500 



SCIENCE. 



[N. S. Vol. XV. No. 378. 



Borbed by the single corpuscle as its full 

 charge. Nernst 's ' Theoretische Chemie ' 

 (1900, p. 394) gives the most reliable esti- 

 mate of the number of molecules of oxy- 

 gen, or any other gas, in a cubic millimeter 

 at standard temperature and pressure. 

 This is 55 thousand millions of millions 

 (which may be written 55TMM). Calcu- 

 lated from this, the oxygen taken in by the 

 single blood corpuscle as a full charge is 

 found to be about 28 hundred millions of 

 molecules. But as the combination is 

 known to be regularly one molecule of the 

 gas to one molecule of hsemoglobin, this re- 

 sult, or in round numbers three thousand 

 millions, is approximately the number of 

 haemoglobin molecules in the blood-cor- 

 puscle (3 TM). 



Dividing this last number into the vol- 

 ume of the haemoglobin in a corpuscle, we 

 obtain the volume of the cubic ' room ' as- 

 signed by chemists to each molecule, and the 

 cube root of this will give the length of the 

 imaginary walls of said room, also nearly 

 the diameter of the molecvile regarded as 

 a sphere in a solid state. The volume is 

 approximately 1/10^^ cubic millimeters, 

 and the linear dimension of the side of a 

 molecule ' room ' is about 1/500,000 of a 

 millimeter. The ' rooms ' of the oxygen 

 molecules in the gaseous condition are much 

 larger than these, because the gases re.joiee 

 in spacious apartments ; in fact, the volume 

 of gas which is insorbed by the blood is 

 nearly twice as great as that of the devour- 

 ing hfemoglobin. 



Nernst states that by multiplying the 

 absolute atomic weight of hydrogen upon 

 the molecular formula of any proteid, we 

 may obtain the absolute weight of the pro- 

 teid. This involves, we think, the assump- 

 tion that no condensation has occurred in 

 building up proteid molecules. In order to 

 test the rule by haemoglobin, we find that 

 this rule gives as the absolute molecular 

 v/eight 1.35 X (10)""" of a milligram. By 



the method of the quantitative absorption 

 given above of oxygen the value comes out 

 as 1.30 X (10)-" of a milligram. The two 

 results differ by less than 4 per cent. This 

 close harmony does not prove that the esti- 

 mated weight of the atom of hydrogen is 

 right, for it enters into both methods; but 

 it does prove non-condensation, and also 

 confirms the quantitative results of Hiiff- 

 ner and others as to the absorption of oxy- 

 gen. It may be added that the oxygen 

 absorbed is, when estimated in its fluid 

 form, about 1/470 the volume of the absorb- 

 ing haemoglobin. 



But probably if the oxygen were ex- 

 amined in the liquefied or solidified condi- 

 tion, its molecular sphere of action would 

 be found not to be so very widely divergent 

 from its rightful proportion of 32 to 16,669. 

 G. Macloskie. 



Princeton University. 



SCIENTIFIC BOOKS. 



Legons sur les series divergentes. Par Emilk 



BoREL, maitre de conferences a ]' Ecole 



Normale Superieure. Paris, Gauthier-Vil- 



lars. 1901. Pp. vi + 182. 



La Serie de Taylor et son prolong ement analy- 



tique. Par Jacques Hadamard. Scientia, 



serie physico-mathematique. Chartes, im- 



primerie Durand. 1901. Pp. viii + 102. 



These two works can appropriately be 



classed together, on account of both their 



authorship and their contents. Among the 



younger French mathematicians who have 



taken their doctors' degrees within the past 



dozen years none are to-day more conspicuous 



than Hadamard and Borel. Their theses were 



published in 1892 and 1894 respectively. A 



few years later both writers were recipients of 



prizes from the French Academy of Sciences. 



In 1896 Hadamard received the 'Prix Bordin' 



for his work on geodesies, while Borel won 



the 'Grand Prix des sciences mathematiques'' 



in 1898 for his investigations upon divergent 



series. Eecently also they have been bracketed 



in a list of nominees to fill a vacancy in the 



Academy of Sciences. 



We have here to consider two representative 



