UC-NRLF 
 
 SB 2fl 
 
LIBRARY 
 
 OF THK 
 
 UNIVERSITY OF CALIFORNIA. 
 
 O-IKT OF" 
 
 Deceived 
 ^Accessions No. 
 
 Class No . . 
 
BY 
 
 ROBERT STEVENSON, C.E..M.E. 
 
 Meml'ter of the American Institute of Mining Engineers; California Academy 
 - iences: Technical Society of the Pacific r-oast. etc., etc. 
 
 TRADE SUPPLIED BY 
 
 THE SAN FRANCISCO NEWS COMPANY 
 SAN FRANCISCO, CALIFORNIA 
 
 A XK\V POTKXTIAL PRINCIPLE 
 IX XATURK 
 
 ELASTICITY A MODE OF MOTION 
 
 BEING A POPULAR DESCRIPTION OF 
 
 A NEW AND IMPOETANT DISCOVEEY 
 IN SCIENCE 
 
 \ 
 
 Si 
 
 PRICE 5O CKNTS 
 

 A XE\V POTENTIAL PRINCIPLE 
 IN NATURE 
 
 ELASTICITY A MODE OF MOTION 
 
 BEIXG A POPULAR DESCRIPTION OF 
 
 A NEW AND IMPORTANT DISCOVERY 
 IN SCIENCE 
 
 BY 
 
 ROBERT STEVENSON, C.E..M.E. 
 
 Member of the American Institute of Mining Engineers; California Academy 
 of Sciences; Technical Society of the Pacific Coast, etc., etc. 
 
 SAX FRAXCISCO 
 
 INDUSTRIAL PUBLISHING COMPANY 
 APRIL, ivx-, 
 
 
 jIITIftSXTT 
 
t, 1895, 
 BY 
 
 ROBERT STEVENSON, C. E. 
 
CIRCULAR LETTER. 
 
 tt_.e-o^ <*- jdc?-a-Ca-dLa-0^. &- 
 
 L.c^.^e~<L~ JL 
 TRUTH c 
 -^t-4-dL-o-Cou 
 
 00 <L~^-t*CL, 
 
 JL e^cx-o^oL.^- c*-^ w^.JL ( 
 TRUE ^^e^ PROXIMATE 
 
 /^r) ) ) 
 
 
 Mu 
 
 0U-< 
 
s 
 
 
 
 iL 
 f 
 
 ff 
 
 t^ 
 
 I I 
 
K. 
 
 The discovery which I am about to describe 
 was first impressed on my attention twenty-eight 
 years ago, when a student attending Sir William 
 Thomson's class in the old college of Glasgow 
 University. But I did not thoroughly appreciate 
 the importance of the matter until about fifteen 
 years ago. Since then, although cognizant of 
 the true cause of gravitation, I have not been in 
 a position to take advantage of the immense 
 power, and wonderful insight, that such knowl- 
 edge confers. 
 
 My business as a mining engineer requiring all 
 my time and attention, and not being a recog- 
 nized authority in natural sciences, my desultory 
 efforts from time to time to call the attention of 
 the recognized authorities on the subject, to the 
 facts of the case, have met with no success. 
 
 I am now preparing to publish my notes, con- 
 taining the mathematical proofs and experiments 
 by which I have established the truth (to my 
 own satisfaction) of the great principle in Nature 
 which is an intermediate and universal agent 
 between the spiritual agency of force, and the 
 
4 PREFACE. 
 
 material energy which produces gravitation and 
 evolution. 
 
 I have so far been able to trace this intermedi- 
 ary principle, as the great potential, and con- 
 servative energy in the material universe. Its 
 elastic resistance to the radical forces of disper- 
 sion, being as necessary to the stable existence 
 of a molecule as it is to that of the planetary sys- 
 tems of the whole universe. 
 
 ROBERT STEVENSON, C. E. 
 
 Academy of Sciences, San Francisco. 
 April 10, 1895. 
 
CONTENTS. 
 
 Page. 
 Preface 3 
 
 ESSAY: ELASTICITY OF MOTION THE TRUE AND 
 PROXIMATE CAUSE OF UNIVERSAL GRAVI- 
 TATION 
 
 Article (1) The Greatest Natural Principle 7 
 
 (2) Its Utility 7 
 
 (3) Gravitation, Its History and Theories 8 
 
 (4) Purpose of this Essay 8 
 
 (5) Newton, His Great Work 8 
 
 ^6) Newton, His Mistakes 8 
 
 <7) Central Force 9 
 
 <8) Newton's Law 9 
 
 <9) Centripetal Force Unnecessary 9 
 
 (10) Free Motion 9 
 
 <11) Its Resultant 10 
 
 (12) Difference Between Free and Constrained 
 
 Motion 10 
 
 <13) (14) Forthcoming Work 11 
 
 (15) The New Theory 11 
 
 (16) Geometrical Description 11 
 
 <17) Kinetic Energy as Taught 12 
 
 (18) Kinetic Stability a Reciprocating Force. 13 
 {19) Ratio of Kinetic Stability to Kinetic 
 
 Energy " 13 
 
 (20) Orbital Motion Elastic 13 
 
 {21 ) Limit of Deflecting Force 14 
 
 <22) Force of Restitution 14 
 
 (23) Stability of Solar System 14 
 
 (24) Molecular Resistance 15 
 
 {25) Elliptical Motion 15 
 
 (26) Rectangular Stress . . . ; 16 
 
 (27) Kinetics versus Kinematics 16 
 
 (28) Laws of Tension . . .16 
 
b CONTENTS. 
 
 Article (29) Law of Attraction 17 
 
 (30) Law of Inertia 17 
 
 (31) Kinematical Results 18 
 
 (32) Law of Specific Gravities 18 
 
 (33) Sunless Systems 18 
 
 (34) Action at a Distance 19 
 
 (35) Discovery on which the New Theory is 
 
 Based 19 
 
 (36) Experimental Proof, 20 
 
 (37) Lord Kelvin's Suggestion 20 
 
 (38) The Law of Superimposed Motions 21 
 
 (39) Illustration of the Law 21 
 
 (40) Different Case 21 
 
 (41) Free Motion. Equation of Curve 22 
 
 (42) Mathematical Proof of New Theory. ... 22 
 
 (43) Elastic Motion 23 
 
 (44) Laws of Stellar Phenomena 23 
 
 (45) Light, Its Production and Transmission. . 23 
 
 (46) Heat 23 
 
 (47) Electricity 23 
 
 (48) The Cause of Sun Heat 23 
 
 (49) How Kinetic Stability Overcomes Gravity 24 
 
 (50) Inductive Capacities and Tidal Motion ... 24 
 
 (51) The Abbe Moigno's Prophecy 24 
 
 THE NEW KINETIC THEORY OF GRAVITATION 
 Part I. A Paper Read Before the Technical Society 
 
 of the Pacific Coast 26 
 
 Part II. Supplement to the Above, Containing Reply 
 to Discussion, and a Description of Two 
 Experiments submitted to the Univer- 
 sity of California and the Stanford Uni- 
 versity 47 
 
ELASTInTT)F MOTION 
 
 THE TRUE AND PROXIMATE CAUSE OF 
 UNIVERSAL GRAVITATION. 
 
 (1) It may appear to be egotistic in me to say 
 that the principle of Kinetic Stability, or that 
 which produces it, which I call The Persistence of 
 Energy, is the greatest natural principle that 
 science has ever discovered, and when it becomes 
 thoroughly known, it will lead to a harvest of 
 knowledge and power for mankind, such as the 
 world has never before experienced. 
 
 (2) It will in fact prove the heavenly key to 
 a realm of spiritual truth, whose grandeur con- 
 sists in this, that it will enable mankind to 
 understand Nature better, and to utilize her more 
 intelligently for the benefit of the human race 
 and the glory of the Divine Individuality, who 
 has created by the spirit of His power all the 
 phenomena of the universe. 
 
8 ELASTICITY OF MOTION. 
 
 (3) It would be out of place in this short 
 explanatory paper to enter into the historical 
 portion of the subject of gravitation; nor do I 
 propose to discuss the merits of the various 
 theories which have been advanced during the 
 last three hundred years. 
 
 (4) I propose therefore to devote myself to the 
 exclusive task of explaining the theory and its 
 application, which I am about to publish, so 
 that those naturalists who take an interest in the 
 great physical principles may understand before 
 hand, and be prepared to criticise the work when 
 it appears. 
 
 (5) Before entering on the explanatory portion 
 of the subject, allow me to say that to the illus- 
 trious Newton belongs the great and undying 
 honor of having rescued the theory of gravity 
 from the grasp of metaphysics, and established it 
 on the firm basis of physical science, where for 
 two centuries it has resisted every attempt to 
 displace it. 
 
