August 8, 1913] 



SCIENCE 



201 



Group Theory, ' ' by Josephine Burns, graduate 

 student at the University of Illinois. 



"Errors in the Literature on Groups of Finite 

 Order, ' ' by Professor G. A. Miller, University 

 of Illinois. 

 Pedagogical Considerations j such as the fol- 

 lowing : 



' ' The ' Foreword ' concerning Collegiate Mathe 

 maties, " by Professor E. B. Hedrick, Univer 

 sity of Missouri. 



"Mathematical Literature for High Schools,' 

 by Professor G. A. Miller. 



"Minimum Courses in Engineering Mathe 

 maties," by Professor Saul Epsteen, Univer 

 sity of Colorado. 



' ' Incentives to Mathematical Activity, ' ' by Pro 

 fessor H. E. Slaught, University of Chicago 

 General Mathematical Information, such as 

 the following: 



"The Third Cleveland Meeting of the American 

 Association for the Advancement of Science, ' ' 

 by Professor G. A. Miller. 



"Western Meetings of Mathematicians," by 

 Professor H. E. Slaught. 



"Notes and News" of events pertaining to 

 mathematics, under the direction of a com- 

 mittee of which Professor Florian Cajori is 

 chairman. 



' ' Book Reviews ' ' and announcements of new 

 books in mathematics, under the direction of 

 a committee of which Professor W. H. Bussey, 

 University of Minnesota, is chairman. 

 Topics Involving a Minimum of Technical 

 Treatment, such as the following: 



"Maximum Parcels under the New Parcel Post 

 Law, ' ' by Professor W. H. Bussey. 



"Precise Measurements with a Steel Tape," by 

 Professor G. E. Dean, Missouri School of 

 Mines. 



"A Direct Definition of Logarithmic Deriva- 

 tive," by Professor E. R. Hedrick. 



"A Simple Formula for the Angle between Two 

 Planes," by Professor E. V. Huntington, 

 Harvard University. 



"Two Geometrical Applications of the Method 

 of Least Squares," by Professor J. L. Cool- 

 idge. Harvard University. 



' ' Problems Proposed and Solved, ' ' under the 

 direction of a committee of which Professor 

 B. F. Finkel, Drury College, is chairman. 

 Topics Involving Somewhat More Technical 

 Treatment, designed to stimulate mathe- 

 matical activity on the part of ambitious 



students and teachers; for example, such 

 as the following: 



"The Remainder Term in a Certain Develop- 

 ment of i^ (a + a;)," by Professor E. D. Car- 

 michael, Indiana University. 



"A Geometric Interpretation of the Function 

 F in Hyperbolic Orbits," by Professor W. O. 

 Beal, Illinois College. 



"Certain Theorems in the Theory of Quadratic 

 Residues," by Professor D. N. Lehmer, Uni- 

 versity of California. 



' ' Some Inverse Problems in the Calculus of 

 Variations," by Dr. E. J. Miles, Yale Uni- 

 versity. 



"Amicable Number Triples," by Professor L. 

 E. Dickson, University of Chicago. 



H. E. Slaught, 

 Managing Editor 



BEANCB MOVEMENTS INDUCED BY 



CHANGES OF TEMPEBATVBE^ 

 That changes occur in the linear dimen- 

 sions of metals following fluctuations in the 

 temperature is common knowledge, but that 

 similar changes result in wood and living trees 

 is not so generally known. Pure water has its 

 smallest volume at 4° C, and lowering the 

 temperature further increases its volume until 

 it freezes; while ice contracts regularly with 

 decreasing temperature and at a greater rate 

 than any of the metals. It is generally sup- 

 posed that marked changes in temperature 

 have some effect upon the volume of tree 

 trunks because radical clefts occur so fre- 

 quently in severe winters and old clefts close 

 during the middle of warm winter days and 

 open again as the temperature sinks during the 

 night. Since freezing water often bursts its 

 container it is popularly held that such tree 

 trunks are burst by the expansion of the freez- 

 ing water in them. Caspary' has shown this 



' This review of the literature of branch move- 

 ments and observations grew out of a study of 

 crown-rot of fruit trees and is published sepa- 

 rately because it is only indirectly related to the 

 main theme. 



' R. Caspary, ' ' Ueber Frostspalten, ' ' Bot. Zeit., 

 13: 449-62, 473-82, 489-500, 1855; "Neue Unter- 

 suchungen Tiber Frostspalten," Bot. Zeit., 15; 

 329-35, 345-50, 361-71, 1857. 



