458 



Popular Science Monthly 



find the correct length by stepping oflf 

 one of the bottom view spaces sixteen 

 times and we will have the pattern for 



Megaphone 



Pattern for a mega- 

 phone which con- 

 sists of two cones 

 with ends cut off 



the complete cone. Fourth, to obtain 

 the pattern line for the part that is cut off, 

 set the pencil dividers at F and then along 

 the line F-G at the point where the small 

 cone is joined to the large cone, draw the 

 arc H-K and the pattern is complete. 

 For the small cone, the method is the same, 

 the apex of this cone being marked L and 

 the bottom view marked M. 



In the illustration for the funnel, Fig. 4, 

 the methods of developing the patterns 

 are the same as for the megaphone. 

 However the following helpful short cut 

 has been introduced. In all of the 

 patterns demonstrated so far, a full 

 bottom view has been drawn. This is 

 not always necessary and it saves time if 

 one half the bottom view is drawn from 

 the center of the base line, as shown at A. 

 We know that the other half is exactly 

 the same. When this pattern is devel- 

 oped, we also know that the other half of 

 the pattern is the same. The apex of the 

 large cone is marked B and that of the 

 small cone C. 



In the last article of this series a method 

 of developing an approximate sphere by 

 means of parallel lines was shown. In 

 that sphere the sections were vertical, in 

 the sphere shown in Fig. 5 the sections 



are horizontal, and the patterns are de- 

 veloped by means of radial lines. The 

 method followed is exactly the same as 

 for the megaphone and funnel. Only the 

 half pattern is shown for segment A 

 and B. The entire pattern is given for 

 C. This sphere may be made of any 

 number of segments, the greater the 

 number of segments the rounder the 

 sphere, and the more difficult the prob- 

 lem will be. 



In Fig. 6, the "hopper," we have a real 

 demonstration of development by radial 

 lines. The other problems in this article 

 have been given as a preparation for this 

 one. Suppose w^e need a pattern for a 

 hopper through which miaterial is shoveled 

 into a machine as is roughly indicated in 

 sketch A . The first thing we must do is 

 to see that the hopper is part of a cone. 

 We must then draw the complete cone 

 as is shown, getting the base, apex and 

 altitude. Second, we must draw the 

 full cone and lay out the part needed for 

 the hopper as shown at B. Third, draw 

 the bottom view C, divide into sixteen 

 parts and draw the lines straight up until 

 they strike the base of the cone. Then 

 draw them converging to the apex. 

 Fourth, draw the arc D-E with the apex 

 as the center. Get the true length of the 

 arc by stepping off the sixteen spaces of 

 the bottom view. Fifth, from each of 



Funnel 

 t Fig. 4 



A pattern for a funnel is the same as for a 

 megaphone but a short method is used 



these numbered points draw a line to the 

 apex. Sixth, comes a part that is some- 

 what difficult to understand. It con- 

 cerns the true and the apparent or false 

 length of some of these lines. The 

 explanation is this: if we measure the 



