ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
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long focus tlie positions in space of the principal focus of the lens, the 
marks on the nearer face, and the internal vertical image of the marks 
on the further face. From the distances thus measured, together with 
a measurement of the thickness of the lens, the true focal length, as well 
as the distance between the Gauss points, can then be calculated. In 
practice, the direct measurement of the thickness of the lens is avoided 
by the device of reversing the position of the lens and repeating the three 
readings from the reversed faces. M. Cornu describes an apparatus 
constructed for him by Duboscq for carrying out these measurements. 
( s ) Mebius’* Method. — This is a modification of the method of Cornu 
for the particular case of negative lenses, and needs no extended notice 
here. 
VI. Method of Obliquity of Bays. — (<) Moser’s + Method. — This 
method is based on the principle that any ray which on entrance 
passes through the first Gauss point at any given obliquity with respect 
to the principal axis emerges with unchanged obliquity, but displaced, 
as if it had passed through the second Gauss point. To determine these 
points the experimental process consists in a series of approximations 
derived from measurement made of the magnification. 
Of the various methods thus briefly reviewed, only those of Pendle- 
bury, Meyerstein, MacGillavry, and Cornu fulfil the conditions of deter- 
mining the values of both / and k without double adjustments. Doubt- 
less, each has its advantages for particular cases. Yet it appears worth 
while to follow out another method which seemed to possess some 
advantages over any yet suggested. 
A New Focometric Method. 
In the new method of focometry which the author has devised, direct 
methods of measurement of lengths only are used ; and double adjust- 
ments are avoided. The method consists in the direct determination, 
firstly , of the two principal foci by placing a transparent micrometric 
screen at each ; and, secondly, when these have been found, the two 
symmetric points by moving the two screens by a double screw motion 
through equal distances until each is the image of the other. The true 
focal length (/) and the distance (k) between the Gauss points are 
therefore given by simple subtraction of scale readings. 
Choice of the Symmetric Points. — It is easy to show that in any deter- 
mination of focal lengths, the most favourable position for an experimental 
measure of any two conjugate points is when these occupy the symmetric 
points; provided the experimental determination of the two conjugated 
foci is assumed to be of equal difficulty. 
Let p and — q be the respective distances of the point-object and 
point-image from the two corresponding principal foci. Then by 
Newton’s rule, we shall have 
/ 2 =ts; (1) 
where / is the true principal focal length. 
* Mebius, ‘ Determination experimentale des elements principaux d’une lentille 
divergente,’ Journal de Physique, 2me serie, ix. p. 511. 
f Moser, ‘ Methode die Brennweite und optischen Hauptpunkte von Linsen zu 
bestimmen,’ Pogg. Annaten, lxiii. (1884) p. 39. 
