158 On the Focal Length weal, Sone 1 BST. 
Give values of n = 
123-29. 122-94. 122-94, 122°94., 
The corresponding values of f are— 
07824 inch. -°07845 inch. °07845 inch. *07845 inch. 
l= 249mm. m=‘07839in. Difference of extremes =*00021 in. 
The increasing change in f for the same variation of the scale . 
reading is clearly seen on comparing the above sets of observations. 
The diminution of the number of divisions measured in a short- 
focus objective is a partially neutralizing circumstance, which can, 
however, be avoided by using a lens of long focus for the eye-piece, 
so as to gain a larger field of view. 
The chief difficulty met with in pursuing this research was that 
of procuring a suitable scale for the object, the image of which was 
to be measured. In the earliest measurements a scale on glass 
ruled to ssa inch was used, but the lines were jagged at the edges, 
their breadth was variable and their spacing unequal. Next, an eye- _ 
piece micrometer belonging to a Smith and Beck’s microscope was 
used, the divisions being 33, inch, but though this was an improve- 
ment on the former, the results were still unsatisfactory. Finally, 
a micrometer reading to 7}, mm. was used, which was all that 
could be desired in clearness and evenness of lines and equality of 
spacing. In some cases, for long-focus objectives a tego Inch micro- 
meter scale was substituted, as before stated. The paper scale used 
to measure the size of the image was divided to +5 or #5 of an inch, 
while these divisions were sub-divided by the eye into tenths, giving 
the measurement to 34, or ¢}y of an inch. The measurements can 
in general be relied upon within 535 or giz of an inch. A scale 
divided into fractions of a millimetre would have been preferable 
had such been easily procurable, as saving labour in the calculation 
of the focal lengths. 
Difficulty was at first apprehended from the expansion of the 
paper scale, especially as this was attached to the microscope tube 
by mucilage, but measurements made at different times both when 
moist and when dry showed no appreciable variation to be ascribed 
to that cause. A steel scale was at one time substituted, but being 
less easily read, its use was abandoned. A glass scale divided to 
half millimetres would be valuable in an extensive application of 
this method, because of the greater ease of estimating to tenths 
with narrow lines, those on printed scales being necessarily some- 
what coarse. 
The present investigation has suggested an inquiry into the laws 
of the foci of systems of lenses as related to variations in the dis- 
tances between them, which, in connection with the law of varia- 
tion of focal length with varying values of J, it is my intention to 
make the subject of further research. 
I would take this opportunity of expressing my obligations to 