 (6) And if it should be the duty of science 
 now to acknowledge that Newton was mistaken, 
 both in his hypothesis and his theory, still the 
 
ELASTICITY OF MOTION. 9 
 
 credit of having discovered and demonstrated the 
 law of the inverse square of the distance, by 
 means of which astronomy has made such great 
 progress, will ever remain as a halo of glory 
 around the illustrious author of the " Principia." 
 
 (7) According to the accepted laws of motion, 
 curvilinear motion is impossible without a cen- 
 tripetal force. 
 
 (8) Newton started on that supposition, and 
 with Kepler's laws as mathematical data, he 
 demonstrated the great law of universal gravita- 
 tion, on which all theoretical astronomy is based, 
 and from the application of which many great 
 discoveries have been made in the times, dis- 
 tances, and motions of the planets and comets of 
 the solar system. 
 
 (9) But if it can be shown that the hypothesis 
 of a centripetal force is unnecessary, then I think 
 there will be no difficulty in establishing the fact 
 that orbital motion in free space is not caused by 
 centripetal force. 
 
 (10) In our every-day experience it is very 
 seldom that we observe a case of free motion in 
 
10 ELASTICITY OF MOTION. 
 
 free space. The nearest approach to it that we 
 meet with is in the case of the cricketer, and 
 baseball player, and curious to say, both of them 
 can throw a "curved ball," a ball which on 
 leaving the hand of the thrower is made to 
 describe a horizontal curvilinear path; and I can 
 prove that if it were not for the resistance of the 
 air, and the force of gravity, it would be possible 
 to make a ball describe a complete horizontal cir- 
 cuit round an imaginary point as a center with- 
 out any tension between the center and ball. 
 
 (11) By this hypothesis the ball receives a 
 longitudinal and transverse energy in the same 
 plane impressed upon it, which causes it to de- 
 scribe a curvilinear path, or in other words, the 
 resultant of two transverse rectilinear energies 
 given to a free body in free space is curvilinear 
 motion. 
 
 (12) What we have been taught of the princi- 
 ples of the composition and resolution of forces; 
 motions, energies, etc., in Dynamical Science, 
 will predispose us to criticise that proposition, 
 but if we will consider for a moment the different 
 conditions between a free body in free space and 
 a body which is constrained to move in a fixed 
 
ELASTICITY OF MOTION. 11 
 
 direction, we will see that the principle which 
 applies to the one may not apply to the other. 
 
 (13) As I have said, this paper is only explan- 
 atory of the principles on the proof of which the 
 new theory of gravitation rests. 
 
 (14) To prove all the propositions necessary to 
 -establish these principles requires a good-sized 
 volume, which I hope to have ready for publica- 
 tion in a very short time, as the manuscript is 
 nearly completed now. 
 
 (15) To thoroughly understand the theory, 
 astronomers must be prepared to look at the sub- 
 ject from a different point of view than that from 
 
 which they have been taught and accustomed to, 
 as the theory bears a similar relation to the New- 
 tonian theory, that the Copernican bears to the 
 Ptolemaic, and in both cases it is simply the dif- 
 ference between an apparent action and a real 
 action. 
 
 (16) In the following diagram let us suppose 
 the mass m to be a body moving in the straight 
 line A B, and for simplicity's sake let us con- 
 
12 
 
 ELASTICITY OF MOTION. 
 
 sider it as a dynamical particle, moving with 
 uniform velocity v in the direction of B w?th 
 independent motion in free space. 
 
 FIG. 1. 
 
 J) 
 
 Then the kinetic energy of m = 
 
 m v 
 2 
 
 (17) When m reaches the point C, let us sup- 
 pose that a transverse impulse superimposes on 
 m an additional kinetic energy E& in the direc- 
 tion of H along C H. Now m is moving with 
 twice the kinetic energy, and therefore its result- 
 ant velocity is represented in direction and 
 
ELASTICITY OF MOTION. 13 
 
 magnitude by the straight line C D, which is the 
 diagonal of the parallelogram COD H, that is 
 what is taught in the universities at present, 
 and that is one point where my discovery proves 
 that such teaching is wrong. 
 
 (18) I find by experiment, and I can also 
 prove it by physical geometry, that m when mov- 
 ing with kinetic energy along A B has also 
 kinetic stability, due to what I call its persistence 
 of energy, and that the kinetic stability acts as a 
 latent or potential energy, which acts with 
 reciprocating effect against a deflecting force or 
 impulse along C H, and consequently the result- 
 ant, instead of being along the diagonal C D, is 
 along the curvilinear line C /, and we can show 
 that the path is elliptical. 
 
 (19) We also prove that the kinetic stability 
 = E* of m along A B is equal to the kinetic 
 energy, and that E^ -j- E* = E = total energy, 
 or vis viva, and that E$ the kinetic stability 
 is inversely proportionate to E^ the potential 
 energy. 
 
 (20) By these propositions we prove that the 
 motion of a free body, such as a planet, is elastic, 
 
14 ELASTICITY OF MOTION. 
 
 and that its orbit is due to the superimposed mo- 
 tions, hence, although it appears to be attracted 
 to a focus, it really contains within itself a 
 couple and a direct force, which constrains it to 
 move in its orbit without any attractive or 
 repulsive force, or any elastic medium of any 
 kind whatever. It is in itself endowed with 
 elastic motion. 
 
 (21) I can also prove that no force, however 
 great, unless it be infinite, can ever permanently 
 deflect a free moving body from the line of its 
 previous motion. 
 
 (22) L,et m be acted on at C with an impulse 
 as great as you please, which is not infinite, and 
 there is always a component tending to bring it 
 back to the line A B, and such a component is 
 inversely proportionate to the radius of curvature 
 at any point in the body's motion. 
 
 (23) Now this fact explains the stability of 
 the solar system. Supposing the sun had kinetic 
 energy due to its inertia and longitudinal 
 velocity, then by some means a transverse 
 impulse is superimposed at a radial distance from 
 its center of inertia, acting as a couple with the 
 
ELASTICITY OF MOTION. 15 
 
 kinetic stability, producing rotation as well as 
 linear velocity, then I can prove that the whole 
 energy due to rotation would be absorbed into 
 the sun's mass as heat; -and if it was great 
 enough the mass would become incandescent,, 
 and sufficient material might be dispersed as' 
 incandescent vapor to produce a nebulous atmos- 
 phere, stretching to the very confines of the 
 present solar system, out of which, as Laplace 
 has shown, the whole planetary system could be 
 evolved by refrigeration, and the persistence of 
 energy of the molecular vortices within the 
 nebula. 
 
 (24) In such a system as this, we can prove 
 that the tendency of each molecule to return to 
 its original line of motion (its persistence of 
 energy) would always cause its apparent centri- 
 petal energy to more than balance its centrifugal 
 energy. Hence the Force of Restitution. 
 
 (25) Returning again to the diagram, Fig. 1, 
 let us suppose the mass m^ m 2 m 3 to be a body 
 moving in the orbit C D E, which we will sup- 
 pose to be a semi- ellipse, whose center is O, and 
 the foci G and 6\, and C E the major axis or 
 diameter, which we may extend both ways to A 
 
 HI7BKSIT7 
 
16 ELASTICITY OF MOTION. 
 
 and B, then suppose m l to move from C to D 
 with a uniform and independent motion. 
 
 (26) Then according to the usual interpreta- 
 tion of the Newtonian laws of motion, for ?n l to 
 describe the curve C m 1 D it is necessary that it 
 should be acted on by a force towards H in the 
 tangent C H, and another and independent force 
 in the direction C E, and that the force along 
 C E should always be at right angles to the 
 tangent at any point of the curve C m l D, so 
 that when the body m reaches m l the direction 
 of the composite forces would be along the tan- 
 gent to the curve at m l , and the radius vector 
 m l G if the orbit was elliptical, and O m t if 
 circular. 
 
 (27) Now as a purely geometrical, or kine- 
 matical problem, that way of looking at it is 
 correct, but when we have to deal with a body 
 which has the physical property of kinetic 
 energy, due to its independent motion, we have 
 to adopt other methods than that used by New- 
 ton in the " Principia " to correctly solve the 
 problem. 
 
 (28) If we suppose O m 1 to be a string fixed 
 at O as a pivot, and attached to m lt or if we sup- 
 
ELASTICITY OF MOTION. 17 
 
 pose the string G m^ G^ fixed at the foci G and 
 G l passing through the center of m^ then we 
 know that such an arrangement will produce cir- 
 cular or elliptical motion if m l be acted on by an 
 independent tangential force, such as that along 
 C H or m l ff^ and the tension on the string 
 would vary constantly with the variation of 
 curvature, and be proportional to the curvature. 
 
