MAGNITUDE OF THE IMAGE. 



the retina would in this case be the ^th part of an inch ; yet 

 such is the exquisite sensibility of the organ, that the object is in 

 this case distinctly visible. 



If the disk were removed to twice the distance here supposed, 

 the angle of the cone c would be reduced to half a degree, and the 

 diameter of the image on the retina would be reduced to one-half 

 its former magnitude, that is to say, to the ^th part of an inch. 

 If, on the other hand, the disk were moved towards the eye, and 

 placed at half its original distance, then the angle c of the cone 

 would be 2, and the diameter of the picture on the retina would 

 bo double its first magnitude, that is to say, the jfgth of an inch. 



In general, it may therefore be inferred that the magnitude of 

 the diameter of the picture on the retina is increased or diminished 

 in exactly the same proportion as the angle of the cone c, formed 

 at the centre of the eye, is increased or diminished. 



33. This angle is called the visual angle or apparent magnitude 

 of the object ; and when it is said that a certain object subtends at 

 the eye a certain angle, it is meant that lines drawn from the 



. extremities of such object to the centre of the eye form such angle. 

 The apparent magnitude of an object must not be confounded 

 with its apparent -superficial magnitude, the term being invariably 

 applied to its linear magnitude. The apparent superficial magnitude 

 varies in proportion to the square of the apparent magnitude. 



'Thus, for example, when the disk A B is removed to double its 

 original distance from the eye, the apparent magnitude, or the 

 angle c, is diminished one-half, and consequently the diameter 

 a b of the picture on the retina is also diminished one-half; and 

 since the diameter is diminished in the ratio of 2 to 1, the super- 

 ficial magnitude of the image, or its area, will be diminished in 

 the proportion of 4 to 1. 



34. It is clear from what has been stated also, that when the 

 same object is moved from or towards the eye, its apparent 

 magnitude varies inversely as its distance ; that is, its apparent 

 magnitude is increased in the same proportion as its distance is 

 diminished, and vice versd. 



It is easy to perceive that the objects which are seen under the 

 same visual angle will have the same apparent magnitude. Thus 

 let A' B' (fig. 3), be an object more distant than A B, and of such a 

 magnitude that its highest point A' shall be in the continuation of 

 the line c A, and its lowest point B' in the continuation of the line 

 c B. The apparent magnitude of A' B' will then be measured by 

 the angle at c. This angle will therefore at the same time 

 represent the apparent magnitude of the object A B and of the 

 object A' B'. It is evident that an eye placed at c will see every 

 point of the object A B upon the corresponding points of the object 



61 



