ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
117 
operation of finding these symmetric points consists, then, in a series 
of double adjustments of the following kind : — One of the micrometers 
being placed at a distance judged approximately as twice the focal 
length, the second micrometer is then moved, until upon its surface an 
exact image of the first is formed. If, on comparing the size of the 
divisions of this image with those of the surface on which it falls, it 
is found that they do not coincide, but are either magnified or minified, 
the distance of the first micrometer is either increased or diminished, 
and the second micrometer is again adjusted to the new position of the 
image, and a fresh comparison made. By successive trials and approxi- 
mations the symmetric points are approached; and, when so found, 
the distance between them is measured, and one-fourth of it taken as 
the focal length. The method is open to the objections (1) that it is 
inapplicable to thick lenses, as it does not take into account the distance 
between the Gauss points, and (2) that it requires a tiresome series of 
double adjustments. The simple modification of this method, suggested 
by Webb,* * * § ' needs no notice here. 
(Z) Donders’f Method. — Donders improved the method of unit 
magnification by substituting for the series of double adjustments a 
simpler mode of equalizing the size of object and image. lie used as 
object an opaque screen provided with perforations, the linear dimensions 
of which from one to another were measured with a Helmholtz’s 
ophthalmometer. The lens to be measured being placed in front of 
this object, an image is then formed on a translucent screen, and the 
lens is then moved to increasing distances until the size of the image, 
as measured by the ophthalmometer, is equal to that of the object. 
(m) Snellen’s $ Method. — This method, which closely resembles that 
of Donders, is carried out by the aid of an instrument called a Phalco- 
meter, consisting of a graduated bench at the middle of which the lens 
is placed. No ophthalmometer is used to measure the sizes of object 
and image, a translucent screen figured with marks serving to detect 
any want of equality between the sizes of image and object. It is 
assumed that the lens has a single optical centre at its centre of 
figure, and a mechanical adjustment serves to move the object and the 
screen at equal rates from the lens at the centre. The scale is divided 
to read off direct in dioptries the focal power of the lens. Snellen 
applies the method to negative lenses and long-focus positive lenses 
by placing them between two positive lenses of equal and known focal 
power ; and in the case of j^uO’Cobycx and meniscus lenses, he 
recommends that to secure symmetry, such lenses should bo taken in 
pairs, back to back, and measured together. 
IV. Methods of Approximate Unit Magnification. — (w) Bessel’s § 
Method. — In this method the object and the apparatus to receive the 
image are placed at a distance from one another, exceeding four times 
* Webb, ‘Literary Gazette,’ 1857, p. 1101; and Fortscliritte d. Physilr, xiii. 
(1857) p. 276. 
f Bonders, ‘ Bepaling van den Brandspunt-afstand van Lensen,’ Versl. en 
Mededeel., xv. (1863) p. 402. 
t Snellen, ‘ Be Phakometer, ter repaling van focus cn centrum van lenzen,’ 
Maandblad voor Natuurwetenscbappen, vii (1876) p. 23. 
§ Bessel, ‘ Astronomisclie Untersuchungen,’ i. p. 137. 
