
 in the same direction as the sun rotates. Clearly the forces caus- 
 ing rotation and revolution of the planet will differently affect its 
 parts. The parts nearest the sun will tend to move towards it, 
 and the remote parts away from it, the planet as a whole moving 
 in an orbit which lies between the lines of such tendencies. The 
 application of such forces will increase the initial elongation of 
 the planet due to gravity alone, and at the same time slightly 
 flatten it, as well as the sun. As these results ensue the force of 
 gravity on the planet as a whole increases. The further the sun 
 and planet depart from a spherical shape the greater will be the 
 attraction of the sun. The concentrated point of attraction near 
 the center of the planet will shift towards the sun. And the sun 
 also will be further elongated towards the planet. The result is 
 that the planet, being subjected to constantly increasing attraction, 
 
 29 
 
winds inward, just as it would do if the mass of the sun were 
 gradually increased. As it winds inward the period of its rotation 
 and revolution and the period of the sun's rotation decrease 
 angular speed of the system increases (the consequent flattening 
 of the sun and planet further augmenting their attraction) 
 while the linear speed of the planet decreases. Thereby both the 
 orbital energy and moment of momentum of the planet are reduced. 
 The superfluous energy is " dispensed with" by dissipation of 
 heat generated in both sun and planet while the lost moment of 
 momentum is gained by the sun. 
 
 The forces exerted upon the planets are continually altering 
 their shapes. A perfect sphere exerts and has exerted upon it 
 for a given mass a minimum force. As it flattens and elongates 
 its attraction progressively increases. The planets are falling 
 into the sun by circuitous routes. "Like drops of rain: however 
 they may linger in the lakes and pools, must sometime reach the 
 sea." 
 
 I am aware that these views are not in harmony with the 
 opinion entertained by Mr. Darwin, but I think his position is 
 clearly untenable. 
 
 He contends ( and is supported in this contention by Lord Kelvin 
 and Professor Moulton) that tidal action is retarding both the 
 rotation of the earth and the revolution of the moon, but that the 
 rate of retardation of the rotation is greater than that of the 
 revolution, and hence that they will ultimately coincide; and, 
 Mr. Darwin asserts, when this occurs the earth and moon will 
 be in stable equilibrium. 
 
 I submit on the contrary, that the revolution of the moon is 
 accelerated by tidal action and the rotation of the earth retarded, 
 and that such acceleration and retardation will last, in diminishing 
 degrees, until the periods thereof are the same. Mr. Darwin and 
 Lord Kelvin ("Natural Philosophy", Vol. 1, p. 255) admit that 
 "in the first place" the moon's revolution will be accelerated, but 
 assert that thereafter it will be retarded. But there is no "in the 
 first place". If it be accelerated "in the first place" it is acceler- 
 ated all the time. Mr. Darwin concedes that his position is 
 "paradoxical". In my opinion it is more than "paradoxical". It 
 amounts to saying that the moon's revolution is both accelerated 
 and retarded by the same force at the same time! 
 
 Mr. Darwin and Professor Moulton say that if at the time of the 
 "first identity" the rotation of the earth were infinitesimally 
 
 30 
 
slower than the revolution of the moon, both periods would de- 
 crease, but that the period of the revolution would decrease more 
 rapidly than the period of rotation. I contend on the contrary, 
 that in such case the revolution of the moon would be retarded 
 as the rotation of the earth was accelerated, and hence that the 
 inequality would be instantly corrected. Inspection of Mr. 
 Darwin's diagram ("The Tides", p. 266) makes it obvious, 
 I submit, that the moon's revolution is accelerated as the earth's 
 rotation is retarded; that is to say that it is more rapid than 
 it would be if the earth were perfectly spherical. The acceler- 
 ation, however, will decline as the rotation is retarded. During this 
 period the revolution of the moon will be above normal and the 
 revolution of the earth (with respect to the moon) below normal. 
 The earth will gain the moment of momentum which the moon 
 loses, and finally they will rotate and revolve as if they were 
 united by a bar extending through them. They will thereafter 
 slide along the bar towards each other, under constantly increasing 
 attraction and increasing angular velocity, until they coalesce. 
 During this time and thereafter the moment of momentum of the 
 system will remain the same. 
 
 The asserted analogy between retardation by acceleration, and 
 acceleration occasioned by a resisting medium, is false. In 
 the latter case the medium does not cause acceleration; it causes 
 retardation. Acceleration is caused by attraction. 
 
 As an indication of the looseness of Mr. Darwin 's grasp upon the 
 subject, I cite his statement (Ency. Brit., p. 375) that the moon's 
 orbital moment of momentum must increase because that of the 
 earth's rotation diminishes. This is not so. It is the retardation 
 of the earth's revolution, with respect to the moon, that requires 
 increase of the moon's orbital moment of momentum. Ketarda- 
 tion of rotation merely dissipates energy. And acceleration of 
 the moon's revolution would, of course, increase its orbital moment 
 of momentum. Hence the assumed necessity for an expanded orbit 
 disappears. 
 
 Mr. Darwin says ("The Tides", p. 356) that "the general 
 question of the limiting proximity of a liquid planet and sat- 
 ellite which just insures stability is not yet solved". It never 
 will be in my opinion. There is no stability short of concentra- 
 tion in the sun of all of the matter in the planets and their 
 satellites, when, as above stated, a condition will have been 
 attained where there will be a minimum quantity of energy for the 
 
 31 
 
fixed amount of moment of momentum in the system. Perpetual 
 revolution is only theoretically possible only where the bodies 
 are weighted points or perfect spheres. 
 
 Further Comments on Mr. Darwin's Views. 
 
