Cancer as a Special Case of a General Degenerative Process 351 



plot. On the other hand, the acute causes of death clearly are fitted by the 

 Gompertzian function. 



The presence of the sixth power relationship in a large number of different 

 situations suggests a general underlying principle. Since we have no knowledge 

 whatever of what this principle is in biological terms, we can only speculate 

 that it could be a very general organizational scheme which provides about 

 five redundant elements within each essential unit. An element might be a 

 molecule, a cell or organelle (internal structural and functional unit of a cell), 

 a group of cells, or a whole organ. The essential units might be separate or 

 overlapping. Carcinogenesis may be a special case of this general degenerative 

 process. 



REFERENCES 



1. J. C. Fisher and J. H. Holloman: A hypothesis for the origin of cancer foci. Cancer 4 

 916-918 (1951). 



2. C. O. Nordling: A new theory of the cancer inducing mechanism. Brit. J. Cancer 7, 

 68-72 (1953). 



3. P. Armitage and R. Doll: The age distribution of cancer and a multi-stage theory of 

 carcinogenesis. Brit. J. Cancer 8, 1-12 (1955). 



4. H. B. Jones: A special consideration of the aging process, disease and life expectancy. 

 In: Advances in Biological and Medical Physics 4, 281-337, ed. by J. H. Lawrence and 

 C. A. Tobias, Academic Press, New York (1956). 



DISCUSSION 



Quastler: Two ditTerent functions have been proposed as representative of the course of 

 the Gompertz function, G{t), for the later part of the life span: 



Gi(0 = fli + b^t 



Gi{t) = ^2 + ^2 In /. 



No author claims that either function is a perfect fit even for a limited interval. Still, it is worth 

 showing that the difference between the two formulae is very small over a limited range. Let 

 the center of this range be /*; then 



and for small values of A//r*, 



AGi = ±^1 Ar 



.c.^*.,n(q^') 



b. 



AC, 



±^A' 



It is said that the mortality rate (in the later part of the life span) doubles about every 8.5 years; 

 hence b^ ■--= 0.082; and that it increases approximately with the 5.2th power of age, or b., = 5.2. 

 These two values are compatible around /* = 63 years, which characterizes the neighborhood 

 in which both are claimed to be valid. 



Yockey: If one plots survival data as Auerbach does, one obtains curves which corre- 

 spond to the Gompertz function for man and for many out bred wild-type organisms. For 

 some in bred strains, particularly those which have a genetic defect, the survival curve may be 

 of the form log ///q = — oc/'-. 



In Fig. 3 of my paper in Part V, I have plotted log ///o against the square of the age for 

 several strains of mice. The dilute brown strain reported by Murray and Hoffman follows the 



