MEASURING THE MAGNITUDE OF MICROSCOPIC OBJECTS. 209
On DEFINING the POSITION and MEASURING the MAGNITUDE of
MICROSCOPIC OBJECTS. By the Rev. W. HODGSON, M.A.,
Incumbent of Brathay.
IT is a matter of great practical convenience that the Microscopical Society have adopted, as one of their standards for
size, a slide which measures exactly three inches by one. Of
the three square inches thus fixed upon, the middle square
inch is that which alone is employed to carry the object.
The inch on the right hand is appropriated to the label, or
name; that on the left may be given up to registering the
position of any object, or may be left unoccupied altogether.
The middle square inch, therefore, is the only one to which
any measurements need refer. Let, then, the bounding lines
of this square inch at the bottom and on the left hand be
taken as what geometers would call the axes of rectangular
co-ordinates, or what, in the language of map-makers and
geographers, would be the equator and the first meridian, and
let the measurements be made in hundredtbs of an inch.
If an object, P (fig. 1), upon a slide represented by the dark
thick lines of the figure, were distant from A C by 67-100ths
of an inch, and from A B 39-100ths, a geometer would at
once understand its position from the values x = "67 and
y = • 39, and the geographer would know what situation was
'intended by long. 67° and lat. 39°.
In order, therefore, to define the place of any object on a
slide, two numbers are all that are essential.
The next step is to bring the point thus defined into the
centre of the field of the microscope. In all modern microscopes, of even the most moderate pretensions, the optical
axis of the instrument will, if produced, pass through the
centre of the stage; so that there exists already, in every such
microscope, a fixed point for the origin of co-ordinates, or
for the intersection of our microscopical equator and first
meridian. With the assistance of a diametral cobweb-line in
the eye-piece of the microscope, the point A (fig. 1) of the
slide, which is situated exactly one inch from its left-hand
extremity, may be brought accurately to the centre of the
stage, so that A B and C D A coincide respectively with the
horizontal and vertical lines through that point. The measurements, therefore, which before were referred only to the
middle square inch of the slide, may now, by means of graduation, be transferred to the stage of the microscope, or to a
supplementary stage with the name of " a finder."
In the simplest case of a plain stage, a piece of sheet brass^
210
HODGSON, ON MEASURING THE
zinc, card, or other material, four inches by two, is prepared
with a central hole of one inch in diameter, and fitted, with
ledges, pins, springs, or some such contrivance, to the stage
of the microscope, in such a condition as to allow the glass
slide to be moved over it in various directions without disturbing its position. An empty slide, on which the line A C
has been drawn with a common writing diamond, is brought,
with the help of the cobweb line in the eye-piece, into the
situation shown at fig. 1. The lines H I, H K, which are
merely the prolongations of the lines A H, G H given by the
edges of the slide, are graduated into tenths and hundredths
of an inch, and numbered both ways from H.
In order to bring an object, P, defined by long. 67° and
lat. 39°, into the centre of the field, place the slide so that
the edge G H cuts the scale H 1 at the 67th division,
while the edge H A cuts the other scale at the 39th division,
as shown in fig. 2. It is desirable to have the graduation of
H K repeated at L M, as an assistance towards keeping the
line A B parallel to its former position. With a plain stage,
the above plan is sufficient for those whose eyes can deal
readily with hundredths of an inch, and whose fingers can
easily make adjustments with the requisite nicety.
When the stage is fitted (as in the Students' Microscopes of
Messrs. Smith and Beck) with dove-tailed grooves, in which
a frame for steadying the slide moves up and down, the
position represented in fig. 1 is obtained with more ease than
with a stage entirely plain. There is also a further advantage in this case, by which minute dividing- may be dispensed
with, without any sacrifice of accuracy. The moveable frame
may have attached to it a piece of thin brass, about an inch
broad, and on this the graduation H I, fig. 1, may be replaced
by a diagonal scale reading to hundredths of an inch, while
the edge on the right hand, or in some other convenient position, may carry a vernier, divided as in the common barometer, by which divisions of tenths on the edge of the stage
may be read to hundredths, instead of having recourse to such
minuteness as is required for the plain stage at H K.
Indeed, minuteness of division may be altogether dispensed
with, even for the plain stage, by adopting the form of Indicator represented in fig. 3. The principle involved is precisely
the same as that employed in fig. 1, and the only difference in
the application of it consists in substituting two diagonal
scales reading to hundredths of an inch, for the other smaller
and less convenient graduations. The divisions in this case
are so large that, with a flat rule and a writing diamond, the
lines may be readily drawn in a few minutes upon a piece of
MAGNITUDE OP MICROSCOPIC OBJECTS.