 (29) Now instead of the string, the Newtonian 
 theory requires an attractive force at one of the 
 foci, say G, acting as a tension between G and 
 m lt which varies as the multiple of the masses at 
 G and m 1 divided by the square of the distance 
 between their centers of gravity, which is: 
 
 G X *, ^ _ m X m l 
 
 ~JT^* ~^~ 
 
 is the Newtonian expression for the universal 
 law of gravitation. A very simple law when we 
 know the true value of each respective mass, and 
 a law which must always be correct when the 
 inverse square of the distance is used to calculate 
 the value of the mass. 
 
 (30) It is not unscientific to suppose that a 
 force may decrease as the square of the distance 
 increases, on the other hand, it is not only un- 
 scientific, but it is perfect nonsense to say that 
 
18 ELASTICITY OF MOTION. 
 
 the resultant force of attraction between two 
 masses varies as the multiple of the masses, 
 when we know that the natural laws only require 
 addition instead of multiplication. 
 
 (31) But, as I say, for pure kinematical 
 
 t- 1 m X mi . , 
 motions such a law is absolutely correct 
 
 when the value of the mass is found by the 
 inverse square of the distance. 
 
 (32) Now whilst such a law may give us the 
 true relative motions of the planets and comets of 
 the solar system, it can never give us the true 
 specific mass or gravity, or the specific energy of 
 each body separately, hence the limit to the 
 utility of the Newtonian law. The law is indeed 
 a kinematical law, whereas the new law will be 
 kinetic, and therefore become the great law of 
 energy, not only in the inorganic but also in the 
 organic and spiritual worlds, and on the proper 
 application of this law not only does the conser- 
 vation of natural energy depend, but the truth 
 and value of eternal life becomes demonstrable. 
 
 (33) In the case of the solar system, with the 
 sun at G, and the planet at m\m 2 m^ the centri- 
 petal force looks as if it might be attractive, but 
 
ELASTICITY OF MOTION. 19 
 
 if there had been no sun in the focal center of the 
 solar system, and only empty space, as we will 
 show might happen in Nature, then the theory 
 of attraction could never have existed. 
 
 (34) The supposed action at a distance we will 
 prove to be only apparent, just as Ptolemy's sup- 
 posed motion of the stars round the earth was 
 apparent only. It is therefore quite unnecessary 
 that there should be a "plenum of vortices," or 
 an "elastic semi- material medium," filling inter- 
 planetary space to produce attraction or apparent 
 tension. 
 
 (35) My theory is based on the discovery 
 that a mass m moving with uniform or accel- 
 erated velocity in the line A B, with indepen- 
 dent motion in empty space, may have another 
 independent motion superimposed on it at C, 
 such that its resultant path (due to these two 
 motions alone) would lie along the semi-ellipse 
 C D E; or in other words, that the resultant of 
 two transverse independent free motions, which 
 have kinetic energy in free space, lies along a 
 curve instead of the diagonal of the parallelo- 
 gram, of which the adjacent sides represent the 
 composite motions. 
 
20 ELASTICITY OF MOTION. 
 
 (36) The experimental proof of this fact is 
 very simple and convincing. Take a magnetized 
 steel ball two inches in diameter, project it from 
 a spring catapult with a velocity of 50 feet per 
 second along a perfectly flat and smooth table, 
 20 feet long by 6 feet wide, dust the top of the 
 table with a white powder, and cover the ball 
 with lamp black, then at a distance of one "foot 
 from where the ball leaves the catapult spring 
 have a fixed electro magnet so arranged as to 
 give an instantaneous transverse repulsion to the 
 ball equal in energy to what the ball received 
 from the catapult, and the line of resultant 
 motion will be seen to be elliptical. If the 
 experiment was carried out in a vacuum, and the 
 surface of the table and ball were perfectly true 
 and smooth, the path would be perfectly ellipti- 
 cal. 
 
 (37) At one time I thought the proof could be 
 better established by using a vacuum tube in 
 some tall tower, such as the Metropolitan 
 Tower, but Lord Kelvin, to whom I mentioned 
 the matter, thought it would not answer, and 
 after considering the matter I saw that he was 
 right, because the tower being a portion of the 
 earth, a body falling within the tower would be 
 moving under constraint, and the resultant 
 
ELASTICITY OF MOTION. 21 
 
 motion in that case would lie along the diagonal 
 of a parallelogram. 
 
 (38) The rule is: That when an independent 
 motion is transversely superimposed on a con- 
 strained motion the resultant lies along the 
 diagonal straight line, but when an independent 
 motion is superimposed on another independent 
 free motion, the resultant is along a continuous 
 curve. 
 
 (39) For instance, if a man walks across a 
 railway carriage whilst it is moving in a straight 
 line, the resultant due to the composition of the 
 two motions is the diagonal straight Hne, accord- 
 ing to the well-known principles of dynamics. 
 
 (40) On the other hand, if the man was to 
 jump from the side of the moving carriage, and 
 was not acted on by any other forces than those 
 due to his own kinetic energy (the one parallel 
 to the carriage, and the other transverse), then 
 he would describe an elliptical curve, and return 
 to the point he jumped from, if the motion of the 
 carriage was uniform. 
 
22 ELASTICITY OF MOTION. 
 
 (41) The difference in these two cases depends 
 on the different degrees of freedom of motion. 
 In the first case, whilst walking across the mov- 
 ing carriage, the mass of the body had momen- 
 tum in the direction of motion of the carriage, 
 and kinetic energy in a transverse direction; 
 whereas in the second case the body had not 
 only kinetic energy transverse, but also kinetic 
 energy parallel to the motion of the carriage, 
 and if the mathematicians will compound these 
 two co-ordinates they will find at once that the 
 resultant must be along a curve whose equation 
 may be expressed thus: 
 
 . 
 
 when x and y are the co-ordinates of the body, 
 and x\ and ji the semi amplitudes. 
 
 (42) When we consider the difference between 
 momentum and kinetic energy it will be found 
 that the mathematical proof of the theory is not 
 very difficult, and by adopting a method of 
 physical geometry the proof becomes not only 
 convincing, but absolutely correct and incontro- 
 vertible. 
 
 (43) We prove thus by means of a number of 
 propositions that free motion in free space is elas- 
 
ELASTICITY OF MOTION. 23 
 
 tic, and follows absolutely the laws of elasticity. 
 
 (44) That the same laws which govern the 
 Stellar phenomena control and produce the 
 atomic motions, and regulate their affinities so as 
 to produce molecular cohesion. 
 
 (45) That light, as the earliest and least 
 material energy in the universe, is due to the 
 vibratory action of the spirit of power, or accord- 
 ing to science it is due to the elastic vibration of 
 radiating atoms, or lines of force in a non- mater- 
 ial field of force. 
 
 (46) That heat is caused by inter-molecular 
 vibration. 
 
 (47) And electricity is produced by the inter- 
 ference of waves of molecular disruption. 
 
 (48) That the sun's heat is due to incan- 
 descence produced by the inter-molecular vibra- 
 tions of the superimposed kinetic energies, due to 
 the sun's straight and rotary motions, and that 
 fact can be proven by the new law with the help 
 of Joule's equivalent. 
 
24 ELASTICITY OF MOTION. 
 
 (49) It can also be proven by this theory that 
 the continuous horizontal velocity of a free body 
 in a vacuum near the earth's surface at 1,036 feet 
 per second will prevent that mass from falling to 
 the 'earth; or, in other words, that the kinetic 
 stability of a body moving with independent 
 kinetic energy transverse to the force of gravity 
 may tend to overcome gravity to such an extent 
 that the body may move in a circle concentric to 
 that of the earth's circumference. 
 
 (50) These, and a number of other facts 
 regarding the motions of the solar system, 
 especially the specific energy inherent in the 
 mass of each planet, and their respective indue-' 
 tive capacities, both for light, heat and electri- 
 city; also an explanation of the cause of the 
 tides according to the new theory, will be 
 given more fully in the book I am about to pub- 
 lish on the subject. 
 
 (51) In conclusion I feel bound to support the 
 prophetic saying of that great seer the Abbe 
 Moigno, who in the Cosmos of 1852 declares: 
 
 "That if there is anything certain in this 
 "world it is that the molecules of bodies and 
 " bodies themselves are not really self attractive; 
 " it is that attraction is not an intrinsic but only 
 
ELASTICITY OF MOTION. 25 
 
 "a developed force; it is that notwithstanding 
 "everything occurs as though bodies mutually 
 "attracted each other; it is incontestably true 
 "that bodies do not attract. Newton, as Euler, 
 " as every philosopher worthy of the name, has 
 "seen in Nature but two things, inertia and 
 4 ' motion, originally impressed by a free will, the 
 "the first and infinite mover. And it is with 
 "these two great facts of inertia and movement 
 " that advancing science shall ultimately explain 
 " all the phenomena of the physical world." 
 
