244 WELCKER, ON MICROSCOPIC MEASUREMENTS. 
From these figures the true thickness of numerous objects 
may be readily estimated from the apparent thickness as 
shown by the focussing of the tube. 
The conditions of bodies having even horizontal surfaces 
present the problem in its simplest form, and bodies of this 
kind may in the first place be considered. For instance, an 
albuminous investing layer of a microscopic object requires 
for the definition of its upper and under surfaces a movement 
equal to 12 notches. For albumen the above table gives the 
number 139. Consequently we have 100:139 = 12:2, and 
obtain the value of 16°6 notches, that is to say (according to 
the value of the division of the screw-head given above), 
0:0297 mm. as the thickness of the investing layer, whose 
apparent thickness (12 notches) would be 0°0215 mm. 
In this way I have several times estimated the thickness 
of horizontal layers in cases where the preparation of verti- 
cal sections and the common mode of measurement were 
inapplicable. 
If it be asked what is the certainty of the above method, and 
to what extent it is applicable, it should be remarked that the 
certainty of the optical focussing is far greater than it would 
at first sight appear to be. The movement of the tube, in de- 
fining the upper and under surfaces of a very thin lamella 
may amount to less than a notch ; but it will be pretty nearly 
the same in repetitions of the experiment. In the hands of 
any one practised in the. precise definition of microscopic 
objects, the results do not readily vary more than a half per 
cent. The uncertainty of the method, however, diminishes 
in proportion to the minuteness of the objects. In the ease 
of a stratum of albumen of the same density as the saliva, 
the depression of the tube amounts to 1:5 to 2°5 notches, as 
may be ascertained with sufficient certainty, and for which 
apparent thicknesses, instead of 0°0027—0:0045 mm. may 
be properly substituted 0:00837—0:0062 mm. If the thick- 
ness to be measured be less than that of a human blood-cor- 
puscle (00020 mm.), the movement is so little, and the num- 
bers denoting the apparent and the true thickness so nearly 
the same, that the method (at any rate with the common 
magnifying powers and the simple apparatus here described) 
appears to be no longer applicable. 
If the refractive power of a body, whose thickness it is 
sought to determine, is not contained in our Table, an 
approximate estimate of it is always possible. 
This arises from the circumstance, that from the optical 
relation which the body in question exhibits with respect to 
the medium surrounding it, and whose’ refractive power is 
