PROTEIN REQUIREMENTS OF CATTLE: MITCHELL 13 



surements secured that bear no definite biological significance. When such 

 measurements are plotted upon coordinate paper it is impossible to con- 

 nect them by a curved line of any simple description, even over narrow 

 ranges of time. The description by a mathematical equation of a series 

 of actual obser\'ations upon the time changes occurring in growing 

 animals is thus not a simple process. A choice must be made of the 

 mathematical function that will be used, based upon what is known of 

 the laws of growth, or upon what function has been used with most suc- 

 cess with similar sets of observations. The constants in the mathematical 

 function chosen must then be determined from the observational data 

 by some method designed to secure a satisfactory fit, so that the curve 

 representing the final equation will pass through the plotted data in the 

 most satisfactory manner. If the data are sufficiently extensive and 

 their interpretation sufficiently exacting, certain criteria of the goodness 

 of fit, based upon the theory of probability, may finally be applied. 



The mathematical equation thus obtained from the observed data 

 expresses in the most satisfactory manner the time changes that would 

 have been observed under ideal conditions. It may therefore be used as 

 a satisfactory substitute for the mass of data from which it was derived, 

 in the same way, and for precisely the same reason, as an arithmetic 

 mean (average) may be used to represent a mass of data clustering 

 about a point rather than a curve. 



The advantages of reducing a series of disconnected observations relat- 

 ing to growth to a continuous mathematical function more than compen- 

 sate for the trouble involved. From such a function the most probable 

 value of the variable measurement, whatever it may be, may be computed 

 for any instant of time. The rate of change at any instant of time and the 

 change in the measurement during any definite interval of time may also 

 be readily computed. The original mass of data cannot, by any other 

 method, be made to yield satisfactory information of this nature. Hence, 

 for the most productive study of growth the application of mathematical 

 methods is essential. 



The differentiation of growth and fattening. — The problem of the food 

 requirements for the growth of animals relates to the change with time in 

 the amount of nutrients contained in their bodies. However, with 

 animals that fatten readily during the growing period, the difl^erentia- 

 tion of growth from fattening is difficult if not impossible except on the 

 quite arbitrary assumption that growth relates to the deposition of 

 protein and the other constituents of protoplasm, but that fattening 

 relates solely to the filling of the adipose tissue cells with inert fat. Yet 

 an animal normally will always fatten to some extent during growth. In 

 fact, it appears probable that growth without simultaneous deposition of 



