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XLV. Intelligence and Miscellaneous Articles. 



SIMPLE MODE OF DETERMINING THE POSITION OE AN OPTIC 

 TMAGE. BY A. RRONIG. 



/^|N looking with one eye at two points which form no, or at all 

 " events a very small visual angle with one another, it is easily de- 

 termined whether one of the points is more distant, and which it is. It 

 is merely necessary, while continuing to look at the two points, to 

 move the eye at right angles to the direction of its axis, and to ob- 

 serve the simultaneous apparent motion of the two points. That 

 point which moves in the same direction with the eye is the most 

 distant. In the annexed figure, let A be the eye which looks at the 



two points P and Q. Let A, P, and Q be in the same right line. 

 The eye is now moved from A to B. The two points P and Q thereby 

 diverge from one another by the angle P B Q, and Q appears to move 

 in the same direction as the eye (to the right, for instance), but P 

 in the opposite direction. Inversely, when P appears to move in 

 the same direction as the eye, it follows that P is more distant from 

 the eye than Q. 



Imagine now an optical apparatus which projects an objective pic- 

 ture of any object. If the image is not sufficiently bright to be 

 caught upon a screen, the law (that of two unequally distant points 

 the further moves in the same direction as the eye) furnishes an 

 easy means of finding the position of an image. The eye is so placed 

 that it views the image. A needle-point is then brought by the hand, 

 or still better by means of a fixed stand, into such a position that the 

 point covers any part of the picture. The head is then moved some- 

 what on one side. If now either the needle-point or the point of 

 the picture moves in the same direction as the eye, this point is 

 further removed from the eye than the other, which moves in the 

 opposite direction. By successively "shifting the needle-point, the 

 position is readily found in which, when the eye is moved, the 

 needle-point coincides with the point of the picture considered. 

 This is the position of the image. If the needle-point, after it has 

 been approached to the reflecting or refracting apparatus till it 

 touches, still appears to move in an opposite direction to the eye, 

 the image is subjective, and not objective. 



In order to extend the same process to subjective images, it would 

 first be necessary to prove experimentally and directly that the image 

 produced by a plane mirror actually occupies the position hitherto 



