March 24, 1911] 



SCIENCE 



469 



of special notice: (1) A general tendency toward 

 an increase in hardness with depth, or with age of 

 the rocks from which the water is drawn. (2) A 

 tendency for the hardness of the water to decrease, 

 if drawn extensively and continuously from a cer- 

 tain sandstone for several years. (3) The clear 

 evidence furnished by the chlorme determinations, 

 of pollution of surface waters and shallow wells 

 in the cities. In south Minneapolis — the older, 

 more densely settled part of town — shallow well 

 waters contain 44 parts per million of chlorine, 

 while in other, less settled parts, 4 parts per mil- 

 lion is the maximum. A few analyses follow: 



Total solids 



Silica 



Iron oxide, etc.... 



Calcium 



Magnesium 



Sodium and pota; 



Carbonate radicle 

 Bicarbonate radici 

 Sulphate radicle... 

 Chlorine 



It is noteworthy that samples number 6 and 8 

 from St. Paul have lower mineral content than 

 samples number 5 and 7 from Minneapolis, though 

 from the same formations. The amount of water 

 taken from these formations in St. Paul is much 

 greater than in Minneapolis. 



1. Lake and river waters. 



2. Waters from wells in glacial drift. 



3. Saint Peter sandstone waters. 



4. New Richmond sandstone waters. 



5. Jordan sandstone waters of Minneapolis. 



6. Jordan sandstone waters of St. Paul. 



7. Dresbach sandstone waters of Minneapolis. 



8. Dresbach sandstone waters of St. Paul. 



Frank F. Grout, 

 Acting Secretary 



SOCIETIES AND ACADEMIES 



THE AMERICAN MATHEMATICAL SOCIETY 



The one-hundred and fifty-second meeting of 

 the society was held at Columbia University on 

 Saturday, February 25. Thirty-eight members 

 attended the two sessions. President Henry B. 

 1 me occupied the chair. The council announced 

 the election of the following persons to member' 

 ship in the society: Dr. Elizabeth E. Bennett 

 University of Nebraska; Mr. Daniel Buchanan 

 University of Chicago; Dr. H. B. Curtis, Columbia 

 University; Mr. L. L. Dines, University of Chi' 

 cago; Professor C. E. Maelnnes, Princeton Uni 



versity; Professor Eva S. Magiott, Ohio Northern 

 University; Mr. R. E. Eoot, University of Chi- 

 cago; Professor Sarah E. Smith, Mount Holyoke 

 College. Six applications for membership were 

 received. 



The following papers were read at this meeting : 



E. J. Miles: "Some properties of space curves 

 minimizing a definite integral with discontinuous 

 integrand. ' ' 



N. J. Lennes: "A necessary and sufficient con- 

 dition for the uniform convergence of a certain 

 class of infinite series. ' ' 



N. J. Lennes: "Duality in projective geom- 

 etry. ' ' 



G. A. Miller: "The number of the abelian 

 subgroups in the possible groups of order 2™." 



C. N. Moore: "On the uniform convergence of 

 the developments in Bessel functions. ' ' 



G. D. BirkhofE: "A direct method for the 

 summation of developments in Lame's functions 

 and of allied developments." 



Edward Kasner : ' ' Equitangentials in space. ' ' 



Edward Kasner : ' ' Conf ormal and equilong in- 

 variants of horn angles." 



J. A. Eiesland : " On a contact transformation 

 in physics. ' ' 



D. C. Gillespie: "Definite integrals containing 

 a parameter. ' ' 



Joseph Bowden: "The Eussian peasant method 

 of multiplication. ' ' 



N. J. Lennes: "A direct proof of the theorem 

 that the number of terms in the expansion of an 

 infinite determinant is of the same potency as 

 the continuum. ' ' 



Harris Hancock: "On algebraic equations that 

 are connected with the cyclotomie equations and 

 the realms of rationality which they determine." 



W. B. Fite: "Irreducible homogeneous linear 

 groups of order p"' and of degree p or p-. ' ' 



The next meeting of the society will be held 

 at the University of Chicago on Friday and Sat- 

 urday, April 28-29. On this occasion Professor 

 Maxime Bocher will deliver his presidential ad- 

 dress, the subject of which will be "Charles 

 Sturm's Published and Unpublished Work on 

 Differential and Algebraic Equations." Except 

 for the summer meetings, this will be the first 

 convention of the whole society since 1896. A 

 large attendance is expected from both east and 

 west. 



The San Francisco Section of the society wiU 

 meet at Stanford University on Saturday, April 8. 



F. N. Cole, 



