72 
Mi'tcMELL^ on the Cobweb Micrometer, 
it is evident, therefore, if tlie value of the divisions had been 
obtained with the micrometer adjusted, to zero when the axes 
of the filaments coincided, the reading would be too great by 
two divisions for every object placed between the filaments. 
But though the quantity is constant, the error is not, for it 
becomes greater as the object is smaller, i. e. as it occupies 
fewer divisions of the micrometer head. For instance, with 
my tV^^ objective one division of the micrometer is equal to 
-^^^,-23-3-rd of an inch, measuring /rom the axes of the filaments. 
If I place between the filaments an object that is measured by 
one hundred divisions, the true measure is evidently but ninety- 
eight, and the result is too great by one fiftieth; but if the object 
be measured by ten divisions, the correct measure is but eight, 
and the error amounts to one fifth ! Thus, the error is always 
in inverse proportion to the magnitude of the object, the 
smallest readings giving the largest errors. In the case last 
supposed an object that measured -^3- Virrtb of an inch would 
appear to measure TT.VaT^d of an inch, i. e. if, as I presume 
is generally the case, the thickness of the filaments be not 
allowed for. 
The means of obtaining exact measurements is readily 
applied ; thus, if the filaments coincide when the micrometer 
head is at zero, a deduction equal to the thickness of one fila- 
ment must be made whenever the object is placed between them, 
or after the value of the divisions has been obtained with the 
filaments coinciding at zero the micrometer head may be 
shifted until it is at zero, when the filaments are parallel. 
The reading will then be correct for all objects placed 
between the filaments, but an addition equal to the diameter 
of one filament must be made to the measurement of all 
intervals between lines, striae, &c. 
The thickness of the filaments is easily obtained by placing 
the movable filament in contact with the fixed one, first on 
one side, then on the other ; half the number of the divisions 
passed over by the micrometer head is the distance which it 
must be set back to place the filaments in contact when the 
reading is zero. 
No stage micrometer that I have seen is ruled sufficiently 
fine for the higher powers. With a one-twelfth the grooves 
are inconveniently wide. A large number of measurements 
will probably give a mean not very far from the truth; but it 
would be more satisfactory to have such lines as the filaments 
would just cover, as is the case with the lower powers. The 
WiTo of an inch would also be a more convenient division 
for the higher powers than the -[--^'^th, which occupies too much 
of the field. 
