THEORY OF THE REFLECTING EXTENSOMETER. - 105 
slight rotation about the pivots the scale will be seen in the field 
of view of the telescope, and a reading may be taken, which say 
is #,. Then rotating the mirror and pivots about the axis so that 
the two pivots exchange positions, and the line joining them is 
consequently again parallel to the scale, a second reading A, is 
obtained. If then « denote the angle between the line joining the 
pivots and a plane at right angles to the axis, and since ¢ is so 
small that the distinction between sine tangent and arc ceases to 
be significant, it is easy to see that 
_ &,- Rf, 
4L 
(9) 
L as before denoting the distance of the scale from the mirror. 
In this way it was found that the errors of the line joining the 
pivots were as follows :— 
Number of Apparatus 1 2 3 4 
Angular Error -l’ +2) -7 +16} 
Absolute errorin 14mm. -004 ‘010 -028 -067 mm. 
The plus sign, when the handle isdownward and when also the 
observer is looking into the mirror, denotes that the standard 
carrying the right hand pivot is too long. The absolute error 
given is for the width of the mirror, viz. for 14 mm. The fact 
that it is nowhere 0-1 mm. is evidence of the excellence of the 
manufacture. 
8. Parallelism of the rotation-axis of the mirror to the knife- 
edges of the prism.—When the angle « referred to in the last 
section has been obtained, the relation between the rotation-axis 
of the mirror and the axis of the knife-edged prism may readily 
be found by reading the scale by reflection, say with the pivots 
and scale parallel to the knife-edges : then turning the knife-edges 
round through 180° and reading the scale again. A second similar 
Set of readings with pivots and scale at right angles to the knife- 
edges is necessary to determine the defect in both planes. After 
allowing for the difference 4: between the readings, the residual 
difference if any, D say, will furnish the required inclination y of 
the axes.- The formula obviously is ; 
