[200° J 
XVIII. On a Novel Instrument jor Drawing Parabolas. 
By Karu Prarson, F.R.S., University College, London*. 
[Plate XV. ] 
5 ee a number of years I have much desired a really 
effective instrument for rapidly constructing parabola 
on the drawing-board. As far as my experience goes exist- 
ing mechanisms for this purpose are occasionally ingenious, 
but always ineffectual. Yet in ordinary drawing-office 
practice the construction of parabolas in both graphical 
statics and graphical dynamics is an almost daily necessity. 
One has only to think of the solution of continuous girder 
problems, of speed-curves from energy-curves, of stability of 
dams, and a variety of other matters to realize how much 
energy is wasted in the drawing of these curves which ought 
to be done rapidly and effectively by aid of a mechanism. 
The grant made by the Drapers’ Company to my depart- 
ment has placed me in a position to carry out, in a practical 
form, some of the needs we have long felt for labour-saving 
mechanisms in our drawing-office, and the following brief 
description of the new “ parabolograph” may be of interest 
to those who have felt the like want. 
The principle made use of in the new mechanism is the 
fundamental metrical property of the parabola. Let PVP’ 
(Pl. XV. fig. 1) bea parabola, V the vertex, and VX the axis. 
If P be a point on the parabola PN?=c x VN, where PN is the 
perpendicular on the axis. Draw PFT parallel to the axis. 
Join VP and take VT perpendicular to VP to meet PFT in T. 
Drop VF perpendicularon TP. Then clearly FV?=FTx FP 
since the angle at V is right. It follows, therefore, that 
FT=c the parameter of the parabola. Hence, if a bar TP 
slide so as always to remain parallel to the axis, with a de- 
finite point F slipping along the tangent FV at the vertex, 
then a bar TVP, bent at right-angles at V, round which point 
it pivots, and passing through a fixed point T on FT, will 
give points on the parabola by its intersection P with the 
same line. 
This simple property was used by my former assistant 
Mr. H. Payne, now Professor of Engineering in the South 
African College, to design a parabolograph. This with 
his consent I forwarded to Herr Coradi, of Ziirich, as the 
man most likely to make a really practical machine, the step 
from perfect theory to effective practice being, as 1 know 
from experience, a rather long one. 
The machine as designed by Payne and executed by Coradi is 
represented in the accompanying fig. 2 (Pl. XV.), which almost 
explains the method of working. Herr Coradi has introduced 
* Communicated by the Author. 
