543 



SCIENCE. 



sity of optic divergence, when the pictures are binocularly 

 regarded through them, if the stereographic interval ex- 

 ceed 80 mm. As this limit is not unfrequently exceeded, 

 optic divergence is often practiced unconsciously in using 

 the stereoscope. Every oculist is familiar with the mode 

 of using prisms to test the power of the muscles of 

 the eyeballs, for both convergence and divergence of 

 visual lines, and knows that 4 or 5 of divergence is 

 not uncommon. Helmholtz (3) refers to the use of ster- I 

 eographs for the same purpose. 



But familiar as is the production of optic divergence 

 by artificial means, little or nothing seems to have been 

 written in regard to the modification which the possibility 

 of it imposes upon the theory of binocular perspective 

 held by both Wheatstone and Brewster, accepted by 

 most writers on vision since their time, and abundantly 

 reproduced in our text books on Physics.* Of these I 

 have not been able to find one that gives any account of 

 the stereoscope except on the hypothesis that the visual 

 lines are made to converge by the use of this instrument. 

 On the uncertainty attached to the judgment of absolute 

 distance from convergence of visual lines alone, Helmholtz 

 ( 4 ) has written more fully than any one else. It is un- 

 fortunate that no English translation of his masterly 

 work on Physiological Optics has ever been published. 

 Although he gives no analysis of the visual phenomena 

 produced in binocular fusion by optic divergence, his dis- 

 cussion of the judgment of distance would certainly tend 

 to cast some doubt upon the explanation of vision through 

 the stereoscope, as found in our text-books. And yet 

 Helmholtz himself employs Brewster's theory in his 

 mathematical discussion ( 8 ) of stereoscopic projection. 

 This discussion, on the data assumed, is a model of 

 elegance; but it contains no provision for divergence of 

 visual lines. It is strictly applicable to the conditions 

 involved in taking photographs with the binocular 

 camera, and to the projection of images viewed in the 

 stereoscope when the convergence of visual lines is iden- 

 tical with that of the camera axes, but not otherwise. 

 Instead of human eyes we may assume a pair of camera 

 lenses, an interocular distance apart, and a pair of sensi- 

 tized plates behind them. Helmholtz's formulas enable 

 us to determine the stereoscopic displacements in the 

 images projected. If proofs from the negatives thus ob- 

 tained be inverted and placed in front of a pair of eyes 

 in such manner that the visual lines passing through cor- 

 responding photograph points shall bear to each other 

 the exact relation that existed between the secondary 

 camera axes that terminated in them, these two points 

 will appear as one, and nearly at the distance of the real 

 point in space to which the camera axes were converged. 

 The effect is much the same as if the eyes, with normal 

 convergence of visual lines, had been substituted for the 

 cameras. But if the proofs be too near together or too far 

 apart, increase of convergence makes the whole picture 

 seem nearer, while divergence makes it farther. The rela- 

 tion between the different parts having been fixed at the 

 time the picture was taken, increased convergence makes 

 the distance from background to foreground seem less, di- 

 vergence makes it greater. No one can have failed to notice 

 the gross exaggeration of perspective often seen in the 

 stereoscope, when the pictures are so far apart as to make 

 the visual lines parallel or divergent, while the angle be- 

 tween the camera axes, when they were taken, was re- 



Fig. 3. 



latively large. But in no case do these conditions cause 

 variations of such magnitude as Brewster's theory of 

 binocular perspective would demand. This is easily 

 illustrated with Wheatstone's reflecting sterescope. ( 5 ) 

 Suppose the stereograph to represent a concave surface 

 with the opening toward the observer, and that the arms 

 of the instrument are properly adjusted. If they are 

 pushed back, so as to make the visual lines divergent, the 

 cavity apparently recedes and deepens ; if pulled forward, 

 so as to make them strongly convergent, it seems to ap- 

 proach and grow shallow. The apparent diameter of the 

 image enlarges in the first case and diminishes in the 

 second, Wheatstone notices this last variation in the 

 account which he gave of his invention and its applica- 

 tions, in 1852, in the Bakerian lecture before the Royal 

 Society ( 6 ) ; but, strange to say, the variation which is 

 produced in apparent distance and depth under the 

 same conditions seems to have escaped his notice, and 

 the possibility of using his instrument to test the pecu- 

 liarities of binocular vision with divergence of visual 

 lines, seems not to have occurred to him. For the re- 

 fracting stereoscope, however, like Brewster, he constructs 

 a table of apparent distances corresponding to various 

 optic angles, and applicable in using the binocular 

 camera for the purpose of taking slightly dissimilar pic 

 tures of the same object. He adds, (') " when the optic 

 axes are parallel, in strictness there should be no differ- 

 ence between the pictures presented to each eye, and in 

 this case there should be no binocular relief ; but I find 

 that an excellent effect is produced, when the axes are 

 nearly parallel, by pictures taken at an inclination of 7 

 or 8°, and even a difference of 16 or 17 has no de- 

 cidedly bad effect. There is a peculiarity in such images 

 worthy of remark ; although the optic axes are parallel, 

 or nearly so, the image does not appear to be referred to 

 the distance we should, from this circumstance, suppose 

 it to be, but it is perceived to be much nearer." This 

 would not have seemed anomalous to Wheatstone, had 

 he supposed binocular vision possible with divergence of 

 visual lines, and entered into an analysis of the resulting 

 visual phenomena. This analysis will be given in a 

 future paper. 



THE WATERS OF PARIS. 



IN one of the previous numbers, La Nature gives an 

 account of the work of an English observer, Mr. J. Hogg, 

 on the waters of London. But since 1850, Mr. Hassall", 

 at the request of the inhabitants of London, examined the 

 degree of purity of the potable waters of that city, and 

 more recently, Professor Farlow, of Boston, make an anal- 

 ogous work at the request of the citizens of that city. b 

 M. A. Gerardin r , however, has studied this question with 

 a certain authority, by observing the cryptogamic vegeta- 

 tion in small streams of water which receive the waste 

 products from the factories and manufactories on their 

 banks. M. Gerardin observed that such industry favored 

 the development of certain particular species which were 



( 3 ) Helmholtz, Optique Physiologique, pp. 616 and 827. 

 («) Ditto, pp. 823, 828. 



( 6 ) For description see Phil. Mag., s. 4, vol.. III., June, 1852, p. 506. 



(") Phil. Mag. s. 4, vol. III., p. 5°4- 



(') Ditto, p. 514. 



(") Opt. Phys., p. 842. 



* Nov. :5th. Since the alovewas put in type, I have received from Prof. 

 C. F. Himes, of Carlisle. Pa., an article written by him in 1862, in which 

 he mentions his successful attainment cf binocular vision by optic diverg- 

 ence, and criticises Brewster's theory of distance in relation to the stere- 

 oscope. Though his observation was independent, as my own was also, I 

 find that he was preceded by a < '.erman, Burckhardt, in i86oori86i. I 

 have already referred to Helmholtz in this connection (Am. Journal of 

 Science, Nov. 1881, p. 361) and therefore have claimed no priority in dis- 

 covering the possihililv of this unusual, but still voluntary , employment 

 of the eyes. Ft is the more remaikable that in our text-books the assump- 

 tion should be so universal, that convergence of visual lines is a necessity 

 in binocular vision for the determination of the apparent point of sight. 



