116 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
method to meet the case of thick lenses. The lens is placed between 
an object and a screen fixed at more than four times the focal length 
apart. Measurement is made of the size of object and image, together 
with the distance of the lens from one of them. The lens is then 
reversed end for end, and is displaced longitudinally until the 
same magnification is obtained as before on the same screen. All 
assumptions about the Gauss points are thus eliminated, for it is clear 
that if in the second observation, after reversing the lens, the same 
magnification is obtained as in the first, the second principal point now 
occupies the position which the first principal point previously occupied, 
and vice versa. From the magnification, the distance between object 
and image, and the measurements of the displacement of the lens, the 
true focal length is calculated. Dr. Meyerstein describes a special 
instrument for carrying out this method. This method was devised in 
1844, but not published until 1877, after the same principle had been 
independently discovered and described by Dr. Hoppe.* * * § 
(i) Hansen’s j Method. — An object of given size being chosen, the 
positions of the lens are found which give (real) images of linear 
magnitudes respectively equal to that of the object multiplied by 1, 2, 
3, &c. ; and from two (or more) of such observations, each of which 
requires a series of double adjustings, the focal length and the distance 
between the principal points are calculated. 
(j) Mergier’s | Method. — This is an elegant mode of carrying out 
one of Hansen’s suggestions. The two symmetric points are found by 
trial and double adjustment, as in Silbermann’s method mentioned 
below, the magnification here being unity. Two micrometers serve as 
respecting object and as receptive surface for the image. This adjust- 
ment being made, then, in order to produce an image in the same place 
as previously but of double magnitude, it is sufficient to displace the 
lens through a distance equal to the focal length, and the object though 
exactly half this distance. This is accomplished by simple mechanical 
means, with two screws connected by wheel- gearing. 
III. Methods of Unit Magnification.— These methods constitute a 
special case of II., but are quite distinctive. 
(1c) Silbermann’s § Method. — In this method the lens (positive) is 
placed at the middle of a graduated bench, upon which two transparent 
micrometers are placed on either side, so that the image of one micro- 
meter falls upon the other. By a well-known theorem, the total 
distance between object and image will be a minimum, when the 
distance between them is equal to four times the focal length, and 
each is situated at one of the symmetric points of the lens. The 
* Hoppe, ‘ Uebcr die Bestimmung der Haupt- und Brennpunkte eines Linsen- 
systems,’ Pogg. Annalen, clx. (1876) p. 169. 
f Hansen, * Untersuchung des Weges eines Liclitstrahls durch eine beliebige 
Anzalil von brechenden spharischen Oberflaclien,’ K. Sachs. Gesellsch. f. Wissen- 
sohaften, xv. (1871). 
% Mergier, ‘ Nouveau foeometre pour la determination des constantes optiques des 
systemes dioptriques en general,’ Seances de la Societe' de Physique, 1887, p. 193. 
§ Silbermann, Comptes Bendus, xiv. (1830) Feb. 22, p. 340. See also Verdet, 
‘ Corns de Physique,’ wherein it states that this instrument was referred to a Com- 
mission, consisting of MM. Arago, Babinet, Biot, and Pouillet. No reference to any 
report of this Commission can be found. 
