118 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
the focal length, and the (positive) lens is placed between them. Two 
such positions of the lens can be found for either of which the distance 
between the two conjugate foci is the same. Bessel gives a formula 
for deducing the focal length from the measurements of the various 
distances. The method assumes the distance between the Gauss points 
to be known beforehand, and therefore fails to give any information 
on the more difficult point to be determined. The advantages of the 
method are that no measurements have to be made from the curved 
faces of the lenses, and that none have to be made of the sizes of 
optical images. 
(o) Oudemans’ * Method is simply the method of Bessel carried out 
by means of a special apparatus, consisting of a simple graduated bench, 
and hair micrometers. Oudemans gives approximate formulae for 
calculating the distance between the Gauss points, for insertion in 
Bessel’s formulae, but confesses that this procedure fails in the case of 
many lens-combinations. 
( p ) Ilasselberg’st Method. — In applying Bessel’s plan, Hasselberg 
employs as objects the real images of spectrum lines as formed in the 
focal plane of the eye-piece of a spectroscope. He compares to some 
hundredths of a millimetre, the performance of a Zeiss’s objective con- 
structed of ordinary glass, but assumes the Gauss points by approximate 
calculation. 
( q ) MacGillavry’s J Method. — This elegant method departs from 
Bessel’s in that it requires measurements to be made of the respective 
sizes of object and image, as well as of the distance between them, and 
of the displacement of the lens between the two intermediate positions 
of adjustment to exact focus. But by this means all assumptions or 
estimates about the distance between the Gauss points are avoided. 
MacGillavry gives three formulas from each of which this unknown 
quantity has disappeared by elimination ; the true focal length being 
given in terms of the quantities directly measured, namely, from the 
relative sizes of object and image in the two positions, and the change 
in any one of the three measured lengths. Apart from the experi- 
mental difficulty of accurately measuring the magnification, Mac- 
Gillavry’s method appears to be very satisfactory. 
Y. Method of Approximate Interior Unit Magnification. — (r) Cornu’s § 
Method. — This is one of a group of possible methods in which the 
respective distances from their related principal foci of two conjugated 
points are measured, and the true focal length (which is their geometrical 
mean) is calculated from them ; the peculiarity of Cornu’s plan being 
that the two conjugate points employed are close to the two Gauss 
points, one of them being always interior to the lens. The lens is 
temporarily marked with ink-lines upon its faces, and the experimental 
process consists in observing by a reading Microscope of sufficiently 
* Oudemans, ‘ Sur la determination des distances focales des lentilles a court 
foyer,’ Archives Neerlandaises, xiii. (1877) p. 149. 
t B. Hasselberg, Bull, de l’Acadetnie des Sciences de St. Pe'tersbourg, xxxii. 
(1888) p. 142 ; and Beibliitter, xii. (1888) p. 782. 
I MacGillavry, ‘ De bepaling der focaal-afstanden van samengestelde optische 
stelsels.’ Maandblad voor Natuurwetenschappen, v. (1875) p. 73. 
§ Cornu, ‘ Determination expe'rimentale des ele'ments principaux d’un systeme 
optique,’ Journal de Physique, Ire se'rie, vi. (1887) p. 276. 