 Mr. Darwin leaves it uncertain as to whether or not 'he con- 
 siders that "tidal friction" operates as a "brake" on the 
 earth's rotation. The illustrations and statement with which he be- 
 gins ("The Tides", pp. 264-5) indicate that he takes the view that 
 it does, but when his subsequent explanation of the operation 
 and effect of the tides is examined closely, it appears that his 
 opinion was that the real function of "tidal friction" is to 
 carry the tidal "protuberance" forward so that it will give 
 occasion for attraction to retard the rotation of the whole earth, 
 just as if it were an elongated rigid body placed obliquely to 
 the line of attraction. Of course the core of the earth would 
 be retarded by the friction between it and the overlying waters, 
 as the waters, while being carried forward by rotation are 
 pulled back by attraction, but the greater the friction the less 
 the waters (part of the earth) would be retarded. Hence the 
 friction between the waters and the core is a false quantity. 
 The loss equals the gain. And as Mr. Darwin himself pointed 
 out, when the waters are carried by rotation past their 
 "proper place" and then pulled back by the force of attrac- 
 tion, the effect on rotation is the same as if the waters, 
 so situated, were rigidly attached to the earth. Hence retarda- 
 tion will take place without tidal friction. 
 
 But Mr. Darwin entertained the view that if the waters were 
 not carried past their "proper place", there would be no retarda- 
 tion of rotation. This, however, is clearly not so. Retardation 
 would occur just the same if the waters were frictionless or 
 the earth perfectly elastic. Retardation is not dependent on 
 friction but on the shape of the earth. The less the friction 
 the greater the response of the waters to the force of attraction, 
 and the elongated core also responds. Where there is friction 
 there is less retardation of water and more of core, and without 
 friction more of water and less of core. It is surprising that 
 Mr. Darwin overlooked this simple proposition. Tidal friction 
 no more retards the earth 's rotation than it would be retarded 
 by plowing a furrow around it from east to west. 
 
 32 
 
Mr. Darwin says ("The Tides", p. 288) that if when the period 
 of the "second identity" is reached there are still "oceans" on 
 the earth, its rotation will be retarded by solar tides. This posi- 
 tion, I submit, is clearly untenable. The rotation of the earth 
 would still be controlled by the moon, not the sun, whose dif- 
 ferential attraction is less. And again on page 289, he says that 
 if there were "oceans" on the moon solar tides would cause it 
 to rotate slower than it revolves. If this were true, then the 
 moon would now be rotating slower than it revolves. The pres- 
 ence of water on it would not alter the forces and laws which 
 control its rotation. And incidentally it may be noted that this 
 view does not harmonize with Ball's contention that the identity 
 of the moon's periods of rotation and revolution is due to the 
 tides in it. Why does not the sun work on these tides and now 
 retard the moon's rotation? This "difficulty" caused Professor 
 Moulton to remark ("An Introduction to Astronomy", p. 458) : 
 
 "It seems probable from this line of thought that some in- 
 fluence, so far not considered, has caused the moon always to 
 present the same face to the earth. ' ' 
 
 The "difficulty", however, is removed by a right understanding 
 of the problem. Tides or no tides, the rotation of the moon is 
 controlled by the earth, not the sun. 
 
 Mr. Darwin assumes that at the time the period of the 
 moon's rotation became coincident with the period of its revolution 
 there were still "oceans" on it. But such assumption has no 
 basis in fact. May not the waters on the moon have dried up 
 while the moon still had superfluous rotation? And if so, how 
 was such rotation dissipated? On the tidal theory it never would 
 be, and yet the strains and distortions to which the rotating moon 
 would in such case be subjected would of course generate heat 
 and cause dissipation of energy. This consideration confirms the 
 conclusion that the retardation of the rotation of a planet or 
 satellite is due to its shape, as I have demonstrated in "In re 
 Newcomb", and not to tidal friction. Attraction would "dispense 
 with" the superfluous rotation of a crow-bar. It is remarkable 
 that Mr. Darwin failed to see this as he saw (p. 279) that tidal 
 friction would accompany acceleration of rotation, which would 
 occur if the moon revolved (as in the case of Phobos) more 
 rapidly than the earth rotated. 
 
 33 
 
Mr. Darwin ("The Tides", p. 338) quotes Mr. Becker as 
 saying : 
 
 "Laplace assigns no cause for the heat which he ascribes to 
 his nebula. Lord Kelvin goes further back and supposes a 
 cold nebula consisting of separate atoms or meteoric stones 
 initially possessed of a resultant moment of momentum equal 
 or superior to that of the solar system. Collision at the center 
 will reduce them to a vapor which then expanding far beyond 
 Neptune's orbit will give a nebula such as Laplace postulates." 
 
 But such a theory is manifestly unsound. A system of revolv- 
 ing meteoric stones would not generate energy. It would 
 dissipate it and the dissipation would continue until all the 
 stones were collected in one cold rotating body. Some influence 
 external to the system would be necessary to produce such a 
 nebula as Laplace postulated. 
 
 34 
 
THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 AN INITIAL FINE OF 25 CENTS 
 
 WILL BE ASSESSED FOR FAILURE TO RETURN 
 THIS BOOK ON THE DATE DUE. THE PENALTY 
 WILL INCREASE TO SO CENTS ON THE FOURTH 
 DAY AND TO $1.OO ON THE SEVENTH DAY 
 OVERDUE. 
 
 
 
 SEP 17 11 
 
 40 
 
 10Apr'52KjJ 
 
 
 
 
 Au. 
 
 
 />x 
 
 
 f 
 
 
 
 
 >'v | 
 
 
 p 
 
 
 V.. j,, 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 LD 21-100m-7,'39(402s) 
 
YC 40575 
 
 ": 
 
 UNIVERSITY OF CALIFORNIA LIBRARY