THE LAWS OF MOTION 301 



should discover that the number of units of length in 0/ 

 (if this represents the acceleration of A due to B) was 

 always in a constant ratio to the number of units of length 

 in OV (or the acceleration of B due to A). If Q^ were 7 

 units and OV 3 units, then whatever other corpuscles 

 were brought into the field, or however the relative position 

 of A and B might be altered, still Ql and QV, be they 

 both large or both small, would always have the ratio of 

 7 to 3. Now here is the beginning of the answer to our 

 first question, and we may state our immediate conclusion 

 in the following words : — • 



T/ie ratio of the acceleration of A due to B to the ac- 

 celeration of B due to A must always be considered to be the 

 same whatever be the position of A and B, and whatever be 

 the surrounding field. 



The ratio of mutual accelerations is thus seen to depend 

 on the individual pair of dancers, and not on their relative 

 position, or the presence and character of their neighbours. 



But the reader may ask : How can science possibly 

 have drawn such a wide-reaching conclusion as this, since 

 even the most metaphysical of physicists has never caught 

 one corpuscle, let alone two, and could not therefore have 

 experimented upon them in every possible field ? The 

 answer is of the same character as that to the problem of 

 the gravitating particles (p. 281). Physicists have ex- 

 perimented on perceptual bodies in all sorts of fields ; 

 they have electrified, magnetised, warmed, or mechanically 

 united by strings or rods, bodies of finite dimensions ; but, 

 whatever the nature of the field, they have found that the 

 smaller the bodies — the more nearly they approached the 

 conceptual limit of particle, — the more nearly they have 

 been able to describe the sequence of their sense-impressions 

 by aid of conceptual particles obeying the above law. 

 They then postulated the above law as true for particles, 

 and, inverting the process, proceeded by aid of this law to 

 describe the motion of those aggregates of particles which 

 are our symbols for perceptual bodies. The validity of 

 the law was then demonstrated by the power it was found 

 to give us of predicting the future routine of our sense- 



