J. Alan Murray 105 



where F and R are respectively the percentages of fat and refuse in the 

 empty weight M and in the live weight M' respectively and ///. is the 

 fat-free empty weight. 



It will be seen, on reference to the table, that the percentage of 

 water in the non-fatty matter diminishes progressively as age (weight) 

 increases, and the percentages of ash and protein are correspondingly 

 increased. There appears to be no consistent relationship between the 

 ratio of protein to ash and the age of the animal ; the variation observed 

 must therefore be ascribed to individuality, i.e. to unknown causes. The 

 mean value of the ratio PjA is 4-392 ± 0-215*. In other words, protein 

 forms from 79 per cent, to 84 per cent, of the dry substance of the 

 non-fatty matter and ash the remaining 16 per cent, to 21 per cent. 

 The mean percentages of these ingredients may therefore be found by 

 the formulae 



P = U-815 (lOU - W); A = 0-185 (100 - W) 



where P, A and W are the percentages of protein, ash and water respec- 

 tively in the non-fatty matter. 



It only remains therefore to find an expression for determination of w. 

 It is obvious that the relationship of water to weight is not one of simple 

 proportion; but when the points are plotted out a definite order can be 

 clearly discerned. The smooth curve in the diagram (Fig. 1 ) corresponds 

 to the formula w = 90Hr '"''*"'', where m is the fat-free body weight (lb.) 

 and w is the percentage of water in the same. The points corresponding 

 to the mean vahies of the observed data are indicated by ^- and it will 

 be seen that the curve passes through or near to most of them. The 



mean deviation, jr, S (d), (of all the individual cases) from the curve is 



0-71. 



In order to test these conclusions the composition of the three cattle 

 analysed by Lawes and Gilbert was calculated from the live weight 

 and percentage of fat and the results are given for comparison with the 

 observed data in the table below. 



The discrepancies between the observed and calculated results do 

 not exceed the limits of individual variation in Haecker's data. In the 

 case of the two oxen they are attributable mainly to deviation from the 

 mean ratio of protein to ash. In the case of the calf they are attributable 

 mainly to deviation from the curve of relationship of water to weight. 



s/y- 



((/-) = 0-319. 



