364 THE RESPIRATION 



reasons which are set forth above, the quotients should be approximately equal in the 

 air collected in the large and in the small spirometers; if they are not so, the condi- 

 tions of the method have not been correctly carried out. 



Since the dead space and the average composition of the alveolar air under these 

 conditions may be considered constant, the percentage composition of the deep expira- 

 tion will differ from that of the mixed sample of several normal expirations in propor- 

 tion as the dead space exerts a greater diluting effect in the small than in the large 

 expiration. This being the case, the data obtained can be combined algebraically to 

 give either the capacity of the air passages or the percentage composition of the 

 alveolar air. . 



Let A = amount of air in large expiration (small spirometer), 

 Ai = amount of air in small or normal, expiration (tidal air), 



B = the percentage of CO 2 or O 2 in the expired air of large expiration, 



Bi = the percentage of CO 2 or O 2 in the expired air of small expiration, 



x the capacity of the dead space, 



y = the average percentage of CO 2 or O 2 in the alveolar air; then, 



A x B = (A - x)y and Ai x Bi = (Ai - x)y. 

 Solving this for x, y remaining constant under the same physiological conditions, we 



A x Ai x (R-Bi) 

 have: x -- ^ , the dead space. Or solving for y, we have: 



y A x B ~ Al x Bl t h e mean percentage of CO., in the alveolar air. In case the 



A Ai 

 dead space for O 2 is desired, B and Bi must be made to equal the O 2 absorbed. 



Clinical Method. The use of the kymograph and pneumo graph, and 

 other complicating factors, make the method as just described quite im- 

 practicable for clinical procedure, but the use of the same apparatus 

 with the following modification will yield satisfactory results for most 

 clinical purposes. 



The patient is made to respire through the valves for a short time, after which the 

 observer collects a single expiration in a small spirometer by turning the stopcock from 

 Position 1 to 2. A sample of this is taken for analysis, and the spirometer is again 

 emptied and a series of successive samples of deeper expirations taken. This is done 

 by directing the patient, after he has started to breathe normally into the spirometer, 

 to breathe more deeply. The amount of air collected in each expiration is controlled by 

 the observer by closing the stopcock when the desired volume is obtained. By this 

 means one can collect several expirations differing from one another by increasing 

 amounts but all occupying the same time. The samples of the various expirations 

 are collected in a series of numbered sampling syringes, and the gaseous composition 

 of each is determined. When the percentage of CO or O t in each expiration is 

 plotted on cross section paper on the ordinates, with the volume of the expirations in 

 c.c. on the abscisste, a hyperbolic curve should be obtained. Any marked deviation 

 from such a curve indicates that some error has been made in taking a sample, and 

 this observation should be discarded. The different observations are then combined in 

 the formula given above. The determination of the CO., percentage of expired 

 air is so simple that a number of specimens of varying depths of expiration can be 

 taken and thus many points on the curve determined. For the most accurate results 

 it is in general best to compare only those expirations which differ from one another 

 by at least 0.3 per cent in CO., and by at least 200 c.c. in volume. This depends on 

 the fact that the diluting effect of the dead space in reducing the percentage of CO^ 



