18 On Uniformity of Nomenclature in regard to 
meters might be called a 1-inch lens, and powers above and below 
rated in proportion. This plan is within reach of the opportunities 
of every microscopist, while the plan of actually employing a single 
lens of small aperture and exactly 1-inch focus as a standard of 
comparison is only adapted to the use of the opticians, and is not 
free from question as to what standard is meant after all. The lens 
made as a standard is probably not a 1-inch lens at all (principal 
focus), for the principal focus is never used in the microscope ; and 
authorities differ as to whether it should have conjugate foci of 
1 inch and 10 inches, or 10 inches apart (1 inch and 9 inches). 
Assuming x 10 as a 1-inch power, would be most easily applicable 
and unmistakable ; and this power (ten), divided by the ascertained 
power of any ocular or objective, would give the equivalent focal 
length of that objective or ocular without comparison and beyond 
dispute. 
The chances of error in this case are the same as in ordinary 
micrometry, with one or two additions, and should in all cases be 
ascertained in order to test the reliability of any series of observa- 
tions. They are due to the uncertain value of the divisions of the 
stage micrometer, to the like (but less important) variability of 
the measuring scale, to the uncertainty as to the exact optical cor- 
respondence of the lines selected for comparison in the two scales, 
and to the uncertainty as to obtaining exactly the assumed distance 
between the upper scale and a given point of the objective. The 
first of these errors is the largest, and its magnitude would surprise 
many who have noticed and admired the remarkable “ perfection ” 
of the common micrometers. A micrometer which ought to be the 
best in the writer’s possession, with lines 100, 1000, and 2000 to 
the inch, has a certain error of • 02 and a limit of error of * 035. 
This is entirely too much latitude for a single source of error, and 
of course it is nearly eliminated by comparing a large number of 
spaces belonging to at least several different scales, rejecting any 
scales which by differing widely from the average standard are 
presumably erroneous, and averaging the rest. The remaining 
sources of error may be similarly reduced by averaging, though 
their aggregate limit of error, ascertained by comparing the average 
measurements with extreme figures beyond which there is no pos- 
sibility of doubt, will be found to be very small and inconsiderable. 
The standard distance of measurement in estimating magni- 
fying powers may be stated to be, at present, 10 inches. The dis- 
tance of 5 inches has been recommended, even somewhat recently,* 
and 8,f 9,J and 10 § inches have been successively used. The 
smaller number were evidently too small, and the last, 10 inches, 
seems to be permanently accepted as most correct theoretically and 
* Brocklesby, N.Y., 1851. f Baker. London, 1742. 
t Martin Fokes, Esq., P.K.S., 1742. § Lardner, Carpenter, Suffolk, &c. 
