OF ARTS AND SCIENCES. 



161 



itself multiplied by the distance of the luminous point from the 

 aperture added to the distance of the aperture from the screen, 

 and divided by the distance of the luminous point from the aperture. 

 Hence it is obvious that the size increases more slowly than the dis- 

 tance of the screen from the aperture, and in the case of a distant 

 object, like the sun, almost imperceptibly. When neither the aperture 

 nor the luminous object is a physical point, each strives to imprint its 

 own figure upon the screen, and the resulting shape will resemble 

 that of the aperture or the object according to the size of the two 

 images which each would separately impress, as calculated above. If 

 the size of the aperture is to the size of the luminous object as the 

 distance between the aperture and screen is to the distance between 

 the luminous body and the screen, the separate images which the 

 aperture and the luminous body will form are of the same size, and 

 therefore their shape is equally influential in forming the resulting fig- 

 ure. When the distance of the screen is thirty feet from the aper- 

 ture, the two images above described are of the same size with solar 

 light if the aperture is between three and four inches. Now when 

 the distance between the screen and the aperture is changed, the 

 size of the image which belongs to the luminous body changes much 

 more than that which belongs to the aperture. Consequently, if the 

 screen on which the images are painted is much farther than thirty 

 feet, the size of the aperture being three or four inches, or if the size 

 of the aperture is diminished, the distance between the screen and the 

 aperture remaining the same, the influence of the sun's form will prevail, 

 and in extreme cases the resulting figure will represent the shape of the 

 sun to the exclusion of all trace of the shape of the aperture. Hence 

 with very small apertures the final image will have no resemblance 

 in shape to the aperture, except when received very near to the aper- 

 ture. But with nearer bodies, as the flame of a candle, the shape of 

 the aperture continues upon the screen at larger distances, or with the 

 same distance when smaller apertures are employed." 



Four hundred and fourth meeting. 



September 12, 1854. — Monthly Meeting. 



The President in the chair. 



The Corresponding Secretary read letters from Sir William 

 Hamilton, accepting his appointment of Foreign Honorary 



VOL. III. 21 



