S. L. Pen field — Stereographic Projection. 125 



western hemispheres accurately plotted in stereographic pro- 

 jection, and transparent protractors constructed on the same 

 scale, such measurements could be made by simply shifting the 

 protractors and noting the angles. Maps of this kind would 

 be very serviceable, and the writer believes that they should 

 and will be made. The most important continental features 

 (promontories, mouths of rivers, lakes, etc.), the islands, and 

 the principal ports and inland cities could be located with 

 great accuracy on a map of 30 cm (nearly one foot) diameter, 

 and it ought to be possible to measure distances between any 

 two points within two or three minutes (two or three nautical 

 miles) of the truth; while the maximum error ought not to 

 exceed ten minutes. If there is an error of judgment in the 

 foregoing statement, it favors greater, rather than less, exact- 

 ness, for on the 14 cm circles a degree of accuracy can be 

 obtained almost equal to that just expressed. 



Without doubt geographers and physical geologists would 

 find many uses for sheets printed from accurately engraved 

 plates giving the meridians and parallels, in both equatorial and 

 meridian stereographic projection, plates II and 111. On such 

 plates, points of given longitude and latitude could be quite 

 accurately located (within half a degree), the outlines of conti- 

 nents sketched, wind and ocean currents noted, etc. ; and, 

 provided with protractor JSTo. Ill, measurements sufficiently 

 accurate for most purposes could be made in a very few min- 

 utes. The writer has not employed such sheets in crystallog- 

 raphy,* but has had the plates prepared to conform with the 

 protractors and scales described in this article, believing that 

 they will prove very useful. 



It is at times desired to shift a stereographic projection so as 

 to bring some special point or pole to the center. By making 

 use of scale No. 3, figure 3, this can be easily accomplished. 

 Plate IY represents a projection thus shifted so as to bring 

 longitude 75°, latitude 40° (practically the location of New 

 York city), to the center. The north pole is shifted 50° from 

 the center, and the equator is an arc of a great circle crossing 

 the vertical diameter 50° from the divided circle. Cutting off 

 scale No. 3, figure 3, from one of the engraved sheets, and 

 matching it along the vertical diameter, the stereographically 

 projected points 10°, 20°, etc., are laid off in both directions 

 from the shifted north pole, and about the respective center 

 points the parallels of latitude (small circles) are drawn. That 

 parallel which is located by actual measurement exactly half- 

 way between the stereographically projected north and south 



* Impressions of an equatorial stereographic projection, essentially like plate II, 

 have been recommended by Fedorow, especially for use with the two-circle or 

 universal goniometer. Zeitschr. fiir. Kryst., xxxii, p. 446, 1900. 



