46 SMITHSONIAN MISCELLANEOUS COLLECTION'S VOL. 5 1 



tance and the eye receives a diverging pencil of rays. Thus the 

 inverted image produced by the two optical systems combined, 

 the eye and the atmosphere, lies inside <p counting from the retina 

 forward; but on account of the great distance of the objects, always 

 so far from the retina that it requires an extraordinary power of 

 accommodation to produce a sharply defined image on the retina. 

 The muscular tension thus excited explains the apparent floating 

 of the moon in the atmosphere. But even with this extraordinary 

 accommodation the image of the moon will only just attain the 

 nerves of the retina, and since this partial touching also occurs in 

 ordinary vision for objects that are at a definite terrestrial distance 

 that we may call D, therefore the eye locates the moon also at the 

 same distance D because it produces the same sensation or excite- 

 ment on the retina, whereby is explained the apparent floating of the 

 moon at a relatively nearby point in the atmosphere. 5 



In relation to the location of the principal point, h, its distance 

 from the corresponding focus is equal to the distance of the opposite 

 focus from its nodal point. 6 

 Therefore we get from fig. 2 



whence 

 and also 

 consequently 



fh = F' and fh' = F 



mh = fm — fh = F — F' 



mh' = fh' - fm = F - F* 



mh = mh' = F — F' 



and thence by substituting from equations (3) and (4) 



in' — 1) R 

 mh = mh' = !_ (1 - A) = about 6463 kilometers . (5) 



57 .3" 



Therefore the two principal points, like the nodal points, coincide 

 in one point h, that is 6463 km. distant from the center of the earth 

 or 96.3 = 6463 — 6366.7 above the surface of the earth at c (fig. 

 2 or fig. 3). Therefore according to the definition of the principal 

 points the object and the image coincide at the point h, that is to 



6 We determine D experimentally by measuring the distance at which an 

 intense flame is sharply seen. 



8 Mousson: 2d Edition, section 731 (2); 3d Edition, section 809 (2). 



