December 29, 192 2] 



SCIENCE 



757 



to the main portion by fourtli difference inter- 

 polation formulas. The upper tail end of the 

 curve -WHS graduated by Wittstein's formula and 

 welded ito the main portion by the application 

 of Spencer's 21-term formula. Glover felt it 

 imiDortant to ail/ter the raw figures as little as 

 possible and apologizes in various places for 

 little roughnesses in the tables, especially 

 around junction or welding points. 



Much might be said about the orthodox actu- 

 arial philosophy regarding the smoothing or 

 graduation of raw data. The present reviewer 

 finds himself in disagreement with some of it, 

 looking at the whole matter fnom the broad 

 standpoint of scientific methodology. But this 

 is clearly not the place to enter upon a discus- 

 sion of this mathematically recondite and emo- 

 tionally delicate subject. Suffice it to say that 

 the reviewer is acquainted with no more honest, 

 through, and skillful application of the stand- 

 ard actuarial methods than that of Glover in 

 the construction of these taibles. 



Altogether this is a substantial and notable 

 contribution to American vital statistics. We 

 may well be proud of it. It stands at least on 

 a level with the very best that any country, not 

 excepting the Registrar-General's Office of Eng- 

 land and Wales, under Earr and Ogle and 

 Stevenson, has produced in the same line. Every 

 health officer la.nd vitail staltistician should have 

 a copy of it on his desk. Two features of the 

 book are especially noteworthy. The first is 

 that the best recent life tables for Australia, 

 Denmark, England, France, Germany, Holland, 

 India, Italy, Japan, Norway, Sweden, and 

 Switzerland are given in full for comparative 

 purposes. The second is that there are givew, 

 for the United States, tables of life annuities, 

 premiums and commutations. This last is an 

 interesting departure for an official -government 

 publicatiion. Hitherto in litigation involving 

 questions of life expectancy in the settlement 

 of estates, etc., the courts have had to depend 

 for their actuarial basis in the main upon the 

 material of insurance companies. Now official 

 tables based upon the experience of the original 

 registration states in 1910 may be used, and all 

 elements of uncertainty as to bias willl be re- 

 moved. Purthennore, by the use of the premi- 



um tables one can make intelligent examination 

 of the alluring proposals made to him for the 

 purchase of insurance, whether toy theoretically 

 grasping commercial institutions or by theoret- 

 ically eleemosynary foundations. 



Finally, it may be pointed out that this vol- 

 ume makes a first rate test-ljook for the system- 

 atic study of the basic elements of actuarial 

 science. The reviewer is using it in this way 

 at the presenit time, in a course in life ta;ble 

 construction, with great satisfaction. It may be 

 purchased from the Superinltendent of Docu- 

 ments at a cost of $1.25 per copy, cJoth bound, 

 a price which is only a small fraction of what 

 amy commercial publisher would 'have to charge 

 for a book so expensive to manufaoture. 



Raymond Peael 



SPECIAL ARTICLES 



X-RAY CRYSTALLOMETRY: X-RAY WAVE 

 LENGTHS. SPACE-LATTICE DIMEN- 

 SIONS AND ATOMIC MASSES 



The fundamental equation in X-ray spec- 

 trometry and crystallometry is 

 X = 2(J sin e 

 wherein d is the perpendicular distance be- 

 tween adjacent planes in the crystal which re- 

 fleet in the first order at a glancing angle of 

 incidence 0, X-rays of wave-length X. Since 

 only 6 in this equation is capable of direct 

 measurement the absolute magnitudes of X and 

 d can only be determined if some other relation 

 between them can be found, or if either can. be 

 determined independently. 



The method first used was to obtain a value 

 of d from the density of the crystal, the number 

 of molecules in its unit of structure, and the 

 mass of a single molecule. The first of the 

 last-named quantities can be measured directly, 

 the second is an integer the choice of which 

 can be guided with sufficient accuracy from the 

 X-ray data, and values for the third have been 

 obtained by a variety of methods, perhaps best 

 by the determination of electrochemical equiva- 

 lents and electronic charge. No othea* relation 

 between X and d than that given above is at 

 present known to exist, i. e., no other quantity 

 than 6 is known to depend upon these two vari- 

 ables onh/, so that the first suggested method of 



