and an optical Illusion, 199 



perfect. Persons who have not this command of their eyes 

 may succeed in obtaining the proper convergence by looking 

 at a finger held about fifteen inches from the face, while stand- 

 ing ten feet from a wall with figures twenty inches apart. 



Apparent distances of objects. — It seems that we judge of 

 moderate distances by a kind of triangulation, the distance 

 between the eyes being a constant base-line. In order to put 

 this to the test, I have several times made the actual measure- 

 ments as in the following cases : — 



Having measured the distance between my eyes, 2*6 inches, 

 the distance between the figures on the wall 21 inches, the 

 distance from the wall 10 feet, the distance of the illusive 

 image was calculated to be 14"7 inches, when it had been mea- 

 sured as near as may be 14<'5 inches. In a second experiment 

 we endeavoured to ascertain the distance of the observer from 

 the wall. The other data were — 



Distance between the eyes . . 2*6 inches. 



Distance between the figures . 21 inches. 



Distance of illusive image . . 16*75 inches. 



Calculated distance of the wall . 12*5 feet. 



Measured distance of wall . . 13*15 feet. 



When it is recollected that the observer is obliged to range 

 lengthwise on his measure while he determines the distance 

 of the aerial image, and that the base-line is only 2' 6 inches, 

 the above results appear quite as accurate as we ought to an- 

 ticipate. 



There is peculiar beauty and accuracy in some of the results 

 of these experiments ; and it had occurred both to Sir David 

 Brewster and myself, that when a strip of wall-paper was placed 

 at a greater or less distance from its fellow than others, the 

 illusive image would not appear in the same place, some strips 

 would advance a little and others would recede, so as to fulfill 

 the conditions of the triangles above named ; even the six- 

 teenth of an inch would be appreciable. 



In the history of my examination of this subject, I would 

 observe that my friend Dr. D, S. C. H. Smith, of Sutton, was 

 present when my paper was read at New Haven. In 1845, 

 my assistant, Thomas K. Beecher, A.M., witnessed and re- 

 peated most of the experiments above named- Among other 

 things we made the equations dependent upon the above tri- 

 angles, and verified our calculations.by actual admeasurement 

 of the distances between the eyes, between the objects, and 

 to the illusive image. I attempted a popular lecture on this 

 topic, but found it difficult to interest an audience in a matter 

 requiring so much previous optical knowledge. In the spring 



