GROWTH AND SENESCENCE. 1021 



potential immortality. That is, barring accidents, disease, etc., it 

 was capable of reproducing itself indefinitely. He assumes, more- 

 over, that this property is exhibited at present in many of the sim- 

 pler forms of life, such as the ameba. This latter phase of his 

 theory has been the subject of much interesting investigation,* with 

 some contradictory results, but it has been shown (Woodruff) that 

 a specimen of paramecium, isolated and kept in a varying culture- 

 medium during three and a half years, passed through 2000 

 divisions at an average rate of three in every 48 hours, without the 

 appearance of signs of senility. Later experiments by the same 

 author continued over five years indicated that the single cell 

 originally isolated "possessed the potentiality to produce similar 

 cells to the number represented by 2 raised to the 3029th power, or 

 a volume of protoplasm approximately equal to 10 1000 times 

 the volume of the earth." Such a result would indicate the essen- 

 tial correctness of Weissmann's view. One of the most significant 

 and definite contributions to the subject of growth has been made by 

 Rubnerf upon the basis of the energy factor. His estimates were 

 made upon data collected for man and the following mammalia, 

 horse, cow, sheep, pig, dog, cat, rabbit, and guinea-pig and they 

 bring out the surprising fact that human growth constitutes a type 

 of its own, differing greatly from that shown by the other mammals 

 named. His conclusions are expressed in two general laws which are 

 founded upon calculations made upon these animals in the first 

 period after birth during the time necessary for doubling the weight 

 of the animal : First, the law of constant energy consumption. During 

 the first period of growth the total amount of energy necessary 

 for maintenance (metabolism) and growth, as expressed by the 

 heat value of the food consumed, is the same for all mammals 

 except man. To form one kilogram of animal weight requires 

 in round numbers 4808 Calories in food; while for man about six 

 times this amount is needed. Since the several mammals con- 

 sidered require very different times to double their weight, it 

 follows from this law that the shorter the time necessary for this 

 result the more intense will be the metabolism, or, expressed in 

 another way, the rapidity of growth is proportional to the intensity 

 of the metabolic processes. Second, the law of the constant growth 

 quotient. In all the mammals considered, with the exception of 

 man, the same fractional part of the entire food energy is utilized 

 for growth. This fractional portion is designated as the " growth- 

 quotient," and it averages 34 per cent., that is to say, for every 



* See Maupas, "Archives de zoologie experimentale et generale," 6, 165, 

 1888; Gotte, "Ueber den Ursprung des Todes," 1883; Woodruff, "American 

 Naturalist," 42, 500; also "Archiv f. Protistenkunde," 21, 263, 1911. 



t Rubner, "Das Problem der Lebensdauer," etc., Berlin, 1908. - 



