104 TEMPORAL ORGANIZATION IN CELLS 



upon the evaluation of a partial or incomplete Fourier transform, and this does 

 not appear to have been done yet. However, these limits will be adequate for 

 our present purposes. We are particularly interested in the dependence of the 

 mean frequency function on the talandic temperature, because this will give 

 us some insight into the temporal effects produced by changes in 6. If the 

 talandic temperature of cells can be influenced to some extent by experimental 

 procedures, then a degree of control over the temporal organization of the cell 

 should result. In the next chapter we will suggest how experimental modi- 

 fication of may be possible, and our present considerations will then allow us 

 to predict the consequences of such control on the temporal behaviour of cells. 

 Let us begin by observing that the modulus of any variable, z, can be written 

 in the form 



00 



— 00 



We have, therefore, 



00 00 CO 



—Pi -Pi — "» 



Now yi=CiXi, and it is convenient to replace cosyiS by e'^''^ so that the 

 real part of the complex integral must be taken later on. The order of inte- 

 gration in the double integral can be reversed, since the integrals are uniformly 

 convergent. Thus we write the expression in the form 



1 — cos zs . 

 as 



s^ 



1 



77 



00 CO 



-Pi 





-Pi 



Concentrating on the inner integral first we make the transformation t = 

 {^Ci/lY'-Xi so that the integral becomes 



00 



00 



^ , [ /2c,/^)-"'e-'V/ (54) 



-iPciiiy'Pi 

 For very large j3, the integral approximates to a Fourier transform of the 

 function e-'\ and we can use the formula 



J e''"e-'-dt = V(7^)e""'^* 



