234 Scientific Intelligence. 



tions of some of the optical constants of a 12-inch Taylor tele- 

 scope objective. The geometrical data are given to three-figure 

 accuracy and are susceptible, perhaps, to a maximum of ten times 

 this precision. The calculations of focal lengths are carried out 

 to seven-figure accuracy, that is to some 1000 times the precision 

 warranted by the data ; it is three or four hundred thousand 

 times as great precision as is deemed important by the designer 

 himself, if we infer that he expected to make the ratio of focal 

 length to aperture the standard for telescopes of this size. Never- 

 theless, this incommensurate labor of calculations is necessary in 

 order to deduce a sufficient value, to two figures only, of the 

 spherical aberration. 



The other case is equally striking. The spherical aberration of 

 the same objective is calculated to a two-figure precision, which 

 is all that is of practical significance, by a tedious computation 

 with seven-figure logarithms by application of Seidel's analysis 

 and with the disappointing error of one hundred per cent. These 

 considerations are enough to show that there is some radical 

 defect in a method which demands such efforts for such meager 

 returns. Probably there is no hope of material improvement 

 until the mathematician informs himself thoroughly as to the 

 relative importance of the magnitudes which enter his analysis 

 and then deals with the physical realities of wave surfaces and 

 refracting surfaces instead of the unnecessary fictions of rays 

 and of radii of lens sm'faces. c. s. h. 



8. Chemische Krystallographie ; von P. Groth. Dritter Teil. 

 Aliphatische und Hydroaromatische Kohlenstoff-verbindungen. 

 Pp. iv, 804, mit 648. Text figuren. Leipzig, 1910 (Wilhelm 

 Engelmann). — This monumental work on Chemical Crystallog- 

 raphy begun in 1906 has now reached its third part, or as esti- 

 mated, three-quarters of the whole. It is devoted to the aliphatic 

 and hydroaromatic hydrocarbons. The whole makes a work of 

 800 pages, with perhaps 1200 or more individual compounds, 

 whose crystallographic and optical constants are given with great 

 thoroughness. In a large number of cases the crystal form is 

 illustrated by figures. The congratulations of those immediately 

 interested are due to the veteran author for his success in carry- 

 ing through a work of such magnitude and importance. 



II. Geology and Natural History. 



1. United States Geological Survey, Thirty-first Annual Re- 

 port (1909-1910) of the Director, George O. Smith. Pp. 131 

 with two plates. Washington, 1911. — This report contains a 

 statement of the work done by the various divisions of the 

 Survey during the fiscal year ending June 30, 1910. The pro- 

 gress in land classification consisted in, first, the preparation of 

 withdrawals covering power sites and coal, oil, gas, and phos- 

 phate lands ; second, the classification of withdrawn lands and 



