A. MATHEMATICS AND ASTRONOMY. n 



THE COMPUTATION OF ABSOLUTE PERTURBATIONS. 



Mr. G. "VV. Hill, of the American Nautical Almanac office, 

 calls the attention of astronomers to the notable abbreviations 

 which are produced in some parts of the formulae for pertur- 

 bations, by the introduction of the true anomaly as the vari- 

 able according to which integrations are to be executed. 

 Professor Hansen, in his later disquisitions, has substituted the 

 eccentric anomaly as the independent variable in place of the 

 mean anomaly (or, what is the same thing, the time), and he 

 regards this step as constituting a remarkable amelioration 

 of the method. The method proposed by Mr. Hill, on the 

 other hand, employs the same co-ordinates as did Laplace, 

 but makes use of the true anomaly in the elliptic orbit as the 

 independent variable. Astron. JYach., LXXXIIL, 211. 



RECENT OBSERVATIONS ON THE SOLAR PHOTOSPHERE. 



ProfessorLangley, of the Alleghany Observatory, near Pitts- 

 burgh, has devoted some years to the special study of the 

 minute structure of the solar photosphere, especially to the 

 nature of the appearances which Mr. Nasmyth likened to 

 willow leaves, and which Messrs. Stone and Donkin compared 

 to rice grains. The difficulties of observation are, in fact, ex- 

 treme; but Mr. Langley determined to rely only upon the 

 direct telescopic study of the minute components of the photo- 

 sphere, thus forming a distinct point of view from that taken 

 by the spectroscopists. Most of the minute phenomena de- 

 scribed by him are unrecognizable, except with telescopes of 

 large apertures. The equatorial used by him has an object- 

 glass of thirteen inches' diameter, and its full aperture has 

 been available only through the use of a most valuable ac- 

 cessory for such study namely, the polarizing eye-piece, 

 which presents a solar image free from unnatural color, and 

 of any brightness desired. The most formidable difficulty in 

 the way of satisfactory observations arises from the disturb- 

 ances of our own atmosphere, and for this there is no remedy 

 but assiduity and patience. The drawing prepared by Professor 

 Langley, a photograph of which accompanies his memoir, is 

 by far the most minutely accurate of any that has ever yet 

 been published, and most of the minutiae given in it can be 

 seen, he states, only in exceptionally favorable conditions of 



