352 



PROCEEDINGS OF THE ACADEMY OF 



[1893. 



Fie. 6. 



ment being measured by a micrometer screw), in the ophthalmometer 

 both glass plates move, and move in different planes, the displacement 

 being deduced from the formula 1=2 T sin (a-b) in which a=the 



cos b 

 angular deviation of the glass plates obtained experimentally. 

 Before developing the formula just mentioned and which is indis- 

 pensable for the working of the ophthalmometer let us first consider 

 the paths of such rays of light as, emanating from a luminous 

 object or its reflected image, pass through its two glass plates, the 

 latter making an angle with each other. 7 



From a consideration of Fig. 7 it will be seen 



^> that as the rays of light from the object a, falling 



upon the glass plate P 1 are projected subjectively 



back to a 1 those falling upon P 2 to a 2 the object will 



be consequently seen double as a 1 a 2 . Now if the two 



images a 1 a 2 are brought into contact with each other tangential ly, 



their total displacement, that is the sum of the displacement of the 



f! ' d rt ' two images to the right and to the left, 



will be equal to the size of the object. 



That such must be the case becomes 



at once apparent, if the object and 



the two images are round bodies as 



represented in Fig. 8, in which a b is 



the displacement to the right, c d the 



displacement to the left and a d the 



diameter of the object. 



It will be observed that while the 

 total displacement — a b + c d=a d the 

 diameter of the object, the distance 

 c b between the outer edges of the 

 two images is twice a d, or twice the 

 diameter of the object. 



Such being the case it is evident 

 that if we can measure the total dis- 

 placement of the two images of the 

 object when the images are in contact we will then obtain the size of 

 the object. 



7 It is unnecessary to say that as long as the two glass plates are in the same 

 plane the luminous object being seen as a single ima^e it is unnecessary to con- 

 sider the paths of the rays of light under these conditions. 



Fig. 7. 



