108 Mr Swan on Methods of ascertaining 



From which, by substitution, we obtain 

 tan i {(f>' - •+') = cot i (^ + 5) cot i (^ + 2 a - 3) tan i d. 

 Having found i (jp' — %)/') by this formula, we have 



<P' = i (^' + •+') + 4 (P' -•+') = ^ ^ + ^ (?' ~ +') 5 and 



rrii sin A sin -d ^ 



Then fi — -~ or ^o, = -r—v-,.* 



' sin <p '^ sin "v^ 



Both these values of fA may be calculated, in order to check 

 the accuracy of the observations and calculation. 



I have thought proper to describe this method of finding 

 refractive powers, as it involves a new application of the sex- 

 tant to stereometry, which may often be found useful when 

 other goniometers cannot be obtained ; and as it may enable 

 individuals to ascertain refractive powers with considerable 

 accuracy, who might otherwise be prevented from doing so by 

 the want of apparatus specially intended for that purpose. 



The applicability of the sextant as a goniometer, is neces- 

 sarily limited by the graduation of the instrument not ex- 

 tending far beyond 120° ; and, therefore, not permitting the 

 angle of a prism, greatly exceeding 60°, to be measured. This 

 range is, however, amply sufficient for determining the angles 

 of such prisms as are generally used for finding the index of 

 refraction. 



II. The second method of finding refractive powers, which 

 is now to be explained, was suggested, as has been already 

 noticed, by the use of the sextant ; and it depends for its effi- 

 ciency on the well known optical principle of that instrument, 

 which is, that the deviation of a ray of light, after two re- 

 flections in the same plane, is double the inclination of the 

 reflecting surfaces. If, then, two plates of glass A B, C D 

 (figs. 3, 5, and 6) be applied to the faces of the prism p r Sy 

 as represented in the figures, a ray of light Imno being re- 

 flected in the glasses at the points m n, will suffer a deviation 

 ntm double the inclination of the glasses A B, C D, or double 

 the angle p r s of the prism. The angle n t m^ and also the 



* For the investigation of similar formulae, the reader is referred to Codding- 

 ton's Optics, chap, vii., or Biot, Traite de Physique, vol. iii. Dioptrique. 



