1881. 13 Trans. Ne Ve AG. SEZ. 
the stereoscope, therefore, optic divergence is nearly always necessary. 
To ascertain the extent to which this is counteracted by the semi- 
lenses of our best stereoscopes, 30 pairs of these were kindly loaned me 
by Mr. H.’T. Anthony, of New York. With very slight variation, their 
focal length was found to be 18.3 cm., and their deviating power not 
sufficient to prevent the necessity of optic divergence, when the pictures 
are binocularly regarded through them, if the stereographic interval 
exceed 80 mm. As this limit is not unfrequently exceeded, optic diver- 
gence 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 (*) refers to the use of stereographs 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 instru- 
ment. On the uncertainty attached to the judgment of absolute dis- 
tance from convergence of visual lines alone, Helmholtz (*) has written 
more fully than any one else. It is unfortunate that no English trans- 
lation of his masterly work on Physiological Optics has ever been pub- 
lished. Although he gives no analysis of the visual phenomena pro- 
duced in binocular fusion by optic divergence, his discussion 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 (®) of stereoscopic projection. This discussion, 
on the data assumed, is a model of elegance; but it contains no pro- 
vision for divergence of visual‘lines. It is strictly applicable to the 
conditions involved in taking photographs with the binocular camera, 
(3?) Helmholtz, Optique Physiologique, pp. 616 and 827. 
* Noy. 15th. Since the above was put in type, I have received from Prof. C. F. Himes, of 
Carlisle, Pa., an article written by him in 1962, in which he mentions his successful attain- 
ment of binocular vision by optic divergence, and criticises Brewster’s theory of distance in 
relation to the stereoscope. Though his observation was independent, as my own was 
also, I find that he was preceded by a German, Burckhardt, in 1860 or 186r.__[ have already 
referred to Helmholtz in this connection (Am. Yournal of Science, Nov., 1881, p. 361), and 
therefore have claimed no priority in discovering the possibility of this unusual, but still 
voluntary, employment of the eyes. It is the more remarkable that in our text-books the 
assumption should be so universal, that convergence of visual lines is a necessity in binocular 
vision for the determination of the apparent point of sight. 
(4) Idem, pp. 823, 828. 
(®) Opt. Phys., p. 842. 
