668 SIR DAVID BREWSTER ON THE KNOWLEDGE OF 



Let R be the right eye and L the left eye, and when at E"' let them be strained 

 so as to unite the points A, B. The united image of these points will be seen at 

 the binocular centre D'", and the united lines A C B C will have the position 

 D'" C. In like manner, when the eye descends to E'", E', E, the united image 

 D'" C will rise and diminish, taking the positions D" C, D' C, DC till it dis- 

 appears on the line C M, when the eyes reach M. If the eye deviates from 

 the vertical plane GMN the united image will also deviate from it, and is 

 always in a plane passing through the eye and the line G M. 



If at any altitude E M the eye advances towards A C B in the line E G, the 

 binocular centre D will also advance towards A C B in the line E G, and the 

 image D C will rise and become shorter as its extremity D moves along D G, 

 and after passing the perpendicular to G E it will increase in length. If the 

 eye, on the other hand, recedes from A C B in the line G E, the binocular centre 

 D will also recede, and the image D C will descend to the plane C M and 

 increase in length. 



The preceding diagram is, for the purpose of illustration, drawn in a sort of 

 perspective, and therefore does not give the true positions and lengths of the 

 united images. This defect, however, is remedied in Fig. 3, where E, E', E', E'" 

 is the middle point between the two eyes, the plane GMN being, as before, 

 perpendicular to the plane passing through A C B. Now, as the distance of 

 the eye from G is supposed to be the same, and as A B is invariable as well as 

 the distance between the eyes, the distance of the binocular centres O, D, D', 

 D", D'", P, from G will also be invariable, and lie in a circle D P whose 

 centre is G, and whose radius is G 0, the point being determined by the 



formula G 0=G D = -r-^ ^ r Hence, in order to find the binocular centres D, 



A > + iv JU 



D', D", D'", &c., at any altitude E, E' &c., we have only to join E G, E'G, &c., 

 and the points of intersection D, D', &c., will be the binocular centres, and the 

 lines D C, D' C, &c., drawn to C, will be the real lengths and inclinations of the 

 united images of the lines AC, B C. 



When G is greater than G C there is obviously some angle A, or E" G M 



C* f 1 



at which D" C is perpendicular to G C. This takes place when cos. A = -, -=-, 



When coincides with C, the images C D, C D', &c., will have the same positions 

 and magnitudes as the chords of the altitudes A of the eyes above the plane 

 G C. In this case, the raised or united images will just reach the perpendicular 

 when the eye is in the plane G C M, for since G C=G 0, cos. A=l, and A=0. 



When the eye at any position, E" for example, sees the points A and B 

 united at D", it sees also the whole lines A C B C forming the image I)"C. The 

 binocular centre must, therefore, run rapidly along the line I)" C : that is, the 

 inclination of the optic axis must gradually diminish till the binocular centre 



