72 Royal Society : — 



coalescence a concave line. The two photographic images will have 

 all their vertical lines bent in the same mannei", and the stereoscope 

 will give the illusion of a pictnre represented on a concave surface. 



when we look at natural objects, the optical axes have to con- 

 verge more for the nearest than for the furthest, in order to obtain 

 a single vision by bringing the same object on the centre of each 

 retina ; therefore by habit we judge of the distances by the angle 

 formed by the optical axes required to obtain a single vision. Again, 

 while we look at one object, while other objects in the same line are 

 situated before and behind that object, we have the sensation of 

 their double images on the two retinae. The double images of nearer 

 objects are situated in the following order : one on the right of the 

 centre of the right retina, and the other on the left of the centre of 

 the left retina ; and the double images of further objects, one on the 

 left of the right retina, and the other on the right of the left retina. 



In looking at the two pictures in the stereoscope, we have to con- 

 verge the optical axes on one poijit which is beyond the plane of the 

 pictures, so that two of their correspondent or similar points appear 

 respectively on the two lines forming the angle of convergence of the 

 optical axes, and each of these points is represented on the centre 

 of one retina. As the two corresponding points of the two pictures 

 are laterally nearer each other for the first plane and more distant 

 for the receding plane, it follows that the optical axes have to con- 

 verge beyond the plane of the pictures on a nearer point for the first, 

 and on a further point for the last. Therefore, the angle of con- 

 vergence by which similar points of the two pictures appear on each 

 axis and consequently fall on the centre of each retina, conveys the 

 sensation of their respective distances ; more convergence indicates 

 less distance, and less convergence more chstance. All the other 

 corresponding points of the two pictures which are not on the op- 

 tical axes or on similar points of the two retinae, form double images ; 

 and when we look at one point, all the points of nearer and further 

 planes appear double in the same order on the two retinae, as when 

 we look in like manner at natural objects ; and the situation of double 

 images seen through the stereoscope indicates the distances of the 

 objects they represent, according as one is on the right of the right 

 retina and the other on the left of the left retina, or one on the left 

 of the right retina and the other on the right of the left retina. 



This being explained, it is easy to understand what will be the 

 stereoscopic result of vertical lines represented as curved, and having 

 their concavities turned toward each other. The two correspondent 

 points of the top and bottom of the two concave lines, being nearer 

 each other, will require more convergence than the two correspond- 

 ent points of the centres of the concave lines, and will appear nearer, 

 whilst the two points of the centre requiring less convergence will 

 appear further ; the intermediate points from the centres to the extre- 

 mities of the two bent lines will appear gradually less distant, there- 

 fore the coalescence of the two lines bent laterally will produce the 

 illusion of a single line conspicuously concave, in a vertical plane at 

 right angles with the plane of the two separate lines. 



Having demonstrated that the semi-lenses of the stereoscope, like 