THE NEW KINETIC THEORY OF 
 GRAVITATION. 
 
 [A paper read before the Technical Society of the Pacific Coast.] 
 PART I. 
 
 The old established theory of centripetal force 
 is that given by Sir Isaac Newton nearly three 
 centuries ago, in the memorable words of the 
 ' ' Principia " : ' ' That every particle of matter in 
 the universe attracts every other particle," and 
 that every deviation from a straight line in 
 absolute free motion is due to that fact of mutual 
 attraction. 
 
 That is the force which bends the body's 
 motion and keeps it revolving in an orbit. 
 
 Newton himself in the "Principia " compares it 
 to the string of a sling which keeps the stone 
 from flying away from the centre. 
 
 Whilst experimenting with bodies at high 
 velocities, I found that it was not necessary to 
 have a solid centre of attraction to produce this 
 centripetal force. I found that bodies in motion 
 are apparantly attracted to imaginary points, 
 lines and planes, where no attractive force can 
 possibly exist; and during the last fifteen years 
 have given this fact some study in my spare 
 
THEORY OF GRAVITATION. 27 
 
 hours, and have discovered what I think is the 
 true cause of this centripetal force, and am now 
 prepared to put it forward in a definite form for 
 the acceptance of science. 
 
 I am fully aware that deep rooted and estab- 
 lished ideas are difficult to remove in the scien- 
 tific, as well as in the religious world. 
 
 We all know how long it took the scientific 
 world to comprehend the idea that it was the 
 weight of the air which forced the water to rise 
 in a vacuum, the " Fuga Vacui " having been 
 the accepted cause for thousands of years. 
 
 We also know how successfully the great 
 mathematician Ptolemy held the scientific world 
 in mental bondage by his beautiful theory of the 
 earth as the centre, round which the whole 
 heavens revolved every twenty-four hours. 
 
 Now I find that the illustrious Newton has 
 fallen into a similar delusion, by means of the 
 analogy of the* sling and stone he failed to 
 comprehend the possibility of constrained motion 
 in an orbit without a pull towards the centre or 
 the focus of the orbit. At first sight it would 
 appear to an observer that there must be a pull 
 to divert a moving body from the line of its 
 motion, indeed the first and second laws of 
 motion in dynamics clearly show that there must 
 be such a force. And Newton was quite justified 
 
28 THEORY OF GRAVITATION. 
 
 in calling it a centripetal force. I accept his- 
 definition of a centripetal force, and I accept his 
 law of the inverse square of the distance, as a 
 true but empirical law of force, but I disagree 
 with his theory that this centripetal force is in its- 
 nature or action " attractive." 
 
 This false theory of attraction has done much 
 to obstruct the progress of physical science; to it 
 is due the fact that mathematical analysis is 
 almost powerless in dealing with high speed 
 machines, and fluid motion at high velocities, and 
 that all the formulae in the molecular constitution, 
 of bodies and chemical physics, as well as the 
 motions of the heavenly bodies, are nearly all 
 empirical. The new theory, which I call the 
 Theory of the Persistence of Energy, will when 
 properly understood open up to mathematics a 
 right of way by which all these branches of 
 science will be fully explored. 
 
 As this paper is only intended to be pre- 
 liminary, and to give just sufficient information 
 as to lead to the discussion of the subject, I will 
 confine myself to the first principles of the sub- 
 ject where they diverge from the established 
 theory of attraction, and leave the application of 
 the theory until we have satisfied ourselves that 
 the theory itself is correct. 
 
 As you may be aware I have already delivered 
 
THEORY OF GRAVITATION. 29 
 
 -a lecture at the Academy of Sciences, on the 
 historical portion of the theory of gravitation, 
 and there discussed the Newtonian theory of 
 attraction; quoting Newton's own words to show 
 that he never believed in the innate and inherent 
 force of attraction in matter, but he always 
 Tioped to be able to prove that attraction was 
 caused by the motion of an 'aetherial medium. 
 All the great natural philosophers since his day 
 have worked at that problem, either to prove 
 that apparent attraction was due to the vibrations 
 of an aetherial medium, or to the vortices of 
 radiant atoms. 
 
 Faraday came nearest to an acceptable proof 
 when he discovered that magnetic attraction was 
 due to the inductive action of a field of force, 
 which surrounds the poles of the magnet. 
 
 Now, you see the question of the attraction of 
 matter is by no means a settled question, al- 
 though the editor of our only scientific paper, 
 in discussing my lecture before the Academy of 
 Sciences, thought I was trying to destroy a law 
 of nature; and consequently made some silly 
 remarks about me, which in the daily press 
 would have been very amusing, but from a scien- 
 tific journal and the only scientific journal of the 
 Pacific Coast, makes one wish for a scientific 
 journal which understands science. 
 
 or TH 
 
 
 UHI78ESITY 
 
30 THEORY OF GRAVITATION. 
 
 Now I defy any scientist of standing to contra- 
 dict me in the assertion that science has never 
 definitely adopted action at a distance ( as 
 attraction is called) as a scientific truth. It has 
 been accepted as a scientific dogma awaiting the 
 true solution of the cause of attraction, hence it 
 is quite legitimate on the part of any scientist to- 
 try to solve the problem, and he who can dis- 
 cover the true cause of gravity has no need 
 to be ashamed of his discovery. 
 
 It is only a few months ago since the greatest 
 of all the great natural philosophers of this age, 
 Lord Kelvin, stated to an admiring audience of 
 scientists in London, that this great problem had 
 for fifty years been constantly in his mind, 
 sleeping and waking it was always there, and 
 yet we are told by our only scientific press that 
 any professor who would spend his time in 
 trying to discover the cause of gravity had most 
 assuredly mistaken his profession. Well gentle- 
 men, I hope before we are through with the 
 discussion of this subject there will be no doubt 
 in your minds as to which has mistaken his- 
 profession, the editor of the scientific press, or 
 your humble servant. 
 
 In my lecture before the Academy, I gave six 
 illustrations of motion, which in each case 
 showed the impossibility of mutual attraction 
 
THEORY OF GRAVITATION. 31 
 
 between matter, but I will in this paper confine 
 myself to one crucial test of the attraction of the 
 earth to matter on or near its surface; a test 
 which this Society can make at very little 
 expense. 
 
 We all know that the law of the attraction of 
 matter is that the force of attraction varies 
 directty as the product of the two attracting 
 masses, and inversely as the square of the dis- 
 tance from their respective centers of gravity, and 
 that the force is constant and produces uniform 
 acceleration in both bodies toward each other. 
 
 Now according to that law a projectile moving 
 at right angles to the direction of the attractive 
 force will be constantly accelerated towards the 
 centre of the earth, and in consequence will 
 describe a parabola in its motion. 
 
 Whatever its horizontal velocity may be it will 
 always fall sixteen feet in the first second, conse- 
 quently it requires a velocity of nearly 25,000 
 feet per second to describe a concentric curve, to 
 the earth's surface. But I find that if I make a 
 catapult projectile travel fifty feet in half a 
 second, the projectile instead of falling four feet 
 in that time, as it should do if it was subject to 
 the force of attraction, it only falls a very little 
 over eighteen inches. Now this is a crucial test 
 of attraction. 
 
32 THEORY OF GRAVITATION. 
 
 If there is such a thing as attraction in matter, 
 no horizontal velocity less than 25,000 feet per 
 second will prevent the projectile from falling to 
 the earth. Now according to my discovery, and 
 the law of kinetic stability, a horizontal velocity 
 of 1,036 feet per second kept constant will enable 
 any weight of projectile from falling to the earth, 
 and I will explain to you how kinetic stability 
 produces that effect. 
 
 First then we know that any mass m with 
 velocity v in a straight line uninfluenced by 
 any other motion, having perfect freedom, has 
 
 as its kinetic energy. It must have had that 
 2 
 
 amount of work expended on it to give it the 
 velocity v, and it is capable of doing that amount 
 of work before it is brought to rest. 
 
 If instead of a mass whose inertia is propor- 
 tional to m we have a weight w on the surface of 
 the earth whose acquired acceleration in one 
 second in falling towards the center of the earth 
 is g = 32.2. Then if E^ = kinetic energy 
 
 That we all know; there is no difference 
 
 o 
 
 in our opinion on that point. 
 
