Group Discussion 289 



subsidiary peaks are concerned, I would be astonished if they were 

 not just the result of random error, q^ is irregular, and so obviously 

 no graduation process has been applied. I assume that the life-table 

 was obtained by following the history of a cohort, and that the Ix 

 figures are in effect the numbers actually surviving to each age, the 

 numbers being reduced to a radix of a thousand. 



Rockstein: That is right. There were about 4,000 animals of each 

 sex there, 3,875 females and slightly more males. 



Perks: That is a technique that with humans we have not found 

 very helpful, because it takes 100 years to follow a cohort through. 

 But even though you get your rates of mortaUty that way, before I 

 would draw any conclusions whatever from bumps on the dx curve 

 I should want to put a light graduation through the q^ values, and 

 then recompute the l^ and dx columns. You would have to apply a 

 goodness of fit test. But a quite elementary graphical graduation 

 would probably be sufficient to get rid of the accidental bumps in the 

 dx column. 



Gerking: What do you mean by a light graduation? 



Perks: I mean putting a smooth curve through the points repre- 

 sented by qxy so that you get rid of, or greatly reduce, the random 

 errors — on the hypothesis that if you had a much larger number in 

 your sample the departures from the smooth curve would largely 

 disappear. I agree that the assumption of the smooth curve for the 

 qx is only a hypothesis, but there is a great deal of observational 

 evidence for that assumption, provided you keep your condition 

 reasonably constant. 



S acker: When you say smooth, you do not necessarily mean 

 simple? 



Perks: No. There is no satisfactory mathematical definition of 

 smoothness. There has been some controversy in the Institute of 

 Actuaries on what we mean by smoothness, and some people suggest 

 it should be absence of roughness ! 



Rotblat: How sensitive is the gamma distribution to the value of n? 



Perks: You can get a wide range of different curves with different 

 values for n. 



Comfort: I am impressed with that remark, because this is almost 

 what Failla or Szilard have suggested is in fact happening, isn't it? 

 (Failla, A. (1958). Proc. Ageing Conf., Gatlinburg. Washington, 

 D.C.: A.I.B.S., in press. Szilard, L. (1959). Proc. nat. Acad. Set. 

 (Wash.), 45, 30). The objects are actually being shot at by radiation, 

 and this may be one of the causes of chromosome deterioration. 



Perks: If you are interested in that, R. E. Beard developed the 

 subject further some years ago (see Appendix, p. 302). If you increase 



AGEING — ^V — 10 



