126 



L. J. RiCHELLE, C. OnKELINX, J. "P. AuBERT 



Though we did not measure the total mass of calcium in our experimental animals, 

 it is possible to evaluate it, by calculating a cumulative calcium balance, between 30 

 and 120 days. This gives a function of time, which is expressed in Eq. 4: 



MUt): 



2292 



1+22.1 e-0.05W 



(4) 



where Mqh , the cumulative calcium balance, is expressed in mg, and t, the age of the 

 rat in days. This expression has been derived by the iterative procedure used for the 

 other M{t) functions, but in the absence of variances of the mean cumulated values, 

 selection was made on the basis of minimal deviation of the experimental points from 

 the regression line, and of the t test of Student. 



Table 1. Numerical values for the parameters of Eq. 1 

 1 + ae-^A^max. < 



M{ty. 



' The sample "diaphysis" and "epiphysi 

 bones (upper and lower legs). 



- In our experimental conditions (; 



refers respectively to the diaphysis and epiphy 

 8; r,^50), the value of F for ;; < 0.C5 is 2.13. 



of the long 



The comparison of the values for a and k Afmax. in Eq. 3 and Eq. 4 with those 

 reported in Table 1 for the calcium in the diaphysis shows that in the three cases, 

 they are of the same order of magnitude. Therefore, it is permissible to consider that, 

 for our purposes, the diaphysis is a representative sample of the skeleton. 



2. Function N{t) 



In order to obtain the function N{t), that is the evolution of the total number of 

 elementary volumes with the age of the animal, one has to transform the functions 

 M{t), expressed in units of mass into functions expressed in number of elementary 

 volumes. 



This transformation is possible if at a given time, one knows the mean specific 

 gravity and the mean calcium content per unit of bone mass. From the series of N{t\) 

 values thus obtained, Eq. 5 has been derived in a way similar to that used for Eq. 1 : 



7V(0 = 



5202 



(5) 



l+14.6e-0.048< 



where, N{t), the total number of elementary volumes present is expressed in number 

 of mm^, and t in days. 



By derivation, one obtains the rate of growth of the population, given by 



dN 

 dt 



.0.926X10--'7V(5202-/V) 



(6) 



