OCTOBEB 1, 1915] 



SCIENCE 



453 



per cent, more than tie nitrate. We have 

 shown that sodium sulphate should be hydro- 

 lyzed to a greater extent than sodium ni- 

 trate; consequently, it should have not only 

 a greater solvent action than the nitrate, 

 but also a greater decomposing action 

 on the organic matter, resulting in the pro- 

 duction of a darker brovm color. In view of 

 the very general and abundant distribution of 

 alkali sulphates in western soils, and granting 

 the presence of sufficient organic matter for 

 the production of a brown color according to 

 the hypothesis of Stewart and Peterson, we 

 should expect to find a uniform distribution of 

 a dark brown surface color throughout the 

 soils of the arid west. This is not the case. 



As a matter of fact, neither the nitrates nor 

 the sulphates are hydrolyzed at all. Stewart 

 and Peterson admit that the sulphates are not 

 hydrolyzed, but claim that the nitrates are. It 

 is indeed difficult to reconcile their claim with 

 the facts in the case. Since the alkali nitrates 

 are not hydrolyzed, and since alkali hydrox- 

 ides could be produced from them in no other 

 way than by their hydrolysis, it is very evident 

 that no alkali hydroxides are formed, and 

 consequently the explanation of the brown 

 color of the " niter spots " as given by Stewart 

 and Peterson is nothing short of preposterous. 



The question raised by the above writers con- 

 cerning the relation of the pigment of Azoio- 

 hacter chroococcum and the nitrate to the 

 brown color of the " niter spots " applies only 

 to the colorless strains of the organism. These 

 have been shown by us to be capable of pro- 

 ducing abundant brown to black pigment when 

 supplied with very small quantities of nitrate 

 (0.01 to 0.03 per cent, sodium nitrate) and 

 some source of energy, both of which are pres- 

 ent in our niter soils. Aside from these color- 

 less strains, their contention is wholly irrele- 

 vant for we have already pointed out^ that 

 four of the seven strains of A. chroococcum, 

 isolated from niter soils have produced, at one 

 time or another, pigments varying in color 

 from a delicate cream, through the different 

 shades of brown, to an intensive brownish 

 black in the total absence of nitrates, thereby 



1 Colorado Experiment Station Bulletin, 179, p. 

 33, June, 1911. 



attesting their ability to produce the pigment 

 independent of the nitrate. 



Walter G. Saokett, 



E. M. ISHAM 



Colorado Experiment Station, 

 Ft. Collins, Colorado 



calculation of the gamma function 



To THE Editor of Sctence: In Science, 

 April 2, 1915, Dr. Eaymond Pearl has de- 

 scribed a method of obtaining an approximate 

 value of log r(n) by interpolating in a table 

 of log-factorial n. 



In a table he compares the values obtained 

 by interpolation, by Forsyth's method of ap- 

 proximation, and those found by using the re- 

 lation 



T(n + l)=n(Ti — l)(n — 2) ■■■ 



(n — r)r(n — r) 

 in conjunction with Legendre's tables, calling 

 the value obtained by the last method the " ex- 

 act " value. 



Dr. Pearl explains that this " exact " value 

 derived its name from the exactness of the 

 mathematical argument upon which it is 

 based, and not from any special accuracy in 

 the numerical values given under that head- 

 ing and he disclaims any greater degree of ac- 

 curacy than can be expected from the summa- 

 tion of a large number of seven-place log- 

 arithms. 



As the subject to be investigated is not how 

 closely the values obtained by different meth- 

 ods agree with one another but how closely 

 the approximate to the true value of the func- 

 tion, I have calculated a " more exact " value 

 for the cases given by Dr. Pearl, using Leg- 

 endre's table and ten-place logarithms and I 

 believe the values so obtained are correct 

 within a half-unit of the seventh decimal 



Another set of values has also been calcu- 

 lated by means of Pearson's approximation 

 formula^ 



i"On a Formula for Determining T(x -{- 1)," 

 Biometrika, Vol. VI., p. 118. 



r(x -I- 1) 



log 



= .3990899 -1- |log x 



+ .080929 sin 



25°.623 



