length of a thick mirror 123 
The focal length was also measured by Gauss’s method. 
The mean value of # was found to be —11°61 cm. Then, by (5), 
_ p(p—2) _ 20-08 x 31-69 
i Spe = Bry ~ 1229 om. 
pe) 20038 x CEEGn) i 
By (6), ea rsares SETH = — 4:50 cm. 
§9. The goniometer method. This method is similar to the 
goniometer method for measuring the focal length of a lens 
system*. Let GF (Fig. 4) be an object of length s in the focal 
Fig. 4. 
plane. Then, if GZ, drawn parallel to the axis, cuts the principal 
plane HZ in Z, the incident ray GZ will give rise to the emergent 
ray ZF. If the angle ZF'H be @, then, for small] angles, 
6 = ZH/HF =s/f. 
Or Pee a eee (9) 
Since G is in the focal plane, all the rays starting from G which 
emerge from the system are, on emergence, parallel to ZF’; it is 
supposed, of course, that the aperture of the system is small 
enough to prevent aberration from being conspicuous. If these 
emergent rays are received by a goniometer, which has been 
focused for “infinity,” an image of G@ will be formed on the cross- 
wire of the goniometer, if the arm of the goniometer is properly 
* G. F. C. Searle, Proceedings of the Optical Convention, Vol. 11. 1912, p. 165. 
