A ship's ventilator may also be constructed in segments, as shown in Fig. 215. In order that the method adopted in obtaining the shape of the segment patterns may be clearly understood, it will be an advantage to first go carefully over the setting out of the pattern for an irregular article whose ends are circular, and not parallel. An elevation of such an article is shown in Fig. 214. This class of object gives good scope for illustrating the use of the method of triangulation in obtaining surface developments, and should, therefore, be taken particular notice of, as by this method any article whose surface is developable can have its pattern set out.

Imagine the circles that form the top and bottom of the article in Fig. 214 divided respectively into twelve equal parts, and that corresponding points be joined; then, on each quadrilateral so formed a diagonal drawn. It will thus be seen that the surface of the article would be divided into twenty-four triangles. The pattern is then built up, as it were, by getting the true shape of each of these triangles and adding them together, as shown in the one half of the pattern in Fig. 214.

Fig. 214.

Let us now go over the construction. From the numbered points on the top line projectors are run down to, and across, the base line; their distance below this being cut off equal in length to the corresponding line on the top semicircle. Thus the dotted lines 4 4° and 5 5° will be respectively equal to the perpendiculars drawn through points 4 and 5 on the semicircle down to the top line, and so on for the other lines. If the points 0, 1, 2, etc., be joined up, it will be seen that the half-plan of top becomes a semi-ellipse. There is no need in practice to draw in the ellipse; all that is wanted being the plans of the points.

For the pattern the mid-line 6 6 is first laid down, being made equal in length to the line 6 6' from the elevation. Now, to obtain the true length of the diagonal for line 6 5 on the pattern, measure from 6° on the ellipse to 5 on the bottom semicircle, setting this distance along the base line from 6°, and so obtaining point 5'. The length of the dotted line 5' 6' from the elevation is now measured off and used as radius from point 6 at the top end of the pattern, and a small arc drawn (shown passing through 5 at the bottom end of the pattern). The compasses are now set to the length of one of the six arcs on the base semicircle, and with point 6 at the bottom end of the pattern as centre, a small arc is drawn to intersect the first arc, and thus fix the point 5. The dotted line 5 5 from the plan is now set along the base line from 5°, and the point 5" marked. The line from 5" on the base line to 5 on the top line is measured off, and used as a radius from point 5 at the bottom end of the pattern to describe the small arc passing through point 5 at the top end. This arc is cut by setting the compasses to a radius equal to the length of one of the six arcs on the top semicircle, and using point 6 at the top of the pattern as centre. Thus point 5 at the top end of the pattern is determined. In the same way the lengths of all the other lines can be found. Thus 5° 4' on the base line equals 5 4 on the plan, and the line 5 4 on the pattern will equal the dotted line drawn from 4' on the base line to 5 on the top line; the distance 4° 4" will equal 4 4 on the plan, and line 4 4 on the pattern equals 4" 4 on the elevation, and so on for the remaining lines.

Fig. 215.

It is well to remember for practical purposes that there is no need to draw any of the dotted lines on the plan or elevation, or any of the construction lines on the pattern. All that is wanted being the fixed points, such as those obtained on the lower half of the pattern by the intersection of arcs.

The above method has been explained at some length, on account of its great importance. The reader should, therefore, find no difficulty in following its application to a