THE STEREOSCOPE : ITS THEORY. 203 



upper base. When the latter is made an object of attention, two 

 dots are seen on the lower base, which apparently broadens out 

 on the two sides ; but the moment the attention is concentrated upon 

 them, unless the observer is a little skilled in indirect vision, they 

 fuse into one, and four instead of two projections are seen at the 

 upper base, which in turn has broadened out. Indeed, very little 

 skill is needed to perceive the distinct duplication of the entire 

 upper base. At the middle of the field of view is an inclined black 

 parallelogram, on which no duplication of any part can be perceived, 

 except by a very steady gaze or by comparison with the black cir- 

 cles above and below ; and these in turn are made to appear at 

 different distances from the observer. The circular arc and straight 

 line, each marked a, combine into a distorted parabola, in which the 

 concavity is perfect at the middle, but at the top and bottom it breaks 

 into two separate lines. The resultant of the lines marked b is quite 

 as distinctly curved, but many persons will fail to notice any duplica- 

 tion at all; and this remark applies still more forcibly to the resultant c. 

 The group d forms a warped surface ; but, if the resultant line at its 

 right be fixedly examined, it will be seen as an oblique cross, the com- 

 bination being effected only by motion of the eyes. The group e pre- 

 sents still greater difficulties. The pair f are nearly horizontal, and 

 are coalescent at the middle, but not combined at the extremities ; 

 each component hence appears no longer straight. The arrows at the 

 left point obliquely, some toward and some from the neighborhood of 

 the observer ; but, if the gaze be rigidly directed to the vertical rod on 

 which they are fixed, a pair of well-practiced eyes will perceive some 

 of them to have very mobile double heads. The circles x, y, and z 

 have a common axis, and are successively nearer to the observer ; x 

 and z are highly lustrous, and, when either is regarded separately, y is 

 by indirect vision seen slightly double. 



The two halves of this stereograph are strikingly dissimilar, but the 

 principle which it illustrates enables us to secure stereoscopy with a 

 pair of absolutely similar figures by so adjusting these in position that 

 advantage may be taken of the almost spherical surface of the back of 

 each eye." The geometric explanation of this is un suited to the present 

 article.* It may be sufficient to state that, if the two pictures be op- 

 positely inclined to the visual lines, instead of being directly across 

 these, the retinal images must be dissimilar, and the subjective combi- 

 nation of these must hence present the appearance of relief, which 

 may be varied at will by varying the inclination of the cards. 



The theory of associated muscular action which has been illus- 

 trated, while undoubtedly true, is still not sufficient by itself to explain 

 all the phenomena of stereoscopy. The perception of distinct relief 

 is possible when the card is illuminated with the electric spark. No 

 motion of the eyes is attainable during so minute an interval. It is 



* See "American journal of Science" for April, 1882, p. 297, and May, 1882, p. 359. 



