104 CORRESPONDENCE. 
the aperture is not sufficient to admit diffracted rays, the objective 
image is devoid of all details minute enough to cause this diffraction, 
and which are therefore ipso facto thrown out of the picture. On this 
fact is based a number of deductions of the utmost importance to the 
theory of the microscope and the limits of visibility, a careful study 
of which cannot but greatly tend to clear up our ideas of “ pene- 
trating” and “ resolving” powers, and the true significance of angular 
aperture. 
It is scarcely necessary to remark that the above-mentioned results 
have no connection with that theory of diffraction occurring in the 
microscope which takes its starting point from the well-known case of 
the passage of bright pencils of light through pin-hole apertures, 
a case which occurs when an objective of great amplifying power is 
employed whose optical aperture is necessarily very minute. 
Professor Helmholtz’s essay deals with the question of light as it 
passes into, through, and out of the instrument, and the law formu- 
larized by La Grange is referred to as a law potentially carrying in 
itself many yet unknown applications. La Grange himself only pro- 
posed to apply a particular deduction from this law as a means of 
determining the amplification effected by the object-glass of a tele- 
scope; whilst Helmholtz employed the formula to demonstrate the 
relation between brightness of image and amplification in the case of 
objectives used in the microscope. The optical law of La Grange 
undoubtedly applies to the focussing function by which an image is 
geometrically delineated, so that each point in the object is pictured 
on the focal plane in an exactly corresponding position, that is, in 
symmetrical disposition round its axis; and Professor Helmholtz has 
shown that the peculiar photometric relations of the microscope image, 
i.e. the relation between amplification and brightness of image 
(which, as he expressly states, is not necessarily the same in the tele- 
scope), are demonstrable from this law. But it is only when am- 
plification is increased and more light needed that the conditions of 
diffraction in the microscope are brought into play, so as to present 
obstacles to further increase of amplifying power. In a letter pub- 
lished in your December number, Dr. Pigott has quoted a passage 
from my translation in support of a statement which scarcely needs 
refutation. I will, however, quote another, in which Helmholtz ex- 
pressly states that “if, perhaps, occasional allusion has been made 
to diffraction as a cause of deterioration of the microscopic image, I have 
nowhere found any methodical investigation into the nature and amount of 
its influence.” 
It seems hardly worth while to notice Dr. Pigott’s allusion to 
the investigations of the German Professors as a mere attempt to 
“popularize” a law of La Grange. No one who has made himself 
acquainted with Professor Abbe’s experimental demonstration of the 
modes in which objectives of wide-angled aperture form images of 
particles in an object which diffract light when placed under the 
microscope, will fail to see that the reference to La Grange’s law is 
entirely irrelevant; and in regard to Professor Helmholtz’s essay the 
demonstration of diffraction of light in its passage through the lenses 
