876 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
If F is negative, the sign before the fraction will be changed. 
Example, let F = — 2. Then 
p.' = 2ft - 1 - = 2/x — 1 + 1/2 = 2*5. 
The above method gives a greater range of readings for indices 
varying from 2*0 to 2*5, and consequently more accurate results than 
the simpler one of filling up a plano-concave lens with the medium, and 
covering it with a piece of plane glass. The formula for this latter 
plan being p! 
The radius of the concave r might with 
advantage be made 2 in., then p! = p + 
If fx = 3/2, and F = oc , p = 3/2 ; if F = 4, p = 2 • 0 ; and if F = 2, 
fi! = 2-5.” 
The following is a simple method of measuring the focus F : — On 
the stage of the Microscope place a slip with some scratch or mark on 
its lower surface. Screw a low power, such as a 1-in., on the nose-piece 
and bring this mark on the lower surface of the slip into sharp focus. 
Place the lenses with the enclosed medium on the substage of the Micro- 
scope, and by means of the substage rackwork carefully focus on the 
same scratch or mark on the lower surface of the slip the image of some 
distant tree or chimney-pot formed by these lenses. It will then be 
easy to measure the distance between the lower surface of the slip and 
the lenses, which will be the focus required. Note, if the Microscope is 
used in a vertical position it will be necessary to employ a mirror ; care, 
therefore, must be taken to see that it is the plane mirror that is used ; 
it would further be advisable to test the plane mirror by the sun’s rays, 
as so-called plane mirrors are sometimes concaves of long foci, in which 
case they are unfit for use in the above measurements. 
Abbe Measuring Apparatus for Physicists.* — Dr. C. Pulfrich 
describes three measuring apparatus for the use of physicists, con- 
structed by Prof. Abbe. The instruments are not new, but have not 
been fully described before. In their construction the following prin- 
ciples were mainly considered : — 
(1) The measurement in all cases, both by contact as well as by 
sight-adjustment, is made by means of a scale, with which the distance 
to be measured is directly compared. 
In this way all irregular and uncontrollable errors, such as are to be 
feared in the case of screws, are avoided. 
(2) The apparatus is so arranged that the length to be measured 
forms a direct continuation of the scale which serves as the standard of 
measurement. 
By this means the comparison of the measured length with the scale 
is made independent of the greater or less perfection of the mechanism 
by which the displacement is made. 
In all three pieces of apparatus the divisions are engraved on plates 
of platinum or silver, which are only fixed at one end, so that they are 
free to expand in all directions. The standard scales are divided into 
* Zeitsohr. f. Instrumentenk., xii. (1892) pp. 307-15. [The Society is indebted 
to Herr Zeiss for the use of the cliches of this article.] 