 But I have discovered that the mass m or 
 weight w has not only kinetic energy in the line 
 of its motion but it acquires kinetic stability 
 transverse to the line of its motion, and that its 
 
THEORY OF GRAVITATION. 33 
 
 kinetic stability always varies in the same ratio 
 as its kinetic energy varies. Now that fact is 
 not known, nor yet accepted, in the science of 
 mechanics or dynamics, and on this fact depends, 
 as I will show you, the whole theory of gravita- 
 tion and the true cause of what has been hitherto 
 considered as due to the mutual attraction of 
 matter. I am sure every one of you in your 
 experience must have noticed that the greater 
 the velocity given to a body it became more diffi- 
 cult to deflect it, and if sufficient force was not 
 exerted it would tend to oscillate, or appear to be 
 attracted to the line it was previously moving in. 
 You have all noticed how a spinning top recesses 
 when it is displaced a little, and how a gyroscope 
 vibrates across the line of its motion; how a 
 bicycle keeps erect in motion, and requires con- 
 siderable force to make it oscillate, but which 
 when at rest has to be supported from falling. 
 
 Those of you who have seen the water issuing 
 from a monitor with a 500-foot head would see 
 the difference in stability from the same water 
 under a 50-foot head. On this principle depends 
 the ejector and injector, and various other me- 
 chanical inventions whose mathematical theory, 
 for want of this simple law of kinetic stability, is 
 as intricate as the trigonometrical epicycles of 
 Ptolemy when he proved that the sun went 
 
34 THKORY OF GRAVITATION. 
 
 round the earth, to the satisfaction of himself and 
 all the scientific papers of the world for 1,400 
 years; and when Copernicus thought the same 
 thing would happen if the earth simply turned 
 on its axis, he was thought an eccentric old fool 
 to try and alter the laws of Nature which God 
 had established from all eternity. 
 
 They even went so far as to say that he might 
 as well try to prove that two and two make nine 
 as to prove that the earth turned on its axis. It 
 was a terrible idea to the multitude to think that 
 the earth turned on its axis, and the comical 
 illustrations of that period are as amusing almost 
 as what appeared the other day in the San Fran- 
 cisco papers about Prof. Stevenson, who did 
 not believe that one piece of matter attracted 
 another. Well let it pass, we are content to be 
 like Copernicus, persecuted for the sake of 
 scientific truth, knowing full well that the laugh 
 will turn some day. 
 
 Now if a body has kinetic stability equal to 
 its kinetic energy, it will vary as the square of the 
 velocity of the body, and in different bodies as 
 their masses, and that is the new law of kinetic 
 stability for a body moving in a straight line. 
 
 Now we will consider the motion of a body in 
 an orbit, which is a circle. If a body moving in 
 a straight line has kinetic stability equal to its 
 
THEORY OF GRAVITATION. 35 
 
 kinetic energy, then so long as the body moves in 
 that line its kinetic stability is latent, and on this 
 fact we can explain many of the latent energies 
 amongst molecules, such as the latent heat of 
 steam, and by a true understanding of this fact 
 we can find out how to convert all their latent 
 energies into kinetic or work-producing energies, 
 which will be one of the earliest outcomes of 
 the application of this discovery to mechanical 
 and economical inventions. 
 
 Now let us investigate circular motion, where 
 the kinetic stability has been all transformed into 
 potential energy, and we will find that the 
 kinetic stability is now active as Newton's centri- 
 petal force, the centripetal force is there, but it 
 resides entirely in the moving body, not in the 
 center to which it tends, as we will prove when 
 we have circular motion without any mass in the 
 center to attract the body, and we believe there 
 are planetary systems in the universe which have 
 no sun in the center of the orbits, and what we 
 call twinkling stars are sunless systems whose 
 planets are themselves suns revolving round a 
 sunless centre, the possibility of which we will 
 prove to you later on. 
 
 We know that the centrifugal tendency of a 
 body constrained to move in a circle is expressed 
 
 for the same body in different circles as 
 
36 THEORY OF GRAVITATION. 
 
 where r is the radius of the circle, and v the 
 linear velocity in the orbit. Now if we simplify 
 the problem by taking a circle of radius 1 we 
 have the centrifugal force proportional to m v 2 , 
 that is, the stress on the cord fixed at the centre 
 to retain the body in the circumference of the 
 circle; now the actual stress due to the body is 
 
 772- 1) 
 
 one half of that, viz: because the other half 
 
 2i 
 
 of the stress is re- action on the fixture at the cen- 
 tre, which we can prove by replacing the fixture 
 by another string of equal length fastened to 
 another body of equal mass, moving with equal 
 velocity in the same. circle. The stress is now the 
 same, although there are two bodies instead of 
 one, but the centrifugal force for both is m v 2 , 
 
 therefore for the one it must be - - - and this is 
 
 another fact from which many mechanical inven- 
 tions will follow. 
 
 Now the centrifugal tendency due to the circu- 
 lar motion of the body is proportional to 
 and if the radius of the circle is unity it is pro- 
 portional to ^~ Now the kinetic energy of 
 
 the body moving in the circle at right angles to 
 the centripetal force, which counteracts the cen- 
 trifugal, is also 'hence the centrifugal force 
 
THEORY OF GRAVITATION. 37 
 
 is equal to the kinetic energy, and the kinetic 
 stability is equal to the kinetic energy, therefore 
 the kinetic stability is equal to the centripetal 
 force, and as we have shown that a body in free 
 motion has only got kinetic energy and kinetic 
 stability, therefore kinetic stability must be the 
 same as the centripetal force, or force of attraction. 
 
 Now 7 we will prove that circular motion does 
 not require any string to hold the body in the 
 curve, and such being the case there can be no 
 attractive force. 
 
 It is almost an impossibility to make a practi- 
 cal experiment in free space to show the effects of 
 kinetic stability, because of the great velocity 
 required to overcome gravity, so that before a 
 body can be said to be moving with perfect 
 freedom on this earth it must have an indepen- 
 dent velocity of at least 1,036 feet per second. 
 
 I suggested the following experiment to Lord 
 Kelvin last summer: To get Sir Edwin Wat- 
 kin's permission to use the 1,200-foot tower now 
 being built near London, have an iron tube about 
 four feet diameter in the centre of the tower, so 
 that it could be exhausted of air, have partitions 
 of steel paper every ten feet, let them be in an 
 electric circuit, so that a record would be made 
 of the instant a bolt fell through each, and the 
 distance from the centre. 
 
38 THEORY OF GRAVITATION. 
 
 Drop a soft iron bolt from the top of the tower; 
 have an electro-magnet placed 200 feet from the 
 top of the tower, of sufficient capacity to deflect 
 the bolt in its passage about one half inch; now 
 if such a bolt had a uniform velocity, and be 
 deflected by an impulse it would in its further 
 passage continue to oscillate across the original 
 line of its motion, due to its kinetic stability, or 
 the persistence of energy. Such an experiment 
 would prove the elasticity of motion, and, as 
 Lord Kelvin says, if proven would be the fulfill- 
 ment of the golden dream of science. 
 
 Now this law of kinetic stability shows that 
 motion is elastic, because if it requires a force 
 greater than the body's kinetic energy to perma- 
 nently deflect a body, then if the force applied be 
 less than the kinetic energy the difference 
 between that and the kinetic energy is a force of 
 restitution, which is the same as the force of 
 gravity, and follows the same law, being 
 inversely proportional to the square of the dis- 
 tance between the centre to which the body tends 
 and the centre of the body itself, and it is that 
 unearned increment of the body's kinetic stability, 
 which we call the force of restitution, or in the 
 case of the planets the force of gravity, and that 
 force varies in all conic curves inversely as the 
 square of the radius vector. Of course in the 
 
THEORY OF GRAVITATION. 39 
 
 case of the circle under uniform velocity there is 
 said to be no force, or rather the centripetal force 
 is balanced by the centrifugal force, but in an 
 ellipse where the radius vector joining the focus 
 towards which the force of restitution tends and 
 the body, the force of restitution is inversely pro- 
 portional to the square of the radius vector. 
 
 I have gone over all Newton's propositions 
 respecting this force in the " Principia," and this 
 force of attraction in every case is the same as 
 the force of restitution, and his calling it an 
 attractive force is simply a case of mistaken 
 identity, in fact a delusion similar in every way 
 to the Ptolemaic delusion. The centripetal force 
 appears as if it was an attractive force, but is in 
 reality only a force of restitution. 
 
 Energy in its most general sense is purely a 
 mode of motion, there must be resistance coupled 
 with velocity, and if m = the resistance, then 
 m v 1 = E = energy, or vis viva, but m may be 
 taken as small as you please, so long as it is not 
 nothing, and v may be taken as great as you 
 
 please so long as it is not infinite. 
 
 m v* . 
 
 Kinetic energy _= E = ~^ is the kinetic en- 
 ergy due to direct force, and is a measure of the 
 work done on a body in motion. 
 
 Potential energy = = E P = the capacity of a 
 body to do work. 
 
40 THKORY OF GRAVITATION. 
 
 Kinetic stability = E s = ^~ is the resistance 
 
 offered by a body moving with independent mo- 
 tion to change of direction, and is always recipro- 
 cally proportional to the potential energy. 
 
