CURTIS: MODERN THEORIES OF SPIRAL NEBULAE 217 



In all the cases except that of the sphere (for which the cal- 

 culations are exact) it must be emphasized that the calculated 

 stresses are the maximum values on the assumption that no 

 rehef takes place by bending. It will be shown in a later paper 

 that the stresses actually occurring approximate very closely 

 to the values thus calculated. 



SUMMARY 



General equations are derived for the elastic stresses produced 

 by temperature dififerences in spheres, cylinders, and slabs when 

 the temperature distribution is symmetrical about the center, 

 axis, or central plane respectively. 



More specific equations are given for the case of the tem- 

 perature distribution due to uniform surface heating, which is 

 the most important case in practice. 



ASTRONOMY. — Modern theories of the spiral nebulae.^ Heber 

 D. Curtis, Lick Observatory. (Communicated by W. J. 

 Humphreys.) 



In one sense, that theory of the spiral nebulae to which many 

 Unes of recently obtained evidence are pointing, can not be 

 said to be a modern theory. There are few modern concepts 

 which have not been explicitly or impUcitly put forward as 

 hypotheses or suggestions long before they were actually sub- 

 stantiated by evidence. 



The history of scientific discovery affords many instances 

 where men with some strange gift of intuition have looked ahead 

 from meager data, and have glimpsed or guessed truths which 

 have been fuUy verified only after the lapse of decades or cen- 

 turies. Herschel was such a fortunate genius. From the proper 

 motions of a very few stars he determined the direction of the 

 sun's movement nearly as accurately, due to a very happy 

 selection of stars for the purpose, as far more elaborate modern 

 investigations. He noticed that the star clusters which appeared 



^ Abstract of a lecture given on March 15, 1918, at a joint meeting of the Washing- 

 ton Academy of Sciences and the Philosophical Society of Washington. The 

 lecture was illustrated with numerous lantern slides. 



