10 REPORT—1849. 
The effect on the eye is diminished, and may be totally destroyed, by the inter- 
vention of a dens, even in the brightest lights. This is explained by the diminution 
intensity in proportion to the superficial magnification, which is most effective at 
the edges. 
In telescopes there is a twofold effect of this kind, one at the focus of the eye, 
another at that of the object-glass; the former may be neutralized by the magnifi- 
cation of the eye-piece. The author has tried many experiments on the image ofa 
card, cut as above, seen in a telescope under apertures of various degrees of con- 
traction, which appear to accord closely with the phenomena of “ the diffraction of 
the object-glass.”” It also follows that there must be a limit to the increase of 
the enlargement of the image, dependent on the diminution of light when the 
aperture is contracted beyond a certain point, which will vary in each individual 
instrument. 
The author suggests a method of measuring the amount of irradiation under any 
given conditions of light, by viewing and measuring micrometrically in a telescope 
the image of a card cut as above, under the given light, placed at the focus of an 
object-glass opposite to that of the telescope, and connected with it by a tube. 
Theoretically, irradiation would explain those singular pheenomena seen in eclipses 
and transits of the planets, of the connection of the edge of the dark disc by necks 
or threads to that of the sun; as also the apparent projection of a star on the bright 
limb of the moon, by simply overlapping the star from irradiation. But the difficulty 
in all these pheenomena is their appearance in some cases and not in others, under 
circumstances apparently similar. 

On a Mode of Measuring the Astigmatism of a Defective Eye. 
By Professor Stoxes, M.A. 
Besides the common defects of long sight and short sight, there exists a defect, 
not very uncommon, which consists in the eye’s refracting the rays of light with 
different power in different planes, so that the eye, regarded as an optical instrument, 
is not symmetrical about its axis. This defect was first noticed by the present 
Astronomer Royal, in a paper published about twenty years ago in the Transac- 
tions of the Cambridge Philosophical Society. It may be detected by making a 
small pin-hole in a card, which is to be moved from close to the eye to arm’s length, 
the eye meanwhile being directed to the sky, or any bright object of sufficient size. 
With ordinary eyes the indistinct image of the hole remains circular at all distances ; 
but to an eye having this peculiar defect it becomes elongated, and, when the card 
is at a certain distance, passes into a straight line. On further removing the card, 
the image becomes elongated in a perpendicular direction, and finally, if the eye be 
not too long-sighted, passes into a straight line perpendicular to the former. Mr. 
Airy has corrected the defect in his own case by means of a spherico-cylindrical 
lens, in which the required curvature of the cylindrical surface was calculated by 
means of the distances of the card from the eye when the two focal lines were 
formed. Others however have found a difficulty in preventing the eye from altering 
its state of adaptation during the measurement of the distances. The author has 
constructed an instrument for determining the nature of the required lens, which is 
based on the following proposition :— 
Conceive a lens ground with two cylindrical surfaces of equal radius, one con- 
cave and the other convex, with their axes crossed at right angles; call such a lens 
an astigmatic lens; let the reciprocal of its focal length in one of the principal planes 
be called its power, and a line parallel to the axis of the convex surface its aséig- 
matic axis. Then, if two thin astigmatic lenses be combined with their axes inclined 
at any angle, they will be equivalent to a third astigmatic lens, determined by the 
following construction :—Through any point draw two straight lines, representing 
in magnitude the powers of the respective lenses, and inclined to a fixed line drawn 
arbitrarily in a direction perpendicular to the axis of vision at angles equal to ¢wice 
the inclinations of their astigmatic axes, and complete the parallelogram. Then the 
two lenses will be equivalent to a single astigmatic lens, represented by the diagonal 
of the parallelogram in the same way in which the single lenses are represented by 
the sides. A plano-cylindrical or spherico-cylindrical lens is equivalent to a common 

