34 THE PHILOSOPHY OF BIOLOGY 



taneity in these two trains of events, and this enables 

 us to assign a certain period of astronomical time to 

 the operation of raising the temperature of the water, 

 in the conditions of the experiment, from 17 C. to 

 100 C. But there is nothing absolute in this interval 

 of astronomical time : what is absolute is that certain 

 successions of events always correspond with other 

 successions of events. A certain number of swings of 

 a seconds-pendulum always corresponds with a certain 

 rise in temperature of a definite mass of water which 

 is in thermal contact with an indefinitely large reservoir 

 of heat at a certain temperature, and, no matter how 

 often we repeat this experience, the same simultaneity 

 is always to be observed. Thus what the physicist 

 considers is not intervals of his own duration but series 

 of correspondences that is, correspondences of certain 

 standard events with the events which he is studying. 

 In reality time, in the sense of the astronomer's 

 time, does not enter into the methods of the mathema- 

 tical physicist. Let us suppose that he is investigating 

 the change that occurs in a material system between 

 the two moments of time ^ and 2 2 , these moments 

 being separated from each other by a period of duration 

 that we can feel. Let the system be, say, the earth 

 and moon ; the first body being supposed to be 

 motionless, and the second being supposed to have 

 a certain tangential velocity of movement. If the 

 interval t { to t. 2 is really an interval of astronomical 

 time, the problem, what is the difference of position 

 of the moon owing to the gravitation of the earth, is 

 incapable of solution, and even if we reduce the interval 

 of time indefinitely while still supposing that it is a 

 finite interval, the mathematical difficulty remains. 

 We then replace the finite interval ^ to t a by the 

 differential dt, which means that the two phases of 



