64 



Messrs. Dreyer, Bay, and Walker. [Sept. 30, 



The ratio between these figures (3*27 and 17"34) is also almost exactly 

 the same as that which was found between the corresponding figures in the 

 case of the blood volume (2), although in that case the mean deviations 

 themselves were much smaller (namely, T39 and 7'82 per cent, respectively), 

 owing to the much greater intrinsic accuracy of the technique. 



From these figures it is seen that if a series of observations of the tracheal 

 area are made and averaged, it follows that if the difference between this 

 average and the theoretical value given by our formula is as much as 

 7 per cent, the tracheal area is probably abnormal, and if it amounted to 

 about 10 per cent, it would be almost certain that the trachea was 

 abnormally large or small. But if the measurements were expressed in 

 percentage of body weight it would only be possible to say with the same 

 degree of certainty that the tracheal area of the animal was abnormal when 

 it differed from the calculated value by 50 per cent, or more. 



The inter-relation of the various constants (for surface, blood, aorta, and 

 trachea) given in the present and in previous papers, together with its 

 significance, will be dealt with in a later communication. But it may here 

 be pointed out that the value of n in the expression W n /a = k has now 

 been shown to be - 70-0 - 72 for the surface area of three different species of 

 mammals, for the blood volume of six mammals, for the aortic area of four 

 species of mammals and four species of birds, and for the tracheal area of 

 two mammals and one bird. Accordingly we regard our formula W n /a = k 

 as a rational formula indicating that the blood volume, the aortic area, and 

 the tracheal area are all proportional to the body surface in warm-blooded 

 animals. From an examination of the large number of data which we have 

 now collected it appears that if one desires rapidly to compare a series of 

 individual observations by means of the formula ~W n /a = k, the value 

 of k may readily be determined approximately by using the power 

 § (= - 67) or the power f (= - 75) instead of the accurate value of 

 1% (0-70-0-72). The results thus obtained will be approximately correct over 

 a moderate range of weight. But as the range of weight increases the 

 residts deviate from the true values, and those obtained with n = § deviate 

 more rapidly than those obtained with n = f . 



The difference in the relative accuracy of the results given by these two 

 values of n has been ascertained in the following manner : — The percentage 

 deviations for the surface, the blood volume, the aortic area, and the tracheal 

 area for four different species of animal, with " best n," with n = ■§, and with 

 n = |, were tabulated, and the figures for these three values of n averaged. 

 The final average deviations thus obtained were 2 - 52 per cent, with n taken 

 as 0-70-0-72, 3-25 with n taken as f, and 3-81 with n taken as §. Thus 



