6io 



SCIENCE. 



jecting lines be drawn from A, B, P and Q to plane IV. 

 It is required to find what relation exists between the 

 horizontal displacements of the projections, a from b, p 

 from q, a' from b', p' from q'. 



Since CC is horizontal, the projected horizontal dis- 

 placements will be the same for all elevations of B and 

 O; these may hence be taken as points on the horizontal 

 trace of plane I. 



Since EC = EC, we have 



Pq 2 -=Pq'a = Ab 2 =Ab 2 



.-. pq = p q'=abf=a b'. 



This equality will not exist if E be not midpoint be- 

 tween C and C. It is true for all points in planes I and 

 II respectively, through which straight lines can be 

 drawn to E. 



Let now C C, fig. 2, be the distance between two 

 camera lenses, for example id""; A and B, objects in the 

 foreground and background of a landscape, on the me- 

 dian line from E; Aa, Aa', Bb, Bb secondary axes ex- 

 tending to the sensitized plate. The stereoscopic dis- 

 placements on the photographic negative, a b and a' b', 

 are equal to each other and to those of any other points, 

 P and 0, related to the midpoint E, as they are in Fig. r 



The camera axes to A make a known angle, 6, with each 

 other. Let E be midpoint also between a pair of eyes, 

 R and L. If proofs from the negative be inverted and 

 placed in front of R and L in such manner that the vis- 

 ual axes through a, and a', shall form with each other an 

 angle, a, equal to 0, then A, and B, are, as nearly as pos- 

 sible, the apparent positions of foreground and back- 

 ground respectively. If a exceed 0, A, will be nearer, if 

 a be less than 9, A- will be farther ; and this will be true if 

 a =o, or a<o. Either of these last conditions is at- 

 tained by simply increasing the distance a,a',. Whether 

 the visual axes are convergent, parallel, or divergent, the 

 subjective effect is that of the union of R and L into a 

 binocular eye which, for the geometrical reasons just 

 given, can be nowhere else than at the midpoint, E. In 

 this the dissimilar retinal images are superposed."£lf 

 those of the points a! and a', coincide, b, appears to The 

 right eye projected outward on the right, to the left eye 

 an equal distance outward on the left ; to the combined 

 eye it is a homonymous double image. Let A 2 be the 

 external projection of the combined images of a, and a',, 

 as seen by the binocular eye at E 2 ; if a = 0, the distance 

 E 2 A 2 is equal to RA, or LA,, which differs but little from 

 EA, unless a be large ; it has been drawn equal to EA,. 

 Then B, and B' 2 will be the external projections of the 

 uncombined images of b a and b' 2 . If the attention be 



transferred to the background, the angle between the vis- 

 ual axes must be diminished by relaxing the internal rec- 

 tus muscles, and this instantly suggests greater remote- 

 ness of the point of sight. The retinal images of b 2 and 

 b'a coalesce and are projected to the more distant exter- 

 nal point between B 2 and B' 2 , while those of a 2 and 

 a' a cross slightly to opposite sides and are projected as a 

 heteronymous double image at its proper distance. The 

 ratio of E 2 A 2 to EA, must depend upon the variation in 

 muscular tension due to the difference between the angles 

 and a. The duplication of the images of the back- 

 ground points when the foreground is regarded, and vice 

 versa, is easily perceived if a properly constructed dia- 

 gram is viewed in the stereoscope, provided the observer 

 be attentive to his own sensations, examining each point 

 of the combined picture separately instead of regarding 



the total effect at once. Let Figures 3 and 4 be exam- 

 ined in the stereoscope, by resting the edge of the page 

 on the cross-bar of the instrument at the proper distance 

 in front of the semi-lenses. In each case, when the 

 foreground circle is seen single, the background dot is 

 seen double, and viceversa. When the background cir- 

 cles of one figure are combined binocularly, those of 

 the other are seen separately by monocular vision. Ax- 

 ial convergence is necessary to combine the circles of Fig. 

 4. The combined image appears nearer, smaller, and 

 less tall in proportion to its base than the combined im- 

 age of Fig/3, which requires axial divergence. The 

 stereoscopic displacement is the same in both figures, 

 and is measured by the distance between the centre of 

 the large circle and that of the small one within it. The 

 stereographic interval for the background is 90 mm. in 



