ZOOLOGY AND BOTANY, MICROSCOPY, ETC. 
509 
measurements were made, and the work carried on under hypercritical 
conditions. An account of these may be of interest. First, a magnifica- 
tion of 1200 diameters by means of a suitable immersion lens was employed 
for the finer ruling, and for the coarse a dry 1/6 x 600 diameters; the 
screw micrometer was on an independent mounting. Care being taken 
with regard to the illumination, &c., a critical image of the lines was 
obtained. The order in which the lines were taken was from left to 
right, as seen in the instrument ; each interval was then designated by 
consecutive letters of the alphabet. The intervals were then most 
carefully wired, and each value set down under its corresponding letter ; 
when the ten spaces were finished they were meaned. 
It was then easy to see which interval differed from the mean, and to 
calculate how much. In the same way comparison can be made with 
any other scale, it matters not whether it is ruled in inches or mm. It 
is most important that both the instrument and the observer be tested. 
To this end I proceeded as follows. The screw value of 20 intervals on 
a badly ruled scale was written down as above, the paper was then put 
away, and the operation performed again. 
On comparing the two papers, the screw values of seven intervals 
were identical, 12 different by one division, and one by two divisions. 
This error of two divisions occurred in the interval H, the first reading 
being 1033, and the second 1031. On careful re-examination of this 
interval, I came to the conclusion that the first reading was the bad one, 
and that the true value was 1031 or 1032. On substituting this last 
value in both sets of readings, the 20 intervals meaned precisely alike, 
viz. 1038. As this forms a suitable illustration of the work, I append the 
two columns. With the exception, therefore, of the interval H, the 
screw readings may be taken as true to ± 1. The point, therefore, we 
have to determine, is the value of + 1. The mean 1038 being the value 
in divisions of the screw-head, for 50 /x, the value of one division conse- 
quently == -000001897 in., or less than 1/500,000 in. 
This might be called ‘ the constant of the instrument, and observer.’ 
We next have to find the greatest errors of the intervals from the mean ; 
G is the greatest, and S the least. Calculation shows that G is 
1/20,000 in. too large, and S 1/40,000 in. too small. 
But, on returning to Powell’s scale, we find a much closer agreement 
than this. Taking the -001 in. first, we find the mean to be 628-0. 
Three out of the ten intervals agree to that mean to + 1 : this being 
4 the constant of the instrument and observer,’ they are without sensible 
error. Four intervals agree to + 2, which is less than 1/300,000 in.; 
two lines B and H agree to + 3, which is less than 1/200,000, and one 
interval G is -j- 4, viz. 1/157,000 in., too large. Now, as we found that 
+ 1 was the limit of observation, we may say that the scale, with the 
exception of B, G, and H, has no sensible error. Practically speaking, 
G is the only interval that is out, and its error is small in compari- 
son with other scales. 
The next scale is the 1/100 mm. 
The • 01 mm. is too small a quantity to treat in the above way ; it 
must be left until we have objectives as perfect as those we have at 
present, but of double their power. 
All that can be done is to take several of the divisions. Eight sets 
