68 DONALD D. VAN SLYKE 



slant will be more or less steep according as the [BHCO 3 ] :[H 2 C0 3 j 

 ratio is great or small. But a constant [BHCO 3 ] :[H 2 CO 8 ] ratio indi- 

 cates a constant pH (see equation of Hasselbalch below). Consequently, 

 we are able by a series of straight, slanting lines on a diagram arranged 

 as described to express all possible [BHCO 3 ] :[H 2 CO 3 ] ratios and pH 

 values. In pure NaHCO 3 - H 2 CO 3 solutions, the isohydrionic lines 

 curve slightly, because the proportion of NaHCO 3 dissociated into !NV 

 and HCO;/ increases slightly with dilution. In blood, where the 1NV 

 concentration is constant, the lines are practically straight. Their slope 

 may be calculated from the equation of L. J. Henderson (1909), 



[II + ] = K! J|. 3 or by the same equation in the logarithmic form 



A. 



used by Hasselbalch (1916), pH = P K X + log 



K being the dissociation constant of carbonic acid, A, the degree of disso- 

 ciation of [BIICO 3 ] into B + and HCO/. pK x is the negative logarithm 

 of Kj. The value of K! for blood was estimated by Haggard and 

 Henderson (1919), from the data available in the literature, as 8 X 10~ 8 , 

 for which the negative logarithm, and therefore the corresponding value 

 of pKj, is 6.10. 



~\ 



The equation pH = 6.10 -{- log rir/i nas accordingly been used 



I_H 2 CO 3 J 



_ 



in plotting the pH lines of Fig. 2 from which Figs. 3 and 4 are derived. 

 That the value 6.10 will be subject to correction in the second decimal 

 place as the result of further work appears probable, but it is sufficiently 

 accurate to serve our present purposes. 



For Fig. 1, since it was desired to use the customary form of CO 2 

 absorption curves, with total CO 2 values, [BHCO 3 -j- H 2 CO 3 ], as ordi- 

 nates, and CO 2 tensions as abscissae, the form of the equation used was 



(total CO 2 )-(0.0672p) 



pH = 6.10 + log ^-- , p being the CO 2 tension in 



U. 



mm. of mercury, 0.0672 the factor by which the tension is converted into 

 terms of volumes per cent of CO 2 physically dissolved (as II 2 CO 3 ) in 

 the blood (Bohr, 1905). 



The conditions represented by the 9 areas within the reaction range 

 compatible with life are shown in the diagram as the following : 



Area 1. Uncompensaled Alkali Excess. The condition has been 

 observed after overdosing with sodium bicarbonate (Howland and Mar- 

 riott^), 1918; Harrop, 1919; Davies, Haldane, and Kennaway, 1920). 

 It has also been caused by the loss of gastric HC1 caused by obstructing the 

 pylorus and systematically washing out the stomach for some days (Mac- 

 Callum, Lintz, Vermilye, Leggett, and Boas, 1920). It is accompanied 

 by an increase in alveolar CO 2 , due to a slowing of respiration in the 



