94 Mr. J. J. Guest on the Strength of 



reflexions at each of the mirrors. The distance between the 

 mirrors will be neglected, as it should be small compared 

 with the distance from the specimen to the scale, or else a 

 lens should be placed between the top mirror and the scale to 

 render the light proceeding from the latter parallel. In the 

 apparatus as rigged for the tests, the distance between the 

 mirrors was 2 or '6 inches, and the distance to the scale over 

 200, so that this condition was satisfied. 



In fig. 13, OC is the axis of the specimen, OA is perpen- 

 dicular to OC and in the plane of the optical axis of the 

 telescope, OB is perpendicular to OA and OC. The line 



7T 



OK, coordinates - — a l5 or a? 1} 0, z 1 , is the optical axis 



of the telescope, and cuts a sphere of unit radius whose 

 centre is in the point K. The normal to the mirror 

 nearest the telescope is represented by OP, coordinates 



IT 



jr + # 1; fa ; or £ p 7) h £i« The reflexion of OK in the mirror 



is OL, coordinates a 2 , fi 2 , or x 2 , y 2 , z 2 , so that OL represents 

 the path of the ray between the mirrors. The normal to the 



7T 



upper mirror is represented by OQ, coordinates t + $2> fa, or 



£2? V21 £2 j this line is shown drawn in the same octant as the 

 other lines for the sake of clearness, though it should actually 

 be reversed ; but a little consideration will show that, by 

 considering the light to come in the direction LO, it will, 

 after reflexion in the second mirror, proceed in the direction 

 OM, coordinates 6, (j> or x, y, z\ while the actual ray of light 

 will merely be in the direction KO, instead of OK. The 

 quantities a; the error of setting the telescope in altitude; U 

 6 2 the errors of setting the mirrors ; and fa and fa, the azi- 

 muthal movements of the mirrors, are supposed small, fa 

 being considerably larger than any of the others. 

 Then x± = 1 nearly, s 1 is small ; 



z 2 =l nearly, x 2 and y 2 are small ; 



x =1 nearly, y and z are small. 



We have to find 6 and <p or x, y, z. 

 Also the coordinates of 



a 2 

 K are x x y t z or l-~5 ®> a i- 



P are & Vi £i> 



sin j- + 6 l cos fa -, suit- +&! sin fa ; cos t- + &i ; 



