54 



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



our animals together the average percentage deviation for the individual 

 animals between the calculated and the observed figures for the aortic area 

 is 9 - 97 when the calculation is made in terms of the body surface, while it 

 is 24'55 (two and a-half times as great) when the area is expressed in 

 percentage of body weight. The corresponding figures for the grouped 

 animals are 3'15 and 15 - 35 per cent, respectively, a deviation nearly five 

 times as large. 



Attention may further be drawn to the fact that although the technique 

 of these aortic measurements is in the nature of the case much less exact 

 than that employed by two of us in measuring the blood volume, and there- 

 fore gives much larger figures for the percentage deviation, yet this deviation 

 is found to be reduced to precisely the same extent in both cases by grouping 

 the animals. Thus in the present instance the ratio between individual 

 and grouped percentage deviations (of course reckoning by the body surface) 

 is 9 - 97/3"15, i.e. 3"2, while in the case of the blood volume experiments it 

 was 4'43/l - 39, or 3 - 2 again. From the table it is also clearly seen that the 

 greater the range of weight of the animal observed the more misleading 

 and erroneous is the result obtained by calculating the aortic area in 

 percentage of the body weight. Thus, while in the case of the ptarmigan 

 and sparrow, where we have only a small range of weight, the difference is 

 comparatively small, in the case of ducks, fowls, and rats, which show the 

 widest range, the difference may properly be spoken of as enormous, being 

 from 13 - 5 to 16 - 7 times as large. This shows that if one were to attempt 

 to calculate .the sectional area of the aorta of a small animal, for example, 

 from the ascertained aortic area of a large one of the same species, expressed 

 as a percentage of body weight, the result would inevitably be grossly 

 misleading, while if it were calculated by our formula a true estimate would 

 be obtained, correct within the limits of the experimental errors. 



In Table XV are given the mean deviations as calculated by the method 

 of least squares for the eight species concerned in these observations, both 

 individually and grouped. From the averages of these it can be seen that 

 if one were to make only a single observation and this differed by 30 per 

 cent, from the theoretical value given by our formula it would be probable 

 that the aortic area in question was abnormal in size, while if it were 

 expressed as a percentage of body weight it would have to differ from the 

 theoretical area by at least 60 per cent, before one could say with the same 

 degree of certainty that it was abnormal. 



If, however, a series of observations were made and averaged, it follows 

 from our figures for the mean deviation for grouped animals that if the 

 difference between this average and the theoretical value given by our 