 Kinetic stability is a kind of latent energy. 
 
 Force =f= m a, is the imaginary agent by 
 which power communicates an action against a 
 resistance, and it may truly be called the spirit of 
 power. An effective force is an unbalanced effort. 
 
 We divide forces into two general classes and 
 several specific varieties. 
 
 First. Conservative Forces are those which 
 increase both the kinetic stability and kinetic 
 energy at the same time, and in the. same pro- 
 portion. 
 
 Second. Radical Forces are those which in- 
 crease the potential energy at the expense of 
 the kinetic stability. 
 
 Specific kinds. First class centripetal force = 
 /cp is generally the tendency of a body in motion 
 to return to the original line of its motion if dis- 
 turbed by a force less than the kinetic stability of 
 the body. 
 
 Second class centrifugal force = f c ? is the 
 tendency of a body to move from the centre, 
 being a component to the tangential motion of a 
 body moving in an orbit. 
 
THEORY OF GRAVITATION. 41 
 
 Force of Restitution /r is the excess of the con- 
 servative forces over the radical forces, and it is 
 equal to the unearned increment of the kinetic sta- 
 bility, and is the same as Newton's force of 
 attraction. 
 
 PROPOSITION I. 
 
 Every body which has independent motion has 
 kinetic energy equal to the work done by a con- 
 servative force in the direction of its motion = 
 
 m = the specific resistance of the body to 
 change of motion, and v the velocity generated 
 by the action of a conservative force in time t. 
 Then the action of a uniform force starting from 
 
 no velocity to v velocity is equal to - 
 
 2i 
 
 Now R s = work done, where R is uniform 
 resistance and s = distance. Now R s =fv t = 
 m z; 2 , and the mean work when /starts from O is 
 m v 1 , 
 ~2~ 
 
 PROPOSITION II. 
 
 Every body which has kinetic energy has also 
 kinetic stability, and its kinetic stability increases 
 with its kinetic energy. 
 
 Let a body moving with kinetic energy 
 
42 
 
 THEORY OF GRAVITATION. 
 
 be disturbed transversely in its course, and we 
 know that the force necessar} 7 is directly propor- 
 tional to the square of the velocity, and inversely 
 as the radius, now if the mass m and the radius 
 r be constant the force varies as the square of the 
 velocity. 
 
 Now we know that the kinetic energy varies as 
 the square of the velocity, hence the kinetic sta- 
 bility increases in the same ratio as the kinetic 
 
 energy, from m to 
 
 m v 
 2 
 
 it i 
 
THEORY OF GRAVITATION. 43 
 
 PROPOSITION III. 
 
 The kinetic stability is equal to the kinetic 
 -energy. 
 
 Let us take the body m moving with velocity v 
 in the straight line A B. Hang another body 
 mi = to m from a point O by an inextensible 
 cord, so that the body m\ will be at rest in the 
 straight line A B, and m will impinge and give 
 up all its energy to m l . See Fig. 2. 
 
 Now mi by means of the cord and fixture at o 
 will be constrained to move in the circumference 
 of a circle of which the cord is the radius, and 
 with the same velocity in the curve that it had in 
 the straight line, which proves that it has the 
 same kinetic energy as formerly. 
 
 But we also become cognizant of another stress 
 or energy, or capacity to do work along the cord, 
 which we can measure by a spring balance 
 inserted in place of the cord and fixed to O, and 
 the measure of that stress as shown by the 
 
 balance is m\ v\ and in different circles is - 
 
 But the actual stress due to m\ = ~ , that is 
 
 2i 
 
 easily proven by using another mass #z 2 = to mi 
 caused to revolve by an extension of the cord, 
 forming a diameter to the circle. There will 
 then be a balanced stress on the fixture, and the 
 
44 THEORY OF GRAVITATION. 
 
 stress on the extended cord will be m v*,. 
 although two equal masses m\ and m<y are mov- 
 ing in the circumference with equal velocities, 
 
 and with a kinetic energy in each equal to * 
 
 2i 
 
 yet the stress on the cord does not alter from 
 m v\ although the masses and the kinetic 
 energies have been doubled, which proves that the 
 transverse stress due to the kinetic energy of m 
 
 2 m\i? 
 is not m\ v , but -' 
 
 Now the mass m\ in describing the complete 
 circle impinges on m, and gives up all its energy 
 to it, that is, supposing the bodies are perfectly 
 elastic and under frictionless conditions. Now m 
 continues with its original velocity in A B, but 
 where is the transverse stress which was shown 
 on the cord whilst describing the circle? We 
 know it is not in m\ , which is perfectly dead, and 
 as no energy can ever be destroyed completely, it 
 must be in some way attendant to m in its 
 motion, and we can prove that it accompanies m 
 as a latent energy capable of being made poten- 
 tial by means of a radical force, and such quality 
 of motion we call the body's kinetic stability, 
 and we have shown that it is equal to the 
 
 , . .. m v 2 
 
 kinetic energy = ' 
 
THEORY OF GRAVITATION. 45 
 
 PROPOSITION IV. 
 
 If a body in motion in a straight line be dis- 
 turbed by a force transverse to the line of its 
 motion, and the amount of that force measured 
 by the energy it produces is less than the kinetic 
 stability of the body, then the body will be acted 
 on by a force tending to make it return to its 
 original line of motion, and such a force I call 
 the force of restitution, and its value is equal to 
 the difference between the kinetic stability and 
 the amount of the disturbing force, that is, 
 
 /r =/g = s /d = E* /d = P 
 
 On the proof of this proposition rests the most 
 wonderful property of energy, the elasticity of 
 motion, the golden dream of all philosophy. 
 The corner-stone of the most enduring edifice 
 which science can ever build, whose foundations 
 were laid in the beginning of time, and on whose 
 glorious turrets rests the spiritual emancipation 
 of the human soul. 
 
 In my next paper I will prove the above pro- 
 position, and show its application to mechanical 
 invention. We will now conclude by stating the 
 Law of Kinetic Stability. 
 
 A body moving in free space with independent 
 motion has kinetic energy in the line of its motion, 
 and kinetic stability tending to prevent displace- 
 ment transverse to its line of motion equal to its 
 
46 THEORY OF GRAVITATION. 
 
 kinetic energy, and should a radical transverse- 
 force be applied equal to the kinetic stability, the 
 body will then move in a curvilinear orbit with a 
 velocity equal to j/~2 X v, v being its original' 
 velocity, and according as the transverse radical 
 force is greater or less than the kinetic stability, so 
 the curve will be one of less or greater stability, and 
 the force of restitution will be less or greater. 
 
 And the Law of the Persistence of Energy: 
 
 Every body moving with independent free motion 
 in a straight line has a specific tendency to continue 
 in that line, varying with and always equal to its 
 kinetic energy, and if displaced in free space by a 
 transverse force there will always be an unbalanced 
 component force in the body' s motion tending to 
 bring the body back to the continued line of its 
 previous motion. 
 
 The unbalanced component is what Newton 
 ascribed to the mutual attraction of matter, but 
 which we now know is due to the Persistence of 
 Energy, and we call it the Force of Restitution. 
 That is the universal force of gravitation; it is 
 always inversely proportional to the potential 
 energy. 
 
 Now as the potential energy of a displaced 
 force varies with the square of the displacement, 
 therefore the Force of Restitution, due to the 
 persistence of energy, will vary inversely as the 
 
THEORY OF GRAVITATION. 47 
 
 square of the distance or displacement. That is 
 the geometrical law, and is true for kinematical 
 motion, but the great kinetic law depends on 
 kinetic and centrifugal energies. 
 
 THE KINETIC THEORY OF GRAVITATION. 
 
 PART II. 
 
 In my former paper on ' 'A New Theory of the 
 Cause of the Centripetal Force," which Newton 
 and his followers have ascribed to the mutual 
 attraction of masses, I mentioned the fact that the 
 kinetic stability of a body which has independent 
 motion in a plane normal to the centripetal force 
 of gravity, would tend to neutralize the apparent 
 effect of that force, and that in a succeeding 
 paper I would show how that result was pro- 
 duced. 
 
 In the discussion on the paper it was suggested 
 by some members that the question was of suffi- 
 cient importance to be submitted to the profes- 
 sional scientists at Berkeley, and Palo Alto. 
 
 Professor Soule of Berkeley endorsed my 
 statement that the experiment of the catapult 
 
48 THEORY OF GRAVITATION. 
 
 properly carried out would be a crucial test. 
 But he said in effect, that the force of the mutual 
 attraction of masses had been a settled doctrine 
 in science so long, and seemed to satisfy every 
 requirement, that he would not be prepared to 
 doubt its existence, until after a most exhaustive 
 proof that it was due to something else. 
 
