igJi 



NA TURE 



[December 27, 1894 



external ; but this does not justify the analysis of their results 

 into two parts. 



Nor does the matter become plainer to me when I follow Mr. 

 Poulion in his applic.ilion of his definition to concrete cases. 

 The 6r5t is the case of the so-called " Exercierknochen," a re- 

 action on an external force resulting in a certain number of 

 change* of tissue. How is it possible to classify those changes 

 into two categories — the one including changes directly due to 

 the external force, the other changesnot directly due to it? If 

 the stress is to be laid on the word "direct," then one must 

 respectfully ask what is its meaning ? how is it to be ascertained 

 and verified ? one must Inquire whether what is said to be 

 an indirect result, means anything but a result which is trans- 

 mitted? in which case we should find ourselves in a vicious 

 circle. I will not follow Mr. Poulton through the other in- 

 slancrs, but I believe the reader will find, like me, that each 

 raises similar difficulties, and that in no case does he analyse the 

 actual result into two distinct and separable parts. 



Mr. Cilton proposes, and Prof. Ray Lankester adopts another 

 definiti'n, v'iz. " Characters are said to be acquired when they 

 are regularly found in those individuals only who have been 

 subjected to certain special and abnormal conditions." Now I 

 suppose that characters can be found regularly only either (l) in 

 individuals exposed to conditions which induce them, or (2) in 

 individuals who have inherited them. To say, then, of a 

 characier that it appears only regularly in individuals exposed 

 10 certain conditions, is to say that it does not appear in indi- 

 viduals by inheritance, and the proposition that acquired 

 characters are not transmissible is thus reduced to an identical 

 one. The possibility ol inheritance is excluded by the defini- 

 tion, and the inquiry whether acquired characters are inherited 

 i< impossible. 



I do not propose to follow your learned correspondents into 

 many of the subjects touched on by them ; but the more their 

 letters are read, the more apparent does it become that they 

 are not at one, either with themselves or with Lamarck or Weis- 

 mann, as to the use of the words " acquired characters ; ' and for 

 myself, I repeat my regret that an inquiry of great moment should 

 he obscured, as I venture to think, tiy a premature use ofclassi- 

 ficalory words before the real classification of nature herself has 

 been ascertained. For the question, " Are acquired characters 

 transmissible?" I hope to see substituted the inquiry " What 

 characters are transmitted? " Ei)\v. Fry. 



The alleged Absoluteness of Motions of Rotation. 



All motion is relalive. This apparently universal state- 

 ment is a particular siatement about ihc meanings of words. The 

 word "motion" means "relative motion," or, more precisely, 

 "the motion of a body" means iis motion relalive to other 

 bodies. We may go further and make the still more funda- 

 mental statement that all position is relative^ or, in other words, 

 the position of a body means its position relative to olher bodies. 

 It is easy for anyone who puts words together without reflect- 

 ing sufficiently on their meaning to put together the noun 

 "motion" or "position" and the adjective "absolute," but 

 the expressions " absolute motion " and " absolute position " 

 are neverlhcless meaningless, just as much so as "white black- 

 ness," " retrograde progress," " the Action between a rough 

 body and a smooth body at their point of contact," or "the 

 potential energy of non-conservative forces." 



The above remarks contain the .standpoint from which it is 

 concluded that motions of rotation are no more " absolute " 

 than motions of translation. Anyone who accepts them for 

 translation, but rejects Ihem for roialion, places himself in an 

 illogical position. Unless I have misunderstood them, this is 

 the posiMon "cciipied by Maxwell and Prof. Greenhill. The 

 slandp<in> ofih.-e » ho assert thai position and motion are in 



all case.' reli' ' 1 to that of Newton, lie 



held thaf th*f ' 1 immovable space, and rcla- 



live poiition v,v., , . , .ind correspondingly ih' re 



are absolu'r and rela ive motions; that absolute motion of a 

 body is its traruference from one absolute place to another absn- 

 lute place ; that we can never determine the absolute place o' a 

 body, l)Ui only iis relalive place ; that in c.Tses of rotation we can 

 dislingui'-h aluolulc from relative motion by the cffeds of 

 "centiilu^;al force." Me gives no indication how to distingiii h 

 absolute and relative motion* of trnnslati<in. From the im|>o«- 

 aibilily of determining ihe ahsidute position o( a body it seems 

 to follow that absolute mutiin of translation cannot be deter- 

 mined ; this view is adopted by Maxwell. 



