LIMIT OF ACCURACY IN THE MIRROR METHOD. 13 



case the scale may be curved along a cylindrical surface, the axis 

 of which coincides with the axis of suspension of the mirror. In 



this case the expression 



x-p 



does not represent the tangent of 



the double of the deviation, but the double of this deviation 

 itself. 



The scale is ordinarily divided in millimetres. The scales on 

 paper cannot be considered as sufficient for accurate measurements ; 

 scales on ivory or on metal are better, but metal scales are dif- 

 ficult to illuminate. 



The divisions may be ruled on glass, and lighted from behind 

 by a reflecting mirror. If the glass is transparent, the lines appear 

 dark on a light ground ; if the glass is silvered, and the division 

 is traced on a layer of silver, the lines appear bright on a dark 

 ground. 



670. In certain circumstances (for instance, in observing 

 phenomena which extend over a long period and which require 



Fig. 131. 



permanent installation, like variations of terrestrial magnetism), it 

 is useful to have a mark in the field of the telescope independent 

 of the cross wires. For this purpose we place, below the movable 

 mirror, a perfectly similar fixed mirror. If the two mirrors were 

 absolutely parallel, the two images of the scale, one fixed and the 

 other movable, would appear superposed; but it is sufficient to 

 slightly incline the fixed mirror to separate them. 



The angle between the vertical planes passing through the 

 perpendiculars to the two mirrors is given by the difference of 

 the numbers of the divisions which coincide with the vertical 

 cross wire ; this difference remains the same when the telescope or 

 the scale for any cause has been slightly displaced. The instrument 

 carries thus its own fixed point, and the relative immobility of the 



