The scale on the present instrument is very inconvenient, as it is
often almost out of sight; the curve it draws, on the other hand, I
consider very satisfactory, when the pencil is loaded, say, with a
planimeter weight. On the whole, I think you will agree with me that
this integraph goes a good way, if not the whole way, toward
fulfilling the conditions of a practical instrument.
I next turn to its construction and the claim it has to be considered
in any way new. Let me briefly remind our members of the process by
which an element Q R of the sum curve (Fig. 1) corresponding to the
point P on the primitive is drawn; P M being the mid-ordinate of L N,
a horizontal element, P B is drawn perpendicular to any vertical line
A B; and O A being a constant distance termed the base or "polar
distance," Q R is drawn between the ordinates of L and W, parallel to
O B. If P' be the point where P M meets Q R, we note the following
relationship of P' to P.
1. If P moves along a horizontal line, O B remains unchanged, and,
therefore, Q R or P' must move in the straight line Q R parallel to O
B.
2. If P moves along a vertical line, P' does not change, but Q R turns
round it, remaining parallel to O B.
[Illustration: FIG. 1, 2, 3]
Without taking the trouble, as I ought to have done, to inquire what
previous investigations had achieved in this matter, I thought, three
years ago, I could get an apparatus to save me the trouble of drawing
sum curves, made somewhat after the following fashion.
P (Fig. 2) is the guide or point to be taken round the primitive. It
is attached to a block, D, which works along the bar, B C, which in
its turn moves on the four wheels, e e f f, upon the frame R S U T
fixed upon the drawing board. O A is fixed perpendicular to R U, and
is such that O may be fixed at various points to determine the polar
distance. O B D is a light bar passing freely through B and forming
one side of a parallel ruler of two or more points, g g, h h, i i.
Along i i is a slot and in this works a loaded block containing a
wheel P', whose plane is always parallel to i i. This block also
passes through a slot in D E, an arm at right angles to B C. A little
consideration will show that P', if worked at all, would trace out the
sum curve of P.
It was only when I showed the rough idea of this to Professor
Kennedy, with the view of ascertaining what would be the amount of
back-lash and friction, that I learned that Mr. Boys had already
invented a very similar integrator. In his model the double parallel
ruler is replaced by two endless strings and pulleys, and the bar, B
C, by a T square.
Although this integrator was afterward made in a less crude form, I do
not think it has ever been a practical instrument for the draughtsman.
Shortly afterward I came across a work by Abdank-Abakanowicz, entitled
"Les Integraphes," being a study of a "new kind of mechanical
integrator."
The new kind of integrator was really only an independent version of
Boys' instrument, but in many respects a great improvement. The real
merit will ultimately belong to the scientific instrument maker who
constructs an instrument reasonably cheap and capable of efficient
practical service. Abdank-Abakanowicz's integrator however certainly
went further in the practical direction than any previously
constructed. The drawing board machines, it is true, of rather a
complex nature, were actually exhibited to the Paris Academy, but no
more have been made. The instrument before me was made by Coradi, of
Zurich, on conditions laid down by me, namely, that the cost should
not exceed £14, and that polar distances should range between one and
ten half-inches. The first machine made by Coradi on these lines was,
by a misunderstanding, sold in Germany, but the one I exhibit is the
first, I believe, that has reached England, and to this extent I may,
perhaps, be permitted to call it new. I look upon it rather as a
suggestion upon which a still more practical instrument can be made in
this country than as a perfect model. I believe there would be a wide
sale for such an instrument were it once generally known to exist,
and, what is more to work efficiently. It remains for me to point out
in what the Abdank-Abakanowicz, or, rather, Coradi, integraph differs
from Boys' instrument.
Two points deserve special attention. In the first place, the fixed
frame is abolished, and the horizontal motion of P (Fig. 3), the guide
point, is produced by putting the whole frame on friction rollers; in
the second place, as a necessary result of the first change, the guide
point carries about with it its own polar system, which renders the
changes in length of "rays" much more manageable. f f, f' f' is a
frame moving on four roughed wheels, e e e e, so that it can only move
in the direction, f', which we may term horizontal. f f and f' f' are
rails guiding the chariots, A and B, from f to f and from f' to f'. Of
these chariots, A contains the guide point, P, to trace out the
primitive with, and B the pencil, P', to draw the sum curve, i.e., the
tracer. The chariot, B, like Boys' tracer, is heavily loaded. g g is a
horizontal bar rigidly attached to the crossbars, q q and q' q', of
the frame. On g g is a movable pivot, to which h, which determines the
pole, k0 h being the polar distance. k0 is the position of a
second point, k, on the chariot, A, when the guide point, P, is on the
initial line, g g. l l is a bar with a long slot in it, in which work
the pivots, h and k; this bar represents the "ray." A projecting arm k
k' has been introduced to enable me to shorten the polar distance down
to 2 in. and under by removing the pivot, k to k'. m m is a bar
attached to the block, n, which runs on l l, so that m m is always
perpendicular to l l. On the chariot, B, is another bar, m' m',
capable of turning round the pivot, d, and always maintained parallel
to m m by the rods, m m', m m'. Attached to m' m' is a wheel, w,
whose axis is parallel to m' m'. This wheel, therefore, always moves
perpendicular to m' m', and therefore to m m; hence it moves parallel
to the ray, h k. A pencil, P', attached traces out the sum curve. If
we wish to use the machine as an integrator, we have merely to measure
the vertical distance traversed by P', or the distance B has run along
f' f'. This is done by means of a scale on f f'. If k be brought down
to k0, w runs parallel to g g, or P' traces out a horizontal
straight line, which is thus the base line. If k be fixed as near as
possible to k0, which is done by means of a screw in f f at k0,
the chariot, B, can be run down f' f' as nearly opposite to k0 as
can be guessed at; a horizontal line may then be drawn as base line,
and the guide point, P, brought into this line by a clamping screw
with which it is provided. The instrument is then ready for action.
There is a brake on one of the roughed wheels to check or stop the
motion of the integraph when required.
The instrument works best when the chariots, A and B, are about
opposite to each other; when they are at opposite extremities of f f
and f' f' respectively, the pull at P tends to produce a skewing
couple. If the chariot, B, could be put upon f f and work, if needful,
by a double parallelogram from m m, we should have, excepting the skew
pull, some great practical advantages. We might throw the whole of the
weight of the machine on the one pair of friction wheels, and replace
the other pair by a single wheel, the portion q' f' f' q' of the
machine virtually disappearing. Three wheels, of course, would be a
real improvement. Further, we should have the sum curve and primitive
drawn to the same base line, and the simplification in the number of
parts ought largely to reduce the cost of the instrument.
To be able to perform "inverse summation" (which in the language of
differential calculus is to find y as a function of x, when we are
given y=f(dy/dx), and not dy/dx=f(x) as usual), we only want a means
of making the plane of the wheel, w, parallel instead of perpendicular
to m' m', and it is easy to design a modification in the construction
which will allow of this change.
I hope the above description of the integraph may have made its
construction and method of working sufficiently clear. Those of you
who have a taste for mechanical work, and the necessary tools, might,
I think, with some patience, construct a workable integraph. I expect
the pivots would be the hardest part of the work. I hope, some day,
myself to have another instrument made with a more readily changeable
polar distance, with trace and guide points working in the same
vertical, and a wheel permitting of inverse summation. If this project
is ever carried out, I hope I may be permitted to communicate further
particulars to our society.
* * * * *
After some forty years of immersion in the waters of the pool of
Echoschacht, not far from Hermannstadt, several human bodies have been
brought to the surface in a state of perfect preservation.
* * * * *