ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
357 
two isolated slots the pictures shown in photos 3 and 4 differ remarkably 
from the original object. 
Experiment 6. — The general arrangement of the apparatus and the 
aerial object remained the same as in the last experiment ; but, instead 
of rectangular slots, annular or zonular slots were used at the back of 
the objective. 
When an annular slot exposed emitting points in a circle 2 mm. in 
diameter, the image discs were surrounded by rings of light. When 
the circle was 4 mm. in diameter, the discs were surrounded by closer 
rings, and the tangential union of diffraction rings between the bands 
(overlapping discs) resulted in intense lines, in comparison with which 
the semi-rings at the ends of the bands appeared faint. 
Now the diffraction pattern is contracted with every increase in 
diameter, and this is true in all diameters, and we know that with circular 
lenses an area of diffracted light varies in extent inversely with the 
square of its diameter or aperture. Therefore the light intensity of 
such an area would vary directly with the square of the aperture, pro- 
vided the amount of light transmitted by the objective were to remain 
the same. But the amount of light transmitted by the objective increases 
with the square of its aperture. This means that, independently of the 
eontraction of the diffraction pattern, an area of light on the projected 
image varies in intensity with the square of the aperture of the lens. 
Increase of aperture, then, adds to the intensity of the diffraction pattern 
in two ways. The increase of intensity gained in one way must be mul- 
tiplied by that gained in the other to get the total increase. Thus : The 
intensity of the diffraction pattern varies ivith the square of the square of the 
aperture. 
Experiment 7. — The object of this was to test the conclusion just 
arrived at. The apparatus and conditions were as in experiment 6, 
except that for the object was substituted an aerial image of a tiny pin- 
hole, and for two or more slots behind the objective, single slots were 
substituted. 
Photo 8 is a double photomicrograph of the aerial object. E had the 
first exposure of 15 seconds, with a slot 3 mm. wide. The aerial object 
was shifted very slightly to the right. F had an exposure of 1215 
{= 15 x 3 4 ) seconds, with a slot 1 mm. wide. Exposed on the same 
plate and developed the same, the two images were strictly comparable 
as to their intensities. The exposures were so timed as to show the 
first diffraction ring in each case. The triple broadening of the disc by 
the lesser aperture at once attracts attention, and it is clear that the 
exposures were as 1 to 81 ( = 3 4 ). In the negative it was impossible 
to say that the two rings differed in intensity, but unfortunately the 
half tone process has failed to reproduce the rings. 
With small apertures the visual pictures of finest particles and lines 
consist chiefly of diffraction spreading. Such diffraction spreading not 
only contracts with increasing aperture, but gains in intensity rapidly 
(with the square of the square of the aperture). Thus, increasing aper- 
ture narrows and intensifies most noticeably the picture of finest details. 
In a similar way, increase of aperture causes diffraction- spreading of 
boundaries of areas to contract and to approach iu intensity that of the 
area, because that of the former increases with the square of the aperture, 
