August 25, 192 1] 



NATURE 



815 



an outward radial pressure, due to kinetic reaction 

 against the normal component of acceleration. It 

 is the necessary correlative of the centripetal force 

 which must be acting on any revolving body. 

 Centrifugal force is not acting on the revolving 

 body, and, strictly speaking, should never be so 

 thought of, or so depicted : it is the pressure or 

 reaction exerted by the body on the groove or rail 

 or aether, or wTiatever it may be that guides and 

 deflects it. 



Part of the mistake, if I may call it so, con- 

 nected with the denial of physical reality to the 

 directly apprehended thing called force, is the iden- 

 tifying of a thing with its measure. Because two 

 things are equivalent it does not follow that they 

 are identical. There is room for both ; and force 

 may be measured statically as well as kinetically. 

 It is only unbalanced force that produces accelera- 

 tion and calls out kinetic reaction. .Acceleration 

 is often prevented by an equal opposite force, but 

 that does not abolish the force. Whether balanced 

 or unbalanced, force is real enough. If Galileo 

 had been put on the rack, the assurance of an In- 

 quisitor that he was only suffering from balanced 

 accelerations would have been no relief. It will 

 be said that force is only one end of a stress, and 

 that attention to the stress is the illuminating 

 thing. That is perfectly true ; but as a fact of 

 experience we came across force before we under- 

 stood about stress, and there are states of stress 

 which we still are not able to understand, because 

 they occur in the aether, and only display them- 

 selves by their " ends " — that is, by the pair of 

 equal opposite forces in which they terminate — 

 called in old phrase " action and reaction." 



The weight of a book, or a stone, or an apple 

 is a force acting on it; this force is due no doubt 

 in the last resort to a stress in the aetheric medium, 

 but we experience it as a force when we resist it 

 muscularly ; and though we may measure it by the 

 mass-acceleration of the body when allowed to 

 drop, it acts equally when the body is resting on 

 a table or hanging from a twig; only then the 

 reasoned and hypothetical aether stress is counter- 

 acted by an obvious stress in the material sup- 

 port. The stress can be measured by resting the 

 body on a spring, or hanging it from a piece of 

 elastic ; and the strain so caused is surely an 

 undoubted reality, about which it would be ex- 

 tremely artificial and confusing to postulate any 

 kind of acceleration. Some day we may be able 

 to dive into deeper constitutional secrets, and 

 explain all stresses and strains kinetically in terms 

 of the gyrostatic rigidity and elasticity of aether ; 

 but that time is not yet. Meanwhile the objects 

 here used in illustration are in static equilibrium, 

 are obeying the first law of motion and moving 

 with uniform velocity, so long as the forces acting 

 on them are equal and opposite and therefore 

 balanced. 



But an unbalanced force can always be equated 

 to the kinetic reaction or mass-acceleration of the 

 body acted on ; and in dynamics unbalanced forces 

 are those which demand attention. All the rest 

 is the statics of strain. D'Alembert's principle 

 NO. 2704, V.OL. 107] 



rather tended to tempt us to contemplate spurious 

 forces, for supposed convenience, so as to reduce 

 kinetics to statics when writing down equations 

 — for there must be equilibrium among the internal 

 forces acting within the confines of any closed 

 system — and a flagrant elementary example of the 

 kind of thing thus led up to was the ordinary text- 

 book treatment of centrifugal force. 



Elementary Repetition. 



If a governor ball or conical pendulum is depicted 

 on paper, the only arrows that ought to be drawn on 

 it are those representing the tension in the string 

 and the weight of the body. But such a diagram 

 looks unfinished ; nothing could rest like that ; the 

 two forces are evidently not in equilibrium ; they 

 clearly have a resultant. The unpardonable, or at 

 least the confusing, thing is for a teacher to draw 

 an arrow indicating a force equal and opposite to 

 that resultant in order to make the diagram look 

 comfortable and static. The fact is that no third 

 force acts on the body ; the body itself reacts, its 

 mass-acceleration is equal to the resultant force ; and 

 that is the proper fact to express in an equation ; 

 you cannot express it in a diagram. The diagram 

 can be completed only by motion, and it ought not 

 to look as if equilibrium were attained by any part 

 of the system. The system as a whole is in equili- 

 brium, or the internal stresses balance, directly the 

 kinetic reaction is taken into account, not otherwise. 

 Centrifugal force, as the term is often employed to 

 signify a force acting on the revolving body, is a 

 fiction. 



Yet centrifugal force is a reality ; it is essential to 

 the equality of action and reaction. There ought to 

 be no objection to the term or idea when properly 

 applied. But it does not act on the revolving body 

 at all. In every instance the real centrifugal force 

 acts, not on the revolving body, but on whatever fixed 

 centre is responsible for holding it in its orbit ; or on 

 the constraint, such as rails or groove or aetherial 

 medium, which is directly effective in guiding and 

 deflecting it. The centrifugal force of the moon acts, 

 not on the moon, but on the earth. It is part of the 

 cause of the tides. No doubt it is primarily exerted 

 on the aetherial medium in contact with each lunar 

 particle, and is thus transmitted to the earth at the 

 other end of the gravitational stress. 



To finish this trivial pedagogic discussion of centri- 

 fugal force in its true, as distinguished from its usual 

 artificial, sense, and the confusion about which body 

 the force really acts on, we may as well point out 

 that the same sort of trifling difficulty — caused by 

 there being always two bodies bounding a stress,* 

 while we are liable to concentrate attention on one — 

 is responsible for that simple old puzzle about the 

 horse and the cart. If the cart pulls back as hard as 

 the horse pulls forward, why does it move? Every 

 good student, sooner or later, asks himself or his 

 teacher this question. The correspondence columns 

 of the Engineer at one time exhibited persistent mis- 

 conception about this elementary matter among quite 

 a large number of readers, and some text-book 

 writers have been bothered by it. The confusion is 

 caused entirely by the tacit assumption that both 

 forces must act on the cart. Not so; one acts on the 

 cart and one on the horse. Two forces and two 

 bodies, one force acting on each. The difficulty dis- 

 appears. The horse must get a grip of the ground 

 to enable him to exert his force on the cart, true ; and 

 the cart exerts its reaction on the horse entirely be- 



' The fact that an advancing wave-front may simulate a body, for this 

 purpose is of high interest. 



