170 THE MECHANISM OF LIFE 



time, t, at which the crest is at a certain position, and then an 

 " interval " of time, dt, after which the crest has attained a new 

 position, dx. But at the moment t the water level was at the 

 position y, and after the interval dt it has dropped to the new 

 level dy. We call the d?s " intervals," but it must be noted that 

 they are " infinitesimal " intervals that is, they may be smaller 

 than any finite lapse of time, no matter how short the latter 

 may be. 



Clearly, then, our differential equation simply gives us a 

 series of connected displacements. As time changes that is, 

 as some standardised mechanism, such as the hands of a clock, 

 are displaced by so much so the crest of the wave is displaced 

 so much in a horizontal direction, and the water level is displaced 

 so much in a vertical direction. Now all this is not at all irre- 

 levant to the work of this chapter, for our differential equation 

 is a perfect example of a scientific " law." 



Science measures motions, or, rather, displacements, and its 

 residts must be expressed in measures of space. 



Next we turn to the study of organic functioning, and we may 

 choose for an example any bodily activity whatever; in the 

 meantime our treatment of the animal is entirely " objective " 

 that is, we are regarding it as a system in the physico-chemical 

 sense, something outside ourselves that we can observe and 

 measure just as we can an ocean wave. We might take the 

 action of the heart, or the interchange of oxygen and carbonic 

 acid between the atmosphere and the bloodvessels of the lungs, 

 or the excretion of urea it does not matter. In all these cases 

 we investigate and express our results as motions, or, more 

 precisely, as measured displacements of something. When we 

 study the circulation we measure the velocity of the blood- 

 stream (that is, the displacement of a blood-corpuscle in an 

 unit interval of time), or the pressure of the blood in an artery 

 (that is, we record the displacement of mercury in a pressure 

 gauge connected with the bloodvessel), and so on. When we 

 investigate respiration we may measure the tension of oxygen 

 in the blood and compare it with the partial pressure of the gas 

 in the air (that is, we observe and measure the volume of a 

 gaseous residue after certain manipulations). When we study 

 the formation and distribution of urea in the blood and kidneys 

 we make quantitative chemical analyses, and in so doing measure 

 the masses of certain substances at certain times and places, and 



