rtical lines S intersect the horizontal lines as P,
are points in the ellipse.

Let it be required to draw a cylindrical body joining another at a
right-angle; as for example, a Tee, such as in Figure 226, and the
outline can all be shown in one view, but it is required to find the
line of junction of one piece, A, with the other, B; that is, find or
mark the lines of junction C. Now when the diameters of A and B are
equal, the line of junction C is a straight line, but it becomes a
curved one when the diameter of A is less than that of B, or _vice
versa_; hence it may be as well to project it in both cases. For this
purpose the three views are necessary. One-quarter of the circle of B,
in the end view, is divided off into any number of equal divisions; thus
we have chosen the divisions marked _a_, _b_, _c_, _d_, _e_, etc.; a
quarter of the top view is similarly divided off, as at _f_, _g_, _h_,
_i_, _j_; from these points of division lines are projected on to the
side view, as shown by the dotted lines _k_, _l_, _m_, _n_, _o_, _p_,
etc., and where these lines meet, as denoted by the dots, is in each
case a point in the line of junction of the two cylinders A, B.

[Illustration: Fig. 226.]

[Illustration: Fig. 227.]

Figure 227 represents a Tee, in which B is less in diameter than A;
hence the two join in a curve, which is found in a similar manner, as is
shown in Figure 227. Suppose that the end and top views are drawn, and
that the side view is drawn in outline, but that the curve of junction
or intersection is to be found. Now it is evident that since the centre
line 1 passes through the side and end views, that the face _a_, in the
end view, will be even with the face _a'_ in the side view, both being
the same face, and as the full length of the side of B in the end view
is marked by line _b_, therefore line _c_ projected down from _b_ will
at its junction with line _b'_, which corresponds to line _b_, give the
extreme depth to which _b'_ extends into the body A, and therefore, the
apex of the curve of intersection of B with A. To obtain other points,
we divide one-quarter of the circumference of the circle B in the top
view into four equal divisions, as by lines _d_, _e_, _f_, and from the
points of division we draw lines _j_, _i_, _g_, to the centre line
marked 2, these lines being thickened in the cut for clearness of
illustration. The compasses are then set to the length of thickened line
_g_, and from point