62 



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



In Table VI the ptarmigan are arranged in five groups in the usual 

 manner. In this case, as in that of the individual observations, the best n 

 is - 71, giving an average value for h of 7"44. The variations of the 

 tracheal constant are without periodicity, but the tracheal percentage falls 

 gradually, and quite regularly, from 2'25 to 2 - 02. Using the above values 

 for n and k, the average deviation between the calculated and the observed 

 figures is - 77 per cent., while it is 3 - 44 per cent, (four and a-half times 

 as great) if the area be calculated in per cent, of body weight. If the 

 value of n be taken as 0*70, k becomes 6'98, and if n be - 72, k is 6 - 93. 



As regards the question of sex it is to be observed that, in the present series 

 of observations, the average k for male animals is somewhat larger than 

 average k for the females. That is to say, the females had slightly wider 

 tracheas than the males. 



In Table VII are tabulated the main results obtained, in such a manner as 

 to show at a glance the range of weight, the best n, the value of k, the 

 percentage deviation, and so forth, for each species of animal, both grouped 

 and ungrouped. It will be seen from the averages brought out at the foot of 

 the table that, taking the species together, the average percentage deviation 

 for the individual animals between the calculated and the observed figures for 

 the tracheal area is 9 - 02, when the calculation is made in terms of the body 

 surface, while it is 14 - 23 when the area is expressed as a percentage of the 

 body weight. The corresponding figures for the grouped animals are 2 - 5 

 and 12 - 28 respectively, a deviation nearly five times as large. 



Just as was seen in our measurements of the aorta, the method used in 

 measuring these tracheas is, in the nature of the case, much less exact 

 than that employed by us in measuring the blood volume, and therefore 

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

 is found to be reduced to very nearly the same extent in each case by 

 grouping the animals ; of course, reckoning by the body surface throughout. 

 Thus, in the present instance, the ratio between individual and grouped 

 percentage deviations is 9'02/2 - 5, i.e. 3'6, while in the other two cases it 

 was shown to be 3'2. 



The mean deviation between the calculated and the observed values, as 

 determined by the method of least squares for the three species (grouped 

 individuals), is 7'08 per cent, for the guinea-pigs, 1'58 per cent, for the 

 rabbits, and 1*16 per cent, for the ptarmigan. The average of these figures 

 is 3'27 per cent. The corresponding mean deviations when the tracheal area 

 is calculated in percentage of body weight are for the guinea-pigs 33 - 42 per 

 cent., for the rabbits 14'32 per cent., and for the ptarmigan 4*28 per cent., 

 giving an average of 17"34 per cent. 



