88 



Mr. Hainan and Dr. Marshall. 



where o-i and er 2 are the standard deviations of log t and body-weights 

 respectively, r is the correlation between them, n is the number of observa- 

 tions, and x 2 is the mean body-weight. Further, it may be noted that there 

 is a high negative correlation between errors in the regression and in the 

 constant term. It is clear from the probable errors given that no stress can 

 be laid on the differences observed, which lie well within the range of 

 differences likely to occur owing to fluctuations of sampling alone ; equally 

 unlikely or more unlikely differences might have occurred, I find, even had 

 both groups been normal, once in some seven or eight trials. 



Applying the same method to Hainan and Marshall's data, I find for all the 

 65 controls and 70 thymusless animals : — 



Thymusless log* = (0-00319±(H)0020) &-0-0384±0'0597, 



Controls log* = (0-00367 + 0-00015)5-0-2032±0-0441 ; 



and for the 43 controls and 49 thymusless under 300 grm., 



Thymusless log t = (0-00210 ± 0-00069) b + 0-2195 ±0 1775, 



Controls log* = (0-00364±0-00057)6-0-2098±0-1465. 



The difference between the constant terms in this last case looks large, but 

 the probable errors are also very large, and the difference is less than twice 

 its probable error, viz., 0-2301. Summarising in the same way as before, I 

 find differences as improbable as those observed might have arisen owing to 

 fluctuations of sampling once in some five or six trials. Hainan and Marshall's 

 data, it may be noted, do not include any animals under 200 grm. and few 

 under 250 grm. and give a low correlation between body-weight and log (testes- 

 weight) for the rather narrow available range of the non-adults. Within the 

 short range of body-weight 250-259 grm., there are 22 thymusless and 

 17 controls, and it may be desirable to give a simple comparison for these to 

 emphasise the magnitude of the probable errors. For controls the mean 

 testes-weight is 0'569, with standard deviation 0*101 grm. ; for thymusless, 

 mean - 519, with standard deviation - 103. The difference, 0-050, is therefore 

 in the direction indicated by Prof. Paton's views, but no stress can be laid on 

 it, as it is only 2'25 times the probable error of the difference, viz., 0-0222. 



Taking Paton's and Hainan and Marshall's data as a whole then, it 

 seems impossible to regard any effect of extirpation of the thymus on the 

 o-rowth of the testes as proved ; if there is any such effect it seems clear 

 that it is small. The data stand in complete contrast with those relating 

 to the effect of castration on the growth of the thymus. Within the 

 limits of body-weight in Hainan and Marshall's data, there seems to be 

 little relation between weight of thymus and body-weight, so the means 

 may be compared directly. I find : — 



