54 COSMOS. 



Telescopes, although in a much less degree, unfortunately 

 also give the stars an incorrect and spurious diameter ; but, 

 according to the splendid investigations of Sir William Her- 

 echel,* these diameters decrease with the increasing power 

 of the instrument. This distinguished observer estimated 

 that, at the excessive magnifying power of 6500, the appar- 

 ent diameter of Vega Lyrae still amounted to 0"36. In ter- 

 restrial objects, the form, no less than the mode of illumina- 

 tion, determines the magnitude of the smallest angle of vision 

 for the naked eye. Adams very correctly observed that a 

 long and slender staff can be seen at a much greater distance 

 than a square whose sides are equal to the diameter of the 

 staff. A stripe may be distinguished at a greater distance 

 than a spot, even when both are of the same diameter. Ara- 

 go has made numerous calculations on the influence of form 

 (outline of the object) by means of angular measurement of 

 distant lightning conductors visible from the Paris Observa- 

 tory. The minimum optical visual angle at which terres- 

 trial objects can be recognized by the naked eye has been 

 gradually estimated lower and lower from the time when 

 Robert Hooke fixed it exactly at a full minute, and Tobias 

 Mayer required 34" to perceive a black speck on white pa- 

 per, to the period of Leeuwenhoek's experiments with spi- 

 der's threads, which are visible to ordinary sight at an angle 

 of 4" - 7. In the recent and most accurate experiments of 

 Hueck, on the problem of the movement of the crystalline 



image of each star of the group on the retina, and substitute a small 

 circle for each point of the former general image ; these circles will 

 impinge upon one another, and the different points of the retina will 

 be illumined by light emanating simultaneously from many stars. A 

 slight consideration will show, that, excepting at the margins of the 

 general image, the luminous air has, in consequence of the superposi- 

 tion of the circles, the same degree of intensity as in those cases where 

 each star illumines only one single point of the retina ; but if each of 

 these points be illumined by a light equal in intensity to the concen- 

 trated light of a star of the seventh magnitude, it is evident that the 

 dilatation of the individual images of contiguous stars can not prevent 

 the visibility of the whole. Telescopic instruments have the defect, 

 although in a much less degree, of giving the stars a sensible and spu. 

 rious diameter. We therefore perceive with instruments, no less than 

 with the naked eye, groups of stars, inferior in intensity to those which 

 the same telescopic or natural sight would recognize if they were iso- 

 lated." Arago, in the Annuaire du Bureau des Longitudes pour Van 

 1842, p. 284. 



* Sir William Herschel, in the Philos. Transact, for 1803, vol. 93, 

 p. "225, and for 1805, vol. 94, p. 184. Compare also Arago, in the An 

 nuairepour 1842, p. 360-374. 



