366 JOURNAL OF' THE WASHINGTON ACADEMY OE SCIENCES VOL. 11, NO. 15 



York, 1896.) An excellent book treating a delicate subject with tolerance, 

 kindness and wisdom. 



Smith, David Eugene. Number stones of long ago. 136 pp. (Ginn and 

 Co., Boston, 1919.) Stories on the history of arithmetic written for children. 

 Accurate and entertaining. Probably the only book on the history of science 

 which was written especially for children. 



Berry, Arthur. A short history of astronomy. 440 pp. (Charles Scrib- 

 ner's Sons, New York, 1910.) Apparently there is no difference between this 

 edition and a previous one published in London in 1898. Perhaps the best 

 general elementary textbook. A very good introduction to the subject. 



Thorpe, Edward. History of chemistry. 2 volumes, 185 and 190 pp. 

 (G. P. Putnam's Sons, New York, 1909-10.) Less complete but more ele- 

 mentary and far more easy to read than Ernst von Meyer's standard book. 



GeikiE, Archibald. The founders of geology. 289 pp. (Macmillan and Co., 

 London, 1897.) The book embodies a series of lectures delivered by this 

 distinguished English geologist before students of Johns Hopkins University. 

 It is a charmingly written account of the beginnings of geological science and 

 of the principal workers in that subject down to the latter half of the nine- 

 teenth century. Only European and British geologists are considered. 

 The book is intended for the mature reader who knows something of geology, 

 but it may be enjoyed as well by those who have no technical knowledge 

 of the subject. 



Merrill, George P. Contributions to the history of American geology. 

 546 pp. Part of Report of U. S. National Museum for 1904. (Washington, 

 1906.) An interestingly written series of sketches of the leaders in American 

 geology since its earliest days, well illustrated, and enlivened with anecdotes 

 and comments. (A new edition is in preparation.) 



LocY, William A. Biology and its makers. 477 pp. Third edition, 

 revised. (Henry Holt and Co., New York, 1915.) Good introduction; 

 simple, clear and entertaining. 



PHYSICS. — The wave lengths of X-rays.'^ Ralph W. G. Wyckoff, 

 Geophysical Laboratory, Carnegie Institution of Washington. 

 (Communicated by Arthur L. Day.) 



It is commonly assumed that the length of X-rays has been uniquely 

 and definitely determined from the study of the structures of crystals. 

 In the following discussion it will be shown, taking the case of sodium 

 chloride as an example, that with the existing knowledge it is impossible 

 to determine definitely the structure of any crystal in advance of a 

 knowledge of the wave length of X-rays. Viewed then from this 

 position only, the problem of the length of X-ray waves and of the 

 structures of crystals becomes indeterminate and recourse must be had 

 to other sources of information. 



The customary method of determining the wave length of X-rays. — The 

 wave length of X-rays has been determined through the following 

 course of reasoning.- If a crystal is considered as composed of a 



1 Received June 16. 1921. 



" W. H. and W. L. Bragg. X-rays and crystal structure. (London, 1918.) 