 Exception w r as also taken by some to the loose 
 way in which I had put the argument, and to 
 the want of details in the catapult experiment. 
 
 The experiment was one of many which I 
 made fifteen years ago, when I first doubted the 
 theory of attraction, but as these experiments 
 were not carried out in a vacuum I did not 
 consider them sufficiently exact to be called 
 scientific experiments, but only approximations, 
 and although they were sufficiently approximate 
 to show me that a body in motion in a plane at 
 right angles to the force of gravity did not fall 
 with the same centripetal acceleration that the 
 same body would do if at rest, yet they were not 
 crucial enough to place before the Royal Society 
 of lyondon. 
 
 In reading up the subject in tracts, published 
 by the late Dr. Hutton of Woolwich Academy, 
 England, on the experiments in gunnery, I found 
 that that eminent mathematician had noticed 
 the same discrepancy between the fall of bodies 
 
THEORY OF GRAVITATION. 49 
 
 due to attraction, and the practice with projectiles 
 at high velocities, which he ascribed to some 
 polarized condition of the air. (The word pol- 
 arized, at that time was a fashionable fad with 
 scientists for explaining away any discrepancy 
 to an established theory, having been brought 
 into prominence by the researches of Dr. Thomas 
 Young and Dr. Brewster in connection with light. ) 
 
 Nearly every scientist since, who has noted 
 the discrepancy, has tried to explain it, by 
 supposing the projectile to kind of hypnotize the 
 layers of air immediately above and below it, so 
 as to prevent it from following the law of falling 
 bodies whilst in motion. 
 
 Instead of accepting that explanation, I always 
 felt sure there was some other cause at work, 
 and the result of my studies and experiments 
 have led to the discovery of the true cause, viz: 
 that the persistence of energy, and the accompany- 
 ing kinetic stability, when subjected to lateral 
 forces, is the true cause of gravity. 
 
 When I mentioned the matter to my old 
 professor, Lord Kelvin, he thought kinetic sta- 
 bility was too intricate a mathematical function, 
 to use in explaining such a simple matter, and 
 to approach the subject mathematically from that 
 hypothesis would exhaust the methods of the 
 analytical calculus. 
 
50 THEORY OF GRAVITATION. 
 
 Consequently in these papers I prefer to go 
 back to first principles, which even the under- 
 graduate can understand and follow, and so build 
 up my theory on the very simplest application of 
 the laws of motion. 
 
 In the discussion, I was pleased to know that 
 Mr. Richards, a past president of the Society 
 had given the weight of his large experience in 
 favor of the theory of kinetic stability as a 
 probable cause of centripetal force, in preference 
 to Newton's theory of attraction. 
 
 He finds in his practice many actions and 
 reactions in high speed centrifugal water pumps, 
 for which empirical formulae have to be substi- 
 tuted for theory, for the simple reason that the 
 present theory of deviating forces does not meet 
 the requirements of the case. 
 
 Now as it seems to be the almost general wish 
 of those members who have considered the 
 matter, to have my theory submitted to one or 
 both of the principal universities in this State, I 
 will therefore devote this paper to a description 
 of the experiments, which, if carried out with 
 scientific accuracy, will prove that my theory is 
 the true one. 
 
 I need riot call attention to the important 
 results to science, which would follow from the 
 acceptance of the theory of kinetic stability as the 
 
THEORY OF GRAVITATION. 51 
 
 true proximate cause of the centripetal force of 
 attraction throughout the universe. 
 
 The past, present and future conditions of each 
 planet, not only physically, but vitally, together 
 with all the actions and reactions between them 
 and their primary, would be calculable from 
 their motions alone. 
 
 Whether they were hollow or solid spheroids; 
 the specific heat of the mass of each; the 
 extent and density of their atmospheres; the 
 specific force of gravity on their surface; the 
 character and bodily structure of their inhabi- 
 tants; would all become mathematical problems, 
 depending for their solution on the ratio of the 
 centripetal to the centrifugal energies of each 
 planet. 
 
 Then when we carry the question of kinetic 
 stability into molecular physics, it opens up to 
 exact science problems which, when solved, will 
 revolutionize all our ideas of matter, soul and 
 spirit, and show us how to produce and control 
 the vast latent forces of nature, with greater 
 efficiency than we have hitherto dreamt of. 
 
 If these are not a sufficient encitement to a 
 proper determination of this scientific subject, 
 then the love of truth itself, which is strong in 
 every true scientist, should be motive sufficient 
 for the purpose. 
 
52 THEORY OF GRAVITATION. 
 
 L,et us now consider proposition IV. 
 
 If a body in motion in a straight line, having 
 
 kinetic energy = - ' be disturbed by a force 
 
 acting transversely to the line of its motion; if 
 the disturbing force be any finite force whatever, 
 the disturbed body will describe a curve as the 
 resultant motion, being acted on by two effective 
 components, the one towards the instantaneous 
 centre of curvature, we call \\ieforce of restitution 
 or centripetal force; the other acting normally to 
 the centripetal force, we call the tangential f 01 ce. 
 
 This proposition has never been accepted 
 hitherto by dynamical science, nor to my know- 
 ledge has it ever been completely demonstrated. 
 
 If the simple action of two impressed forces 
 acting at right angles, will cause a body to 
 describe a curve as the resultant motion, then 
 where is the need for the mutual attraction of 
 masses to cause curvature? 
 
 I need not refer to the established principle in 
 dynamical science, called the resolution of forces 
 or motions, which proves that the resultant of 
 two forces or motions, is the diagonal of the 
 parallelogram whose adjacent sides represent the 
 forces or motions in amount and direction. 
 
 That I acknowledge as a cardinal principle of 
 the science of dynamics, but it only applies to 
 
THEORY OF GRAVITATION. 53 
 
 cases of constrained motion, and I am dealing 
 with independent motion in free space. 
 
 To illustrate my meaning; suppose a ball be 
 rolled across the platform of a car in motion, 
 then the resultant motion, both in direction and 
 amount, would be expressed by the length and 
 direction of the diagonal of the parallelogram, 
 whose adjacent sides represented the direction 
 and amount of the respective motions. 
 
 But suppose we give the ball a certain finite 
 velocity along the car, independent of the car's 
 motion, and also give it a transverse velocity 
 across the car, then although the diagonal of the 
 parallelogram as above would give the velocity 
 due to the constrained motion or momentum, yet 
 the resultant of the independent motion would be 
 a curve. 
 
 I can demonstrate that fact with mathematical 
 accuracy, and can show the value of the coordi- 
 nates of the curve under various forces, and one 
 remarkable result of the geometry of the subject 
 is, that however small the kinetic energy of the 
 body may be, so long as it is Jinite; and however 
 great the transverse deviating force may be, if it 
 is not infinite, the body can never be permanently 
 displaced from the original line of motion, but 
 will always have a component force acting as 
 Newton's centripetal force apparently towards a 
 focus. 
 
54 THEORY OP GRAVITATION. 
 
 And that is a most wonderful fact which 
 explains the constitution of the universe as a 
 stable or conservative system, which no radical 
 force less than that of Omnipotence can ever 
 destroy. 
 
 And it also teaches us another most wonderful 
 principle in the constitution of the universe, viz: 
 that the forces necessary to give it stability, must 
 have been controlled and directed by some power 
 independent of and unaffected by the phenomena 
 produced. 
 
 That in fact the Creator of the physical 
 universe, must have done work to produce the 
 phenomena which we call the universe. It is 
 that principle of independent action, which act- 
 ing against kinetic stability makes stable motion. 
 
 Again let me explain my meaning. If a body 
 like a railway train, or a cannon ball, be con- 
 strained to move in a curve, by means of a fric- 
 tionless guide, then no additional energy has been 
 communicated from without, but simply the 
 resistance of a frictionless guide; hence no energy 
 has been added or extracted from the moving 
 body. The orbit has been described by means 
 of the inherent energy, or vis viva of the body, 
 and the result is that the moment the guide is 
 removed, be it a string fixed at a centre, or an 
 attractive force from a centre, or a rigid friction- 
 
THEORY OF GRAVITATION. 55 
 
 less guide, then the moment that it is removed 
 the body goes off on a tangent to the curve it has 
 been constrained to move in. 
 
 But suppose the cannon ball receive an impulse 
 from an independent outside force, acting trans- 
 versely to the line of motion of the cannon ball, 
 equal to twice the kinetic energy of the ball, 
 then the ball will forever move in an orbit which 
 is curvilinear, and if the deviating force exceed 
 twice the kinetic energy, the ball will move in 
 an orbit which is an ellipse of any eccentricity 
 whose centripetal force will vary inversely as the 
 square of the distance from one of the foci, and 
 the resultant motion is perfectly stable, the same 
 as the universe, or the solar system. 
 
