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SUMMARY OF CURRENT RESEARCHES RELATING TO 
equidistant each from its own optical centre. But hitherto it has been 
found difficult to ascertain the position of the principal planes of a lens 
combination. Optical instrument makers generally have no information 
on the subject that they can furnish. They can tell us approximately the 
focal length, hut they cannot, or do not, tell us the position of the optical 
centres or principal points from which this focal length is to be reckoned. 
Beginners in microscopic work, when they come upon an objective 
marked “ 1/4-inch,” expect to find that the object must he placed 
1/4 in. below the front surface of the lens, and are often puzzled to find 
that the distance is perhaps only 1/10 in. Naturally they ask the 
question, from what point does the maker measure his quarter of an 
inch ? The correct answer is that the 1/4 in. should be measured from 
the principal plane which corresponds to the front focus of the lens. 
But where this principal plane lies is never marked on the brass mount 
of the lens, though it ought to be. Again, the beginner often asks what 
is the correct way to reckon the true tube-length of the Microscope 
between objective and eye-piece? Must he measure from the lowest 
point of the eye-piece to the highest point of the objective, or how ? 
The right answer is that the true distance between objective and eye- 
piece is not the mere length of the tube, but is the distance between the 
second principal plane of the objective, and the first principal plane of 
the eye- piece. But how is the unfortunate possessor of the instrument 
to measure this if the constructor has omitted to mark on the eye-pieces 
and objectives the positions of the principal planes ? 
It is one of the purposes of this paper to describe an instrument for 
measuring lenses, and ascertaining the precise position of these principal 
planes. Therefore, a few more preliminary words about the principal planes 
and the two Gauss-points through which they pass, will be appropriate. 
In ordinary single lenses, if not very thick in proportion to diameter, 
the distance between the two principal planes is approximately one- 
third of the thickness of the lens at its middle. Exact formulae are 
given in various modern treatises on geometrical optics. In lenses that 
have their two faces of different curvatures tbe principal planes do not 
lie symmetrically between the two poles* of the lens, but are shifted 
toward the more highly curved face, or even beyond it. In piano lenses, 
Fig. 9. Fig. 10. Fig. 11. 
whether convex or concave, one of the two principal planes is a tangent 
to the curved face. These matters are illustrated by the sketches in 
figs. 9, 10, and 11. * 
* I have used this term for years to denote the middle-points of the two faces of 
the lens, and find it very convenient. 
