Jitnc 14, 1877] 



NA TURE 



123 



Yet in the definition of the equality of two lapses of time there 

 is a logical fault. It is not allowed implicitly to introduce in a 

 definition what is to be defined. There is no body of which we 

 know i; priori that no force tries to alter its velocitv ; in order to 

 ascertain this, we must find out in consistency with the usual 

 definition of force, given in § 217, whether it moves through 

 equal spaces in equal times. 



The definition of § 246, therefore, really says : The times, in 

 which a body that goes through equal spaces in equal times 

 moves through equal spaces are equal. It is evident that we 

 are reasoning in a circle. 



I am very well aware of the objection which will be made. 

 We have it in § 245 : " Auch werden wir spater sehen, dass ein 

 voUkommen glatter spharischer Korper, welcher aus concen- 

 trischen Schalen bestch', deren jede von gleichformiger Material 

 und iiberall von derselben Dichtigkeit ist, sich, wenn man ihn in 

 eine Drehung um eine Axe versetzt hat, trotz hinzutretender ein- 

 wirkender Krafte mit gleichformiger Winkelijeschwindigkeit 

 dreht, und seine Rotationsaxe in einer absolut festen Richtung 

 erhallt." Thereupon it is said in § 247 that the earth is a body 

 which fulfils these conditions very nearly, and that therefore its 

 rotation gives us the means to measure time. But this assertion 

 is not at all proved. 



I now' lequest my readers to be so good as to follow the ex- 

 position of 7}iy view. I assume that we are able to decide 

 whether two lapses of time are equal. How this is done I shall 

 dwell on afterwards. 



When the conception of time is combined with the conception 

 of motion we arrive at the building up of kinematics, in which 

 the ideas of velocity and of acceleration are introduced. In 

 abstract dynamics the idea of force is firU introduced, wholly 

 separated from any definite physical sense. As soon as the state 

 of motion of a body (which is determined by the magnitude and 

 the direction of its velocity) undergoes a change, we think of a 

 cause of this change, and call this cause a force. We ascribe to 

 a force magnitude and direction. If a body, which primarily is 

 in rest, acquire a rectilinear motion, the force has constant direc- 

 tion. The magnitude of a force of constant direction is judged 

 by the increase of velocity, which it gives in a definite time to a 

 body primardy in rest. If the increases of velocity in equal 

 times be equal, the force has constant magnitude. Two forces 

 of constant direction and magnitude are in the same proportion 

 as the increases of velocity which they give in equal times to the 

 same body. Unity of force is the force which in unity of time 

 gives to a particular body unity of increase of velocity. 



It is conceivable that equal forces acting on different bodies 

 cause different accelerations. Therefore another idea is intro- 

 duced — the idea of mass. It is settled by definition that the 

 masses of two bodies are in inverse proportion to the accelera- 

 tions which they receive from equal forces. To a particular body 

 unity of mass is ascribed. Unity of force is the force giving 

 to unity of mass unity of acceleration. 



I need not dwell on other ideas which are introduced, e.g., 

 moment, work, energy, &c. The whole building can be con- 

 structed, and there is room for every investigation which belongs 

 to so-called theoretical mechanics. So it is demonstrated that a 

 centrobaric body, which has kinetical symmetry in respect to its 

 centre of gravity, and which has been brought in rotation about 

 an axis going through the centre of gravity, retains constant 

 angular velocity, when no forces are acting on the surface, and 

 on the component parts only central forces which are in the same 

 proportion as the masses of the parts. 



Before kinematics and abstract dynamics can be applied in 

 interpreting phenomena, we must be enabled to measure time. 



What is time? TLere are mental conceptions which cannot be 

 described by words, and I reckon "time" amongst them. But 

 I shall try to answer the question how the conception of time 

 originates with us. 



The lormation of the conception of "time" is preceded by 

 the formation of the idea of "lapse of time." The idea of 

 " lapse of time " we arrive at by the simultaneous observation of 

 two phenomena, in conjunction with the observation of two phe- 

 nomena not occurring simultaneously, in such a manner that we 

 receive the impression of the second phenomenon when the im- 

 pression of the first one is not yet effaced from our memory. 



A lapse of time, from the nature of the idea, is limited. If 

 we abstract the dtfinite limits, we have the conception of time. 



It is clear that in speaking of the measuring of lime we 

 properly mean the measuring of lapses of time. 



