1887 .] Professor A. Cayley on a Formula for i jn i . 153 
-h 
Writing X x = — f- , X 
-2 i 
we have 
n c 
A w O' 
hi r 1 
o- = c-M l+r^o + TT -- + 
?)!■ 
which is the foregoing approximate value. 
2. On the Fossil Flora of the Eadstock Series of the Somer- 
set and Bristol Coal Fields. (Upper Coal Measures.) 
Part I. By E. Kidston, Esq., F.Gr.S. 
3. On the Achromatism of the Four-Lens Eye-Piece: New 
Arrangement of the Lenses. By Edward Sang, LL.D. 
In designing a telescope for a particular class of observations, it 
was found desirable to have a field-bar in the focus of the object- 
glass, and, at the same time, to have an image of that object-glass 
exterior to the eye-lens. These desiderata cannot both be got by 
the achromatic arrangement of two lenses made of one material ; they 
are combined in the ordinary four-lens eye-piece. 
While investigating the action of the four lenses with a view to 
a third condition, found, however, to be unattainable, I was led to 
notice a porism altogether new to me, and which guides us to a 
new arrangement of the lenses. Believing that this porism has 
hitherto escaped notice, I venture to submit it to the Society. 
Let B, C, D, E represent four thin lenses, all of one material, 
arranged along the axis of a telescope, whose object-glass A is at a 
distance beyond the limits of the page, and let us denote their 
focal lengths by / 13 f 2 , / 3 , / 4 , 
f/ f2 
B 
C 
D 
E 
bl 
b2 
b2> 
while their distances are 6 1} U, & 3 ; then the condition of achromatism 
is contained in the equation 
