24 S. L. Penjield — Stereographic Projection . 



should leave the engraver's hands practically perfect. An elec- 

 trotype of the plates is next taken, and the copper depositing in 

 the grooves made by the engraver's tools furnishes the relief from 

 which impressions are taken. Finally, in order to prepare the 

 electrotype for printing, the copper, stripped from the plate, is 

 strengthened by casting some easily fusible metal upon the back 

 of the electrotype. This casting causes a slight shrinkage of 

 the plates, amounting to about 0"5 mm for a distance of 140 mni 

 (the diameter of the protractors). It has been ascertained that 

 the shrinkage is practically uniform and proportional in all the 

 plates, so that no appreciable errors can arise from using engrav- 

 ings of this kind. Still, the plates are not absolutely perfect. 



Copper or steel engravings would be preferable to engravings 

 made by the wax process, but both the plates and impressions 

 therefrom would be more expensive. If it is thought best to 

 have another set of scales and protractors on a larger scale, the 

 desirability of having them engraved on steel or copper should 

 be carefully considered. Even impressions made from steel 

 engravings might not be absolutely perfect, for paper changes 

 somewhat under varying climatic conditions, and expansion and 

 contraction are not always alike in every direction. 



Another thing to be considered is that celluloid shrinks, and 

 protractors printed from accurately engraved plates may become 

 inaccurate in a few months. Except for its tendency to shrink, 

 however, celluloid is exactly the kind of transparent material 

 upon which to print the protractors, and a very simple correc- 

 tion serves to offset the slight shrinkage. For example, some 

 impressions of protractor No. II, printed on newly purchased 

 celluloid five months prior to the time of writing, have shrunk 

 so that with a zero point of the protractor matched exactly at 

 one end of a diameter of the divided circle, figure 3, the 180° 

 point falls one-half a degree short of coincidence with the 

 opposite end of the diameter. In other words, a distance of 

 179° 30', stereographically projected upon a diameter of one 

 of the engraved sheets, figure 3, is measured as 180° by means 

 of the protractor ; hence, from measurements made by the 

 protractor, 5 7 should be deducted for every 30°, equivalent to 

 30' for 180°. It is believed that, in time, celluloid will become 

 seasoned, so to speak, and that it will cease to shrink. Accord- 

 ingly a rather large stock of this material has been purchased 

 with the hope that in the course of a year or two it will be 

 possible to print protractors which will not change. 



Taking into consideration all imperfections of the plates, 

 especially those due to shrinkage in casting, errors arising there- 

 from are quite insignificant when compared with the errors 

 involved in plotting points and constructing arcs when the con- 

 struction is based upon so small a scale as a 14 cm circle. 



(To be continued.) 



