THE EYE. 



A' B'; so that if the object A B were opaque, and of a form similar 

 to the object A' B', every point of the one would be seen upon a 

 corresponding point of the other. In like manner, if an object 

 A" B" were placed nearer the eye than A B, so that its highest 

 point may lie upon the line c A, and its lowest point upon the line 

 c B, the object being similar in form to A B, would appear to be of 

 the same magnitude. Now it is evident that the real magnitudes 

 of the three objects A" B", A B, and A' B', are in proportion to their 

 respective distances from the eye ; A' B' is just so much greater 

 than A B, and A B than A" B", as c B' is greater than c B, and as 

 c B is greater than c B". 



Thus it appears that if several objects be placed before the eye in 

 the same direction at different distances, and that the real linear 

 magnitudes of these objects are in the proportion of their distances, 

 they will have the same apparent magnitude. 



35. A striking example of this principle is presented by the 

 case of the sun and moon. These objects appear in the heavens 

 equal in size, the full moon being equal in apparent magnitude to 

 the sun. Now it is proved by astronomical observation that the 

 real diameter of the sun is, in round numbers, four hundred times 

 that of the moon ; but it is also proved that the distance of the 

 sun from the earth is also, in round numbers, four hundred times 

 greater than that of the moon. The distances, therefore, of these 

 two objects being in the same proportion as their real diameters, 

 their visual or apparent magnitudes are equal. 



36. It is evident from what has been explained, that objects 

 which have equal apparent magnitudes, and are therefore seen 

 under equal visual angles, will have pictures of equal magnitude 

 on the retina, a fact which proves that the visual angle is the 

 measure of the apparent magnitude. 



37. If the same object be moved successively to increasing 

 distances, its apparent magnitude will be diminished in the same 

 proportion, exactly as its distance from the eye is increased. 

 Thus, if L M (fig. 4), be such an object, its apparent magnitude at 



Fig. 4. 



the distance E M will be measured by the angle L E M, at the 



distance E M' by the angle I/ E M', and at the distance E M" by 



the angle L" E M" ; and when the actual magnitude L 3i bears a 



62 





