Geology. 545 



of the chemical elements are equally valid for molecular num- 

 bers and compounds. These formulae are Nv — nv A and 

 Nv= ()i -f- i)v A , where N = molecular number, n = small posi- 

 tive integer, v = characteristic frequency, and v A = ' ' frequency 

 number" = 21 XlO 12 sec -1 . 



Three papers on this subject, by the same author, are devoted 

 to testing these relations. The data for a large number of 

 organic and inorganic compounds have been used and the equa- 

 tions have stood the test in such a great majority of cases as 

 to leave little room for the suspicion that the agreement arises 

 from an accidental play of numbers. Then, too, the physical 

 constants have been derived from many sources and the calcu- 

 lations based on data of different kinds. For a small number 

 of compounds the results of low-temperature measurements 

 were available and the characteristic frequency was deduced 

 from the specific heat. In many cases v was calculated from 



Lindemann's formula, which is v= hT s M V, where T s = 

 absolute temperature of the melting-point, M = molecular 

 weight, V = molecular volume, and k = 3-08 X 10 12 (Nernst's 

 value). In still other cases the required frequencies were 

 obtained directly from the wave-lengths of the "residual rays" 

 isolated by repeated reflections from the surfaces of crystalline 

 solids. Allen's formulae are doubtless expressions of a funda- 

 mental property of the solid state of matter, and their form sug- 

 gests a probable connection with the quantum theory. — Phil. 

 Mag., 35, 338, 404, 445 ; 1918. h. s. u. 



II. Geology. 



1. Thirteenth Report of the Director of the State Museum 

 and Science Department, State of Neiv York; by John M. 

 Clarke. Pp. 307, many plates. Albany, 1917. — In this vol- 

 ume the present conditions and aspirations of the most extensive 

 of the state museums are set forth, and also the present status of 

 the various scientific reservations in New York. Among the 

 scientific papers are the following: The Philosophy of Geology 

 and the Order of the State, by John M. Clarke; Geology and 

 public Serviee, by G. 0. Smith ; Plastic Deformation of Gren- 

 ville Limestone, by D. H. Newland; Geological Features at the 

 Champlain Assembly, Cliff Haven, by G. H. Hudson; Some 

 structural Features of a fossil embryo Crinoid, by G. H. Hud- 

 son; Devonian glass Sponges, by John M. Clarke; Primary and 

 secondary Stresses, by John M. Clarke ; The Mining and Quarry 

 Industry of New York State, by D. H. Newland. 



Still another paper entitled "Strand and Undertow Markings 

 of Upper Devonian Time as Indications of the prevailing Cli- 



Am. Jour. Sct. — Fourth Series, Vol. XL VI, No. 273. — September, 1918. 

 22 



