1 88 1. 13 Trans. N. Y. Ac. Set. 



the stereoscope, therefore, optic diverg-ence 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 Q-) 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, .iccepted 

 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. 6i6 and 827. 



* Nov. 15th. Since the abovp was 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 attain- 

 ment of binocular vision by optic divergen'.e, 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 Gernan, Burckhardt, in i860 or 1861. I have already 

 referred to Helmholtz in this connection {Am. Journal of Scie-ncey Nov., 1881, p. 361), and 

 therefore have claimed no priority in discovering the possibility of this unusual, but still 

 voluntary, employment of the eves. 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. 



(*) Idem, pp. 823, 828. 



(*•> Opt. Phys.. p. 842. 



