TRANSACTIONS OF SECTION A. 523 



other direction, both outwards, so that two pencils of rays are deviated to the 

 full power of the prisms. In the intermediate positions part of the prismatic 

 efl'ect is resolved in a direction at right angles to the line joining the 

 centres of the frames, and can be neglected as only producing parallel displace- 

 -ment of the image, and part is resolved in the direction of this line so as to produce 

 apparent separation or approximation of the images. This amount is read off from 

 the graduation which is constructed on to the following principle. 



Suppose a ray of light XAO perpendicular to the plane of the paper meets the 

 paper at (see figure). Suppose a prism be introduced at A having an angle of 

 deflection B, the ray of light now falls on the paper at B. 



If the piism be rotated through angle |8, the ray now falls on the paper at C. 



Join OB, 00, and resolve 00 into vertical and horizontal co-ordinates CD, OD. 



CD being neglected as described, we wish to find OD the horizontal component 

 of the deflection. 



Since OB = OC 



• ^ = 2£ 

 • * OB OC 



OD 



OA ^ op 



OB OC 



OA 



tan a 



= cos/3 



tan d 



Log cos jS = Log tan a — log tan 0. 



Two other frames are placed in front of the prisms. They contain grooves to 

 told lenses or combinations of lenses, and are graduated so that cylindrical lenses 

 can be set at any desired angle. The frames can be separated or brought nearer 

 with greater accuracy by a wedge, and the distance of the centres of the glasses is 

 marked on the bearing. The whole is carried at the end of a graduated bar which 

 carries a sliding support for an object. This bar is graduated in inches for use in 

 calculation and also in focal lengths of a set of dioptric lenses. 



A third prism is attached so that it can be placed between one of the frames 

 and the object. When it is in position, the rays going through it to the eye 

 appear to come from an object higher than when it is absent. Double vision is 

 produced, and the eyes are left free to find their most comfortable position undis- 

 turbed by any efibrt to make the two images coalesce. 



To use the instrument, the spherical and cylindrical elements of the spectacle 

 required are first found either by some of the ordinary methods or by the ophthalmo- 

 meter described in the Annual Volume for 1880, and the required lenses from the 

 trial case put in the appropriate frames. The third prism is interposed, and an 

 object, such as a vertical line, viewed at reading distance. If the images seen by 

 the two eyes are exactly one above the other, the prismatic adjustment is presum- 

 ably correct, the third prism is removed, and trial is made whether reading can be 

 carried on for some time without fatigue. 



If the images are slightly displaced externally, trial is made whether shifting 

 the centres of the lenses nearer or further off, suffices to bring them into position. 

 If so, the distance is noted and sent as a direction to the optician. If the displace- 

 ment be more than can be corrected by this means, the prisms are rotated till the 

 desired effect is produced, and the amount of prismatic deviation to be given to the 

 proposed spectacles read off. The third prism is removed and reading practised as 

 above. 



4. On the Effects of the Lunar and Solar Tide in increasing the Length of 

 the Sidereal Day. By the Rev. Samuel Haughton, M.D,, F.B.S. 



On the Effects of Oceanic Currents upon Climates. By tlie Rev. Samuel 

 Haughtox, M.I)., F.B.S. See Reports, p. 451. 