211
glass of proper size placed over fig. 3 : and if the lines across
and near the centre are drawn by VERY light touches, so as to
be scarcely visible to the unassisted eye, the centreing of the
instrument is more easily effected, while no perceptible defect
results in the illumination of the object.
More elaborate instruments, possessing movements in horizontal and vertical directions by means of fine screws with
micrometer heads, have already the powers requisite for
defining the place of an object, when once the commencing
position, fig. 1, has been carefully ascertained, and either
marked upon the instrument or registered for reference.
The principle, therefore, is simple in its character as well
as perfectly general in its application, and supplies the want,
which has been expressed, of a " UNIVERSAL INDICATOR" for
the microscope.
With reference to the measurement of the magnitude of
microscopic objects, I have to suggest a modification of the
ingenious and elegant micrometer of Welcker, described in
No. X I V . of the Microscopical Journal, by which all graduation is dispensed'with, except such as is found upon the
ordinary scales supplied with the commonest sets of mathematical instruments, viz., a scale of half-inches divided to
tenths and hundredths. By means of cross-lines drawn on
the diaphragm of the eye-piece, and with a stage micrometer
divided to hundredths and thousandths of an inch, the radius
of the circle traced out by the intersection of the cross-lines
is carefully measured. The positions C D , erf (fig. 4), show
the method of effecting t h i s ; and if it should be found that
the radius of the dotted circle does not coincide exactly with
some number of thousandths of an inch, this inconvenience
may be easily rectified by means of the draw-tube. For
example, in an instrument which I have recently applied to a
Student's Microscope by Messrs. Smith and Beck, the radius
of the dotted circle was found to be • 0145 inch very nearly :
by drawing out the tube to the extent of 3" 4 inches the radius
was measured exactly by • 01 inch.
The modification which I propose for the external part of
Welcker's instrument consists in substituting a right-angled
triangle for the circular sector, and suppressing all graduation.
A glance at fig. 5 will explain the matter at once. The angle
at E is a right angle, and the distance O E is exactly five
inches. The method of measuring the object is shown in
fig. 6. The object is brought so that one extremity of it is at
the intersection of the cross-lines, while the index O F coincides with the line O E on the triangle. By the rotation of
the eye-piece, the diametral line is made to touch the other
212 MEASURING THE MAGNITUDE OF MICROSCOPIC OBJECTS.
extremity of the object, as shown by a O b, fig. 6. The index,
which is attached to the eye-piece, is by this movement brought
into the position O F, and the distance E F, when read by
means of the rule with the diagonal scale, gives the dimensions of the microscopic object to three places of figures. Let
the distance E F, for example, when measured by the scale,
be 3*45 half-inches ; this gives at once as the length of the
microscopic object "00345 inch.
When a higher power was applied to the microscope, the
radius of the dotted circle was measured exactly by • 004 inch
on the stage micrometer; but if the radius is accurately known
in thousandths of an inch, there is no difficulty in adapting
the method above suggested to this or any other radius.
Suppose, for instance, that an object, much smaller than the
former, from its being more highly magnified, still appears of
the same size as M N, fig. 6, and that the reading given by
the scale is as before 3*45 half-inches, then the length of the
object will be, not • 00345 inch, but a quantity bearing the
same proportion to it that 4 does to 10: nothing more,
therefore, is requisite than to add a cipher to the left and
multiply the result by 4 : thus • 000345 inch x 4 = • 000138
inch, which is the length of the object.
For those who prefer greater accuracy and more expensively-divided instruments, the plan of measuring by the
tangent is more easy in manipulation, and the trigonometrical
calculation is more simple, than when the chord is employed.
The equation,
log. M N = log. O M + log. tan. M O N,
gives all that is necessary at once; and if the radius O M be
unity, it is sufficient to find the number corresponding to the
log. tan. of the degrees and minutes, &c. of any observed angle.
In the case chosen above, the angle M O N was taken to
be 19°, of which the log. tan. = 9 -536972, and the number
corresponding with this gives, for the length of M N,
with the lower power, • 034432
and with the higher, • 00137728.
The error, therefore, by the plan now proposed, is less than
one ten-thousandth part of an inch in the one case, and less
than one hundredth-thousandth in the other. The triangle
can be made of wood, brass, zinc, card-board, or any other
suitable material, and is recommended on the score of cheapness, portability, facility in use, and accuracy of result.