PHASES IN THE LIFE OF THE INDIVIDUAL 703 



nucleus. From this fact Loeb x concludes that the nucleus itself, or 

 one of its constituents, acts as a catalyser in the synthesis of nuclein 

 in the fertilised ovum. Robertson, 2 quoting partly from Loeb, writes 

 as follows : " If the mass of the original fertilisation nucleus be m, 

 the mass of nuclear material increases during the first segmentation 

 period to 2m, during the next to 4wt-, and so on in geometrical 

 progression. The duration of the various periods of segmentation, 

 however, matters very little. Hence in the first unit of time after 

 the beginning of cell division, a mass m of nuclear material is 

 formed, in the second a mass 2m, in the third a mass 4w, and so on ; 

 thus the velocity of the synthesis increases with lapse of time and 

 with the mass of nuclear material already formed. This is a 

 characteristic of that class of reactions known as autocatalytic, in 

 which one of the products of the reaction, or, in this case, one of the 

 constituents of ~ the nucleus, accelerates the reaction. During the 

 process outlined above, an emphatic disproportion between nuclear 

 and protoplasmic material has been established. As the nuclear 

 synthesis becomes slower, however, the disproportion tends to adjust 

 itself until, finally, the growth of the organism consists almost 

 entirely of the growth of protoplasmic material, and in the final 

 re-establishment of the equilibrium between cytoplasm and nuclear 

 material." 



Robertson has investigated mathematically the quantitative 

 relations which exist between the amount of growth and the time 

 of growth. He concludes that there are two or more growth cycles 

 representing autocatalytic processes which make up the total growth 

 of an individual. In man there are three maxima of rate of growth, 

 representing three phases or growth cycles. One of these is intra- 

 uterine, but it is probable that this is not quite complete at birth. 

 The second growth cycle seems to attain its maximum annual 

 increment at about the fifth year, since the increment in weight 

 at that age, as deduced from an investigation on growth in English 

 boys, considerably exceeds the annual increments for the years 

 immediately following. A third maximum in yearly increments 

 occurs in males at about the sixteenth year, that is, at about the time 

 of puberty. In the rat, according to Donaldson, 3 there are two 

 intra-uterine growth cycles, while there is only a single well-defined 

 extra-uterine cycle. Robertson suggests that the first growth cycle 



1 Loeb, " Weitere Beobachtungen iiber den Einfluss der Befruchtuiig, etc.," 

 Bio. Chem. Zeitsch., vol. ii., 1906. "The Chemical Character of the Process of 

 Fertilisation and its Bearing on the Theory of Life Phenomena," Seventh 

 Internat. Congress, Boston, University of California Publications, vol. iii., 1907. 



2 Robertson, loc. cit. 



3 Donaldson, " A Comparison of the White Rat with Man in respect to the 

 Growth of the Entire Body," Boas Anniversary Volume, Anthropological Papers, 

 New York, 1906. 



