682 SCIENCE AND HYPOTHESIS 



of mechanics with which Kirchoff is identified, he opposes a school 

 which is quaintly called the " Thread School." 



This school tries to reduce everything to the consideration of 

 certain material systems of negligible mass, regarded in a state of 

 tension and capable of transmitting considerable effort to distant 

 bodies systems of which the ideal type is the fine string, wire, or 

 thread. A thread which transmits any force is slightly lengthened in 

 the direction of that force ; the direction of' the thread tells us the 

 direction of the force, and the magnitude of the force is measured by 

 the lengthening of the thread. 



We may imagine such an experiment as the following : A body A 

 is attached to a thread; at the other extremity of the thread acts a 

 force which is made to vary until the length of the thread is increased 

 by a, and the acceleration of the body A is recorded. A is then de- 

 tached, and a body B is attached to the same thread, and the same 

 or another force is made to act until the increment of length again is a, 

 and the acceleration of B is noted. The experiment is then renewed 

 with both A and B until the increment of length is (3. The four ac- 

 celerations observed should be proportional. Here we have an ex- 

 perimental verification of the law of acceleration enunciated above. 

 Again, we may consider a body under the action of several threads in 

 equal tension, and by experiment we determine the direction of those 

 threads when the body is in equilibrium. This is an experimental 

 verification of the law of the composition of forces. But, as a matter 

 of fact, what have we done ? We have defined the force acting on the 

 string by the deformation of the thread, Avhich is reasonable enough; 

 we have then assumed that if a body is attached to this thread, the 

 effort which is transmitted to it by the thread is equal to the action 

 exercised by the body on the thread ; in fact, we have used the principle 

 of action and reaction by considering it, not as an experimental 

 truth, but as the very definition of force. This definition is quite as 

 conventional as that of Kirchoff, but it is much less general. 



All the forces are not transmitted by the thread (and to compare 

 them they would all have to be transmitted by identical threads). If 

 we even admitted that the earth is attached to the sun by an invisible 

 thread, at any rate it will be agreed that we have no means of mea- 

 suring the increment of the thread. Nine times out of ten, in con- 

 sequence, our definition will be in default; no sense of any kind can 

 be attached to it, and we must fall back on that of Kirchoff. Why 

 then go on in this roundabout way? You admit a certain definition 

 of force which has a meaning only in certain particular cases. In 

 those cases you verify by experiment that it leads to the law of accel- 

 eration. On the strength of these experiments you then take the law 

 of acceleration as a definition of force in all the other cases. 



Would it not be simpler to consider the law of acceleration as a 