NO. 131 3. VOL. 5 I ] 



Assuming that it is the object of the Science of Mechanics to 

 give as simple a description as possible of the observed facts 

 about the motions of bodies, the assumption at Ihe outset of 

 absolute motions or positions about which we can know nothing 

 appears an unnecessary complication. 



From a logical point of view the cardinal statement in the 

 discussion is that all position is relative. It appears to be con- 

 ceded by Newton, and has been insisted upon by Maxwell, that 

 all knowable position is relative. To say that at any instant a 

 body has an alisolute position in space, but that we can never 

 know where it is except by reference to other bodies, that 

 is to say that every body has an absolute position, although we 

 can only know its relative position, is to introduce an unneces- 

 sary complic.Tlion, if it is not to talk nonsense. 



What is done in practice is to determine the position of a 

 point by reference to a Cartesian system of axes, or by an 

 equivalent method. What is called " the velocity of a body" 

 is its velocity relative to the axes : what is called " the acceler- 

 ation o( a body" is its acceleration relative to the axes ; a body 

 has a motion of rotation when the angles between lines of the 

 body and any axis are changing with the time. It is part of the 

 solution of a mechanical problem, as presented by any set of 

 observed facts, to determine the system of axes with reference 

 to which the description of the observed motion becomes as 

 simple as possible, and there exists a calculus for transforming 

 the expression of a motion from one system of axes to another 

 when the relalive motion of the two systems is known. 



The question how Ihe axes are to be determined has beei» 

 much discussed, but no general answer appears possible. Par- 

 ticular answers apply in particular cases. In general any three 

 points, not in a straight line, determine a set of coordinate 

 axes. For one of the points may be chosen as origin, the line 

 joining this point to another of the points may he chosen as one 

 coordinate axis, and the plane of the three points may bechisei> 

 as one coordinate plane. For the three points any identifiable 

 parts of bodies may he taken ; but, in general, axes so chosen 

 will be inconvenient, or, what comes to the same thing, the 

 description of a motion by reference to them will not be simple. 



The description of motion is generally made in terms of the 

 concept force, that is to say, we stale the acceleration relative 

 to the .axes which a free body placed in a given position relative 

 10 the axes, and moving with a given velocity relative to the 

 axes would have, and the nature of the constr.ainis which give 

 rise to differences of acceleration in a constr.amed and a free 

 body moving through the same position with the same velocity 

 relalive to the axes. In an actual problem the acceleration of a 

 free body whose other circumstances (position and velocity rela- 

 tive to the axes) are known, must be found by experiment. It 

 does not concern the matter now under discussion that among 

 these circumstances posilion is generally predominant over 

 velocity in determining accelerations. What is of more import- 

 ance is the fact that the foi\e acting on a hotly Jepcniis on the 

 system of axes chosen. I'^or the force is a vector quantity whose 

 line of action coincides with the line of the acceleration relative 

 to ihe axes, and whose magnitude is proportional to this 

 .acceleration. This point has been noted by Maxwell. The 

 result that Ihe field of force depends partly on the axes is 

 frequently a guide to the choice of convenient axes of reference, 

 namely, we choose axes with respect to which Ihe expression of 

 the held of force is simple, and it oden happens that in this way 

 all motional forces, other than friclional resistances, can be 

 made to disappear. .'Vn e.asy and striking example of the dif- 

 ferences introduced by changing the axes can be found by con- 

 sidering the motion of two particles which move in one of the 

 planes chosen as coordinate planes with uniform velocities in 

 different lines relative to the coordinate axes. If a nevy set of 

 axes is constructed by taking one of the ))articles as origin, and 

 the line joining the particles as one axis, the .acceleration of Ihe 

 olher panicle relative to the new axes is directed towards the 

 first particle, and varies inversely as Ihe cube of the distance 

 lielwecn the two particles. Another very interesting example 

 IS furnished by Foucault's pendulum, to be discussed presently. 



These remarks will serve as a preparation for the way in which 

 we interpret, in accordance with tl'.e principle of the relativity 

 of motion, ihose experiences which have been held to favour 

 Ihe view thai molions of rotation .admit of absolute determina- 

 lion. The history of the discussion appears to show that little 

 would have been heard of this doctrine apart from Ihe desire lo 

 rxpluin lo a public unused to regard motion as relalive the 

 theory of the rotation of the earth. To one who h.as mastered 



