A. MATHEMATICS AND ASTRONOMY. 23 



notably less than when determined by means of the sun's 

 transit over the meridian. The large discordances between 

 the numbers adopted by different astronomers to represent 

 the solar diameter are due, as he concludes, both to irradi- 

 ation proper, and to the persistency of luminous impressions, 

 the nature of the retina being such that the image of any 

 point upon it is subject to an expansion, or an increase in its 

 diameter. As this irradiation would, therefore, affect the in- 

 tensity of the brightness of minute points, he proceeds first 

 to investigate that subject. The expansion is due, he con- 

 cludes, to the deformation of the cone of rays, after passing 

 the crystalline lens of the eye, and also to the imperfect ad- 

 justment of the eye for all distances, and, thirdly, to the ordi- 

 nary phenomena of diffraction. To these must also be added 

 the influence of the tremulous condition of the atmosphere, 

 causing a general deviation of the light of the fixed stars. 

 As regards the expansion of the image resulting from the 

 imperfections of the eye, he has made a number of measure- 

 ments upon the visibility of stars close together, and con- 

 cludes from these that the mean diameter of the exagffera- 

 tion caused by the human eye is about 3 minutes of arc, 

 when the pupil has its maximum opening, and not less than 2 

 minutes when the pupil is contracted. These considerations 

 serve to explain why the horns of Venus are invisible to the 

 naked eye. In order to determine the enlargement produced 

 by a telescope, he turns it upon certain double stars, and finds 

 that the correction for the expansion is constant, and equal 

 to the least opening of such binary systems as are resolvable 

 with a given magnifying power. In respect to the atmos- 

 pheric perturbations, he finds its effects to vary from between 

 4 to 15 seconds, depending upon the magnitude of the star. 

 In applying his conclusions, drawn from the observations of 

 fixed stars, to the case of the solar diameter, he concludes 

 that the latter, as ordinarily accepted, is subject to a correc- 

 tion for irradiation of from nothing to 1.7"; to a constant 

 correction for expansion of 2.3"; and to a correction for at- 

 mospheric expansion varying between and 10". In order 

 to deduce the angular diameter of the sun at its mean dis- 

 tance from the earth, from an observation of its meridian 

 transit, it is necessary to multiply 14.345 by the number of 

 seconds contained in the apparent error of the duration of 



