198 
iui. A method of drawing ellipses. 
A square frame hinged at the corners has a number of 
parallel strings, on these are arranged a number of concentric 
circles marked on the strings by beads or paint. When the 
square is drawn into the form of an oblong the circles become 
ellipses, and the two elastic strings stretched from corner to 
corner are the diameters, the equi-conjugate axes being parallel 
to the sides of the frame. This is manifest from the equation 
x“ +y* =a’ in the square remaining as 2+ y’=a’ in the rhom- 
bus. If ¢ be the angle of the rhombus, sec fae gives the 
eccentricity. Or the portions of the elastic strings forming the 
diameters might be measured to suit the particular ellipse re- 
quired. The frame can then be placed on a piece of paper and 
the ellipse dotted off between the parallel threads. Properties 
of ellipses and other curves may thus be compared with similar 
properties referred to rectangular co-ordinates. 
iv. Method of drawing in perspective. 
ABCD is a drawing frame. 
The base CD is bisected in Z. EFG is perpendicular to 
CD on the plane of the frame and projecting below the frame. 
EG is the distance of the eye. GF the height of the eye. If 
the plan of any building be drawn to scale at its true angle to 
and distance from CD, any point of it, K, is thrown into per- 
spective thus: an elastic thread extends from F' to G; it is 
stretched to K; let GK meet CD in WV, and let MS perpen- 
dicular to CD meet KF in S; 8 is the perspective of K. The 
corresponding height of the AKT is found by producing MS to 
meet 7’ in Z This operation is facilitated by drawing on 
paper ruled parallel to a side of the frame perpendicular to OD. 
v. Steam-ship to convey trains from Dover to Calais, 
Two tubes of wood (or iron) 200 metres long and 4 metres 
diameter give carrying power of -tubes when completely sub- 
merged = 5000 tons. Two parallel lines of rails to take trains, 