 As the mathematical proof of this proposition 
 is purely theoretical, I will not complicate this 
 paper by introducing it here, but will proceed to 
 sketch out a method of experimental demon- 
 stration, which will establish the fact that curvi- 
 linear motion is the true resultant in all free 
 independent motions. 
 
 EXPERIMENT I. 
 
 Take a slab of polished marble or glass, or any 
 other polished surface, perfectly horizontal, or 
 level in every direction on the surface, about 
 fifty feet long, and ten feet broad. At one end 
 fix a catapult arrangement, which will project 
 
 UHI7BRSIT7 
 
56 THEORY OF GRAVITATION. 
 
 a spherical steel ball (of the size of a billiard 
 ball), along the top of this slab in a straight line 
 longitudinally with a velocity of one hundred 
 feet per second. 
 
 About one foot from the initial point of motion 
 of the longitudinal catapult, place a transverse 
 catapult, having its initial point of motion one 
 foot from the line of the other. Let both cata- 
 pults be capable of giving the same velocity to 
 the same ized balls of steel. Let the springs of 
 both catapults be held back by the one string, 
 the centre of which is placed between the carbon 
 points of an electric machine, which by burning 
 the string allowed both catapults to act instanta- 
 neously. Then, if proper precautions are taken, 
 the transverse ball will strike the longitudinal 
 ball one foot from its initial point, with the same 
 kinetic energy as the longitudinal ball has. 
 
 The resultant motion of the longitudinal ball 
 will be curvilinear, and whatever energy the 
 transverse ball loses, the other will receive, less 
 the friction of course and the viscosity of the 
 balls, and the various energies of heat, light and 
 electricity, dissipated by the concussion. The 
 curve can be shown by having a black slab and 
 a whitened ball. 
 
 By careful experiment in a vacuum, with 
 various degrees of energy, the coordinates of 
 various curves can by this means be almost 
 exactly determined, and so one of the most 
 important principles in the whole realm of dyna- 
 mical science can be demonstrated by experi- 
 ment. And I have no hesitation in saying, that 
 the professor, and the university, which demon- 
 strates the truth of this principle most correctly, 
 will earn for themselves a name and a fame, 
 which will be esteemed and honored whilst the 
 world lasts. 
 
THEORY OF GRAVITATION. 57 
 
 To such an institution the ambitious youths 
 from every nation will come for instruction, 
 because the establishment of this principle of 
 kinetic stability, is one of more far reaching 
 importance to science in general, than we can 
 imagine at present, as not only physical phe- 
 nomena, but vital and spiritual phenomena all 
 depend on it largely for true scientific treatment. 
 In this great principle resides the hidden power 
 which through the method of evolution does its 
 work. And on this latent energy depends the 
 influence which enables faith to control the 
 phenomena of the spiritual world. 
 
 The theoretical proof will be given by me in 
 another paper, as soon as the experimental proof 
 is ready for publication; to show what is the 
 difference between theory and experiment. A 
 knowledge of the theory tends to make the 
 experimenter imaginative, and unreliable in the 
 statement of results, hence the theoretical demon- 
 stration will be witheld for the present. 
 
 The second problem is to prove experimentally, 
 that a body near the surface of the earth moving 
 horizontally with kinetic energy, will not be 
 influenced by the force of gravity with the same 
 acceleration towards the centre of the earth, as 
 if the same body had been at rest relative to the 
 earth. Or in other words, a horizontal projectile 
 
58 THEORY OF GRAVITATION. 
 
 moving one hundred feet in one second, will not 
 fall sixteen feet during that second. 
 
 To prove this by experiment exactly, and find 
 the law of its acceleration under various horizon- 
 tal velocities, requires a very complete and 
 elaborate apparatus, such as only a university 
 can provide, but this would be a crucial test of 
 the two theories: 
 
 Kinetic stability versus attraction of matter, and 
 as I know that kinetic stability is the true one, 
 and is bound in the near future to work a great 
 revolution in all science, it is well worthy the 
 earnest attention of all teachers of science, and 
 those who wished to be honored as the leaders of 
 the scientific world, will do well to look to their 
 laurels. 
 
 Here is a simple experiment, .which if carried 
 out carefully in a vacuum will upset the best- 
 established theory in all the domain of natural 
 science, which will cause half of the scientific 
 books in the world to be re- written. 
 
 Can we rest satisfied, and continue to teach fal- 
 lacies to the world, and dignify them with the 
 name of science, when such a simple experiment 
 will forever correct and remove this error? 
 
 Although this proposition can also be demon- 
 strated with mathematical accuracy by using the 
 principle of kinetic stability, yet the three laws 
 
THEORY OF GRAVITATION. 59 
 
 of motion will not enable us to demonstrate it, 
 hence it is necessary that an experiment of a 
 crucial character should establish the fact before 
 the scientific world will believe in it. 
 
 Now the question is, to which university shall 
 the honor belong in having with the strictest 
 scientific accuracy demonstrated to the world this 
 important fact; viz: that a body moving horizon- 
 tally with independent motion will not fall six- 
 teen feet in one second, the distance it would fall 
 if at rest? 
 
 Although I would prefer to leave to the experi- 
 menter the choice of methods to determine the 
 truth, yet there are certain precautions to be 
 taken which it may be well for me to mention. 
 
 1st. The experiment must be carried out in a 
 vacuum, as explanations have already been 
 attempted, to prove that the air carries the body, 
 and vSO prevents the fall. 
 
 2nd. The velocity should exceed fifty feet per 
 second. 
 
 3rd. The apparatus should be as rigid and 
 unaffected by vibration as possible. 
 
 4th. The air-exhausted tube or case should be 
 at least fifty feet long with a properly -stretched 
 diaphragm mounted on a square frame placed at 
 distances apart of one foot; two transverse lines 
 cutting each other at the center of the dia- 
 
60 THEORY OF GRAVITATION. 
 
 phragm, as impressions or water marks in the 
 diaphragms should be ranged exactly by means 
 ot a transit instrument, the diaphragms should 
 be white and the projectile blackened. 
 
 5th. The vacuous box should have one side 
 removable with great ease to enable the trajec- 
 tory to be exactly measured. 
 
 6th. The time should be if possible one 
 second. 
 
 As the value of this experiment to mechanical 
 and astronomical science cannot be overestimated, 
 it behooves the experimenter to use the greatest 
 care in devising and describing each and every 
 detail. 
 
 As aerial locomotion is bound to depend very 
 largely on the fact that a body in motion does 
 not fall the prescribed sixteen feet in a second, it 
 can easily be seen of what immense importance 
 the knowledge of this fact will be to the mechani- 
 cal and political world. 
 
 Important as that fact is to mechanics, it is no 
 less so to astronomy, as the law of attraction 
 depends at present on the multiplication of 
 masses. If 10 units of mass be multiplied by 20 
 units of mass the resultant attraction is at 
 present equal to 200 units of mass, but we know 
 that the quantity of matter contained in two 
 bodies, one of which contains 10 unks of matter, 
 
THEORY OF GRAVITATION. 61 
 
 and the other 20 units of matter, can never be 
 more than 30 units of matter. 
 
 Now although the law of the inverse square of 
 the distance enables astronomers to make close 
 approximation in the motions of the planets, the 
 law of the multiplication of the masses enables 
 them to make ignorant guesses at the specific 
 gravity of each planet, and the specific heat 
 which the mass contains, and by this means the 
 world is kept in complete ignorance of the con- 
 ditions of the inhabitants in the other planets. 
 
 Now when we look at this subject from every 
 possible point, it behooves us as a Society, either 
 to act alone, or in conjunction with the Astronom- 
 ical Society, and use all the influence possible to 
 have this matter correctly determined by one or 
 both of our great universities. 
 
 It behooves us also to act promptly, as the 
 matter will be taken up by other institutions in 
 the Eastern States, who, from the many let- 
 ters I receive, seem to be acting in earnest, and 
 appear to take more interest in the subject than 
 the scientists of this Coast. 
 
 That California should have the high honor of 
 demonstrating to the world the principles of 
 kinetic stability, and proving that the force of 
 the mutual attraction of masses is simply a fal- 
 lacy and a delusion, is the most sincere wish of 
 a humble member of the Technical Society. 
 
 gsSS. 
 
 or THB 
 
 'innVBKSITT 
 
UNIVEESITY OF CALIFORNIA LIBRARY 
 BERKELEY 
 
 THIS BOOK IS DUE ON THE LAST DATE 
 STAMPED BELOW 
 
 Books not returned on time are subject to a fine of 
 50c per volume after the third day overdue, increasing 
 to $1.00 per volume after the sixth day. Books not in 
 demand may be renewed if application is made before 
 expiration of loan period. 
 
 SEP 19 19! 
 
 
YC 1523 
 
 
 UNIVERSITY OF CALIFORNIA LIBRARY