another, and terminating all the Light which falls upon the Paper from
the point where the edges of the Knives meet; _eis_, _fkt_, and _glv_,
three hyperbolical Lines representing the Terminus of the Shadow of one
of the Knives, the dark Line between the first and second Fringes of
that Shadow, and the dark Line between the second and third Fringes of
the same Shadow; _xip_, _ykq_, and _zlr_, three other hyperbolical Lines
representing the Terminus of the Shadow of the other Knife, the dark
Line between the first and second Fringes of that Shadow, and the dark
line between the second and third Fringes of the same Shadow. And
conceive that these three Hyperbola's are like and equal to the former
three, and cross them in the points _i_, _k_, and _l_, and that the
Shadows of the Knives are terminated and distinguish'd from the first
luminous Fringes by the lines _eis_ and _xip_, until the meeting and
crossing of the Fringes, and then those lines cross the Fringes in the
form of dark lines, terminating the first luminous Fringes within side,
and distinguishing them from another Light which begins to appear at
_i_, and illuminates all the triangular space _ip_DE_s_ comprehended by
these dark lines, and the right line DE. Of these Hyperbola's one
Asymptote is the line DE, and their other Asymptotes are parallel to the
lines CA and CB. Let _rv_ represent a line drawn any where upon the
Paper parallel to the Asymptote DE, and let this line cross the right
lines AC in _m_, and BC in _n_, and the six dark hyperbolical lines in
_p_, _q_, _r_; _s_, _t_, _v_; and by measuring the distances _ps_, _qt_,
_rv_, and thence collecting the lengths of the Ordinates _np_, _nq_,
_nr_ or _ms_, _mt_, _mv_, and doing this at several distances of the
line _rv_ from the Asymptote DD, you may find as many points of these
Hyperbola's as you please, and thereby know that these curve lines are
Hyperbola's differing little from the conical Hyperbola. And by
measuring the lines C_i_, C_k_, C_l_, you may find other points of these
Curves.
For instance; when the Knives were distant from the hole in the Window
ten Feet, and the Paper from the Knives nine Feet, and the Angle
contained by the edges of the Knives to which the Angle ACB is equal,
was subtended by a Chord which was to the Radius as 1 to 32, and the
distance of the line _rv_ from the Asymptote DE was half an Inch: I
measured the lines _ps_, _qt_, _rv_, and found them 0'35, 0'65, 0'98
Inches respectively; and by adding to their halfs the line 1/2 _mn_,
(which here was the 128th part of an Inch, or 0'0078 Inches,) the Sums
_np_, _nq_, _nr_, were 0'1828, 0'3328, 0'4978 Inches. I measured also
190