Febeuaey 3, 1911] 



SCIENCE 



189 



integers a -\- hi. Several errors appear on 

 page 376; in the line below (2) and that 

 above (3), m must be replaced by m^; while 

 the use of p^, p,, • • • for Sj, 8,, • ■ • is merely an 

 oversight. At the bottom of page 255 the 

 author speaks of introducing ideals into a 

 number field. 



Many of the proofs employed by the author 

 in his case of quadratic fields are mere substi- 

 tution of 2 for n in the standard proofs on 

 algebraic fields of degree n. In one place he 

 says : " This proof could have been somewhat 

 simplified had greater use been made of the 

 fact that the realm under consideration was 

 quadratic, but it seemed desirable to give the 

 proof in a form at once extendable to realms 

 of any degree." The reference is to his three- 

 page proof that every quadratic field has a 

 basis! Now the real justification of a special 

 treatment of the quadratic field lies in the 

 fact that particularly simple proofs may be 

 given and the reader made acquainted with 

 an important example without the algebraic 

 difficulties inherent in the general field. The 

 above remarks will serve to show how the 

 author has filled 300 pages with properties of 

 quadratic number, without entering upon a 

 discussion of the class number, characters, 

 genera and other important topics on quad- 

 ratic numbers. 



In the matter of references the author has 

 been particularly unfortunate. In a book 

 bar/ely entering upon the threshold of the 

 theory, a scarcity of references woiild have 

 been entirely justifiable. But to give hun- 

 dreds of references to a certain report on the 

 subject (excellent although it be) and to com- 

 pletely ignore the literature and not even 

 mention the names of the discoverers of the 

 theorems is against all scientific traditions. 

 L. E. Dickson 



/ SPECIAL ARTICLES 



THE RELATION OF COLLOIDAL SILICA TO CERTAIN 

 IMPERMEABLE SOILS 



The interpretation of recent soil bacterio- 

 logical studies upon the Truckee-Carson Irri- 

 gation Project at Eallon, Nev., is in many 

 cases difficult because of the impermeability to 



irrigation water on certain shortly defined 

 areas. These impermeable areas support 

 practically no crop growth, although the soil 

 is very similar to that of the good areas in 

 appearance and soluble salt content. During 

 the past two years it has been my belief, based 

 upon rough estimations of the silica that 

 could be washed out from samples of soil 

 from good and poor spots upon the United 

 States Experimental Farm at Fallon, Nev., 

 that at least in some instances the permeabil- 

 ity and impermeability bore some relation to 

 the occurrence of silica in a colloidal condi- 

 tion. Certain peculiarities of the behavior of 

 soil samples from good and poor spots toward 

 colloidal silica have been noted in the labora- 

 tory. These facts are only indirectly con- 

 nected with our soil bacteriological studies 

 and seem of themselves of sufficient interest 

 to warrant publication at this time. 



The following is a brief summary of labor- 

 atory results which seem to confirm the theory 

 that in certain soils impermeability is associ- 

 ated with the occurrence of colloidal silica: 



One-gram samples of good soil shaken in 

 ten cubic centimeters of carefully dialyzed 

 colloidal silicic acid of specific gravity of 

 1.0108 coagulates in from three to eight hours 

 at 28° C. 



One-gram samples of bad soil similarly 

 treated not only do not coagulate the silica but 

 hold it in a colloidal condition even after the 

 check tube of pure silicic acid has coagulated. 



The mixing of small quantities of calcium 

 chloride, calcium sulphate or dilute acids 

 with samples of bad soil before their addition 

 to the silicic acid enables them to coagulate 

 the tube of colloidal silicic acid in as short a 

 time as that necessary for samples of good 

 soil. 



The treatment of samples of bad soil with 

 calcium chloride, calcium sulphate, or dilute 

 acids destroys their impermeable character, in 

 some cases enabling water to percolate 

 through them as rapidly as in the case of good 

 soils. 



In these experiments it has been found that 

 the two essentials are, first, a high degree of 

 purity of the colloidal silicic acid; and, 



