1893.] NATURAL SCIENCES OF PHILADELPHIA. 353 



Let us consider now the development of the formula, 1=2 T 

 sin (a-b) in which I is the total displacement, T the thickness of 



cos b 

 the glass plates, a the angle of incidence or angular deviation, b the 

 angle of refraction. Let ABCD (Fig. 9,) be one of the glass plates 

 placed in front of the objective of the telescope and a c an incident 



ray emanating from the image 

 of the luminous object whose 

 size is to be determined. Such 

 being the case the ray a c, 

 according to the law of refrac- 

 tion, will be bent as c I toward 

 Fig. 8. the perpendicular u K as it 



passes through the glass and away from the perpendicular as 1 1 and 



parallel with a c as it emerges 

 from the glass. The angle 

 a c u will be equal to the angle 

 1 I m, parallel rays falling 

 upon parallel surfaces. Call- 

 ing the angle of incidence a 

 c u, A, and the angle of refrac- 

 tion I c K,B,we will have sin A 



sin B 

 =index of refractional - 524 

 or sin A=sin B, from which 



1^524 

 equation we can obtain the 

 value of B and cos B from 

 trigonometric tables, A being 



Fig. 9. 



ang- 



obtained by observation. Such being the relation of the 

 les of incidence and refraction the point a to the eye of an 

 observer at 1 would appear to be at b, the glass plate effecting 

 therefore a lateral displacement of the point a to an extent a b 

 which is measured by determining the equal distance c f. 



Inasmuch, however, as c f=c I sin c I f , i t follows that if we can 

 determine c I and sin c I f we will obtain c f or its equal a b. As K c 

 =cl cos B, it follows that cI=K C and as K C=the thick- 

 cos B 