In order to measure lapses of time we must know when a 

 lapse of time is twice as long as another. We easily come to 



this on its having been established which lapses of time are 

 equal. 



If we wish to compare the length of two bodies we place the 

 one beside the other, or if circumstances prevent us from doing 

 so, we successively place a third object beside each of them. 



For the comparison > f two lapses of time we lack such means 

 and have to follow another way. 



In nature ptenomena present themselves that persistently 

 return. Nor^o we simply settle by definition that the lapses of time 

 betivecn the first occurrence of a particular phenomenon and the 

 second is equal to that bet'ceen the second and third occurrence. 

 Which phenomenon is to be chosen ? Flu.x and rellux? Earth- 

 quakes? For the application of kinematics and abstract dy- 

 namics in interpreting phenomena, the choice is no indifferent 

 matter. 



I confine myself to the phenomenon which is s>ill the usual 

 base of the measurement of time. It is settled by definition that 

 the lapses of time between the successive culminations of a 

 definite fixed star in a definite place are equal. To divide these 

 lapses of time themselves into equal parts, it is settled that the 

 apparent motion of the fixed star, and therefore of all fixed stars, 

 is uniform. 



The results arrived at in the attempts at interpreting pheno- 

 mena show that a very good hit has been made. But it is not 

 impossible that after greater development of science we may have 

 to make the measurement of time independent of the rotation of 

 the earth. The application of abstract dynamics to the theory 

 of the motion of the earth round the sun and of the mi'on round 

 the earth has furnished admirable results. But in comparing the 

 results of calculation with the accounts of eclipses found in 

 ancient chronicles, a difference is met with, and in the opinion 

 of some it is too considerable to be accounted for by the imper- 

 fection which may adhere to ancient descriptions. Therefore 

 the theory of the motion of the earth and of the moon is incom- 

 plete. But hitherto no omission can be poin'ed out. For this 

 reason some men of science are inclined to settle by definition that 

 the theory of the motion of the earth and of the mo.m is com- 

 plete, and to make it]thc base of the me.isurement of time. Then, 

 of course, the former definition must be abandoned, and two 

 arbitrary intervals between successive culminations of a fixed 

 star no longer are equal. 



Prof. Clerk Maxwell says (" Theory of Heat," second edition, 

 p. 81) : " This shows that time, though we conceive it merely 

 as the succession of our states of consciousness, is capable of 

 measurement, independently, not only of our mental states, but 

 of any particular phenomenon whatever." In my opinion this 

 assertion is erroneous. If we reject the rotation of the earth as 

 the base of the measurement of time, we must have recourse to 

 the motion of the earth round the sun or to that of the moon 

 round the earth, or to any other phenomenon. Thomson and 

 Tail, in § 406, already allude to a metal spring oscillating in 

 vacuo. It should then be settled by definition, for example, that 

 such a spring has a harmonical motion. If we proclaimed the 

 lapses of time between the successive arrivals of flux and reflux 

 at a particular station to be equal, and if we admitted, in order 

 to divide these lapses of time into equal parts, e.g., that the 

 water sinks and rises uniformly, then the whole ofi kinematics and 

 abstract dynamics would retain the same form ; even then a cen- 

 trobaric body with kinetical symmetry in respect to its centre of 

 gravity, would show the peculiarity already mentioned. But it 

 would be seen that our kinematics and abstract dynamics were 

 but a highly deficient aid for the interpretation of phenomena ; 

 and the earth would not at all be a body with the same motion 

 round its axis, as if it were a centrobiric body with kinetical 

 symmetry in respect to its centre of gravity. 



Of course it is wise to maintain provisionally the definition by 

 which the earth in equal times rotates through equal angles. 



In applying abstract dynamics to the interpretation of pheno- 

 mena, we are led to identify the idea of mass with the idea of 

 quantity of matter, and this has furnished excellently satisfying 

 results. From tills, in conjunction with experiment, it follows 

 that two bodies which have equal weight, possess equal quantities 

 of matter ; that no matter is annihilated or created, &c. 



This article is already too long for me to dwell on other con- 

 sequences which follow from my view. Only a few words on 

 the conservation of energy. This law threatens to be considered 

 an axiom. Vet I believe it desirable that we should always re- 

 member that it is the result of experiment. If the measuring of 

 time were founded on a different basis, it would not hold. Still 

 the experiments do not give perfectly satisfying results. Usually 

 this is ascribed to the imperfection of our methods and instru- 



