390 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
thoroughly scientific, incontrovertible in its theory and capable of giving 
most excellent results in the hands of an expert, is yet, from its very 
nature, far too complicated in the details of its manipulation and ab- 
struse in its mathematical principles to meet the requirements of the 
average worker, whose possession of apparatus is seldom of such an 
extent as to warrant his undertaking an optical research of no small 
magnitude, and who frequently hesitates to trust his conclusions to 
figures obtained by the exercise of a long-forgotten skill in the solution 
of algebraic equations. 
Under these circumstances I beg to call your attention to a simple 
method of estimating the tube-length which will not involve the use of 
difficult formulas or any apparatus beyond an ordinary stage micrometer. 
It is based upon the increase in power obtained by extending the 
draw-tube through some measured distance, and is carried out thus : — 
A careful estimate is made of the power of the Microscope with the 
draw-tube pushed home as far as it will go, then, having determined 
this, the eye-piece is withdrawn three or four inches, the exact amount 
being noted, and the increased power of the instrument remeasured. 
We are now in possession of all the data necessary to calculate, not 
the actual optical tube-length, but its arithmetical equivalent, a distinc- 
tion to be observed, though the difference is immaterial to the purpose 
in view. 
As it is a rule in optics that the relative sizes of images formed by a 
lens at different points in its axis are in strict proportion to the distance 
of those points from the focus of the lens, we may arrange the following 
formula : — 
Where A = amplification of the instrument with the tube closed, where 
B = distance the ocular has been withdrawn, where C = increase in 
power produced by the effect of B. D is, therefore, the equivalent of 
the distance separating the focus of the objective from the anterior focal 
plane of the ocular. 
To illustrate this simply, suppose an instrument magnifies 100 
times, and that on withdrawing the eye-piece 3 in. the power is found to 
be increased 130 times, the equivalent of the tube-length will be by the 
above rule 10 in. 
That it can be nothing else can be shown by the old Euclidean pro- 
cess of assuming it to be something else, and ascertaining how far this 
hypothesis agrees with observation, which of course, will end in a 
reductio ad absurdum. 
The chief drawback of this proposed method is that it does not 
enable the worker to place his finger on any point on the tube and say 
with certainty, “ Here lies the posterior focus of the objective and there 
the anterior focus of the ocular,” but it faithfully gives us a figure 
which is the equivalent of the distance separating these two points, and 
this, after all, is the only concern of practical import. 
In conclusion, I may point out that there is frequently an extraordi- 
nary discrepancy between the true optical and the actual mechanical tube 
lengths ; thus in the case of an instrument in my possession a certain 
combination of lenses gave an optical tube-length of 4.J in., whilst the 
