250 Penfield- — Use of the Stereographic Projection for 



as applied to map measurement, will be illustrated by numer- 

 ous figures later. The protractor shown in figure 3 is nothing 

 else than a series of great circles and small circles, corresponding 

 to the meridians and parallels of half of a hemisphere, stereo- 

 graphically projected upon the plane of a meridian. The lines 

 may be printed or engraved on some transparent material, such 

 for example as celluloid, which is almost ideal for the purpose. 

 When the stereographic protractors were described by the 

 present writer he was not aware that similar devices had ever 

 been made use of before, and he is indebted to Mr. G. W. Lit* 

 tlehales of the Hydrographic Office at Washington for calling 



Stereographic Protractor with great circles and small circles ; five degree 



graduation. 



his attention to the fact that for purposes of navigation Chau- 

 venet had previously suggested the use of a protractor based 

 upon the same principles. Chauvenet's discovery seems to be 

 known to but few, and the only information which the writer 

 has been able to find concerning it is contained in a letter from 

 Mr. Littlehales, as follows : " The original plates of the Great 

 Circle Protractor now in the possession of the Hydrographic 

 Office show by the inscriptions engraved upon them that 

 the Protractor was originally known as Professor William 

 Chauvenet's Great Circle Protractor. The plates appear to 

 have been purchased by the Bureau of Navigation from 

 Professor Chauvenet about the year 1867 and used for many 

 years thereafter by the Hydrographic Office for the issue of 

 prints. I am unable to discover when the method was origi- 

 nally devised by Professor Chauvenet." 



Chauvenet seems never to have developed the full possibili- 

 ties of his protractor, though they must have been evident to 

 him ; moreover, at the time his protractor was first described 

 it could scarcely have been regarded as a wholly practical and 



