AucasT lo, 1888.] 



SCIENCE. 



63 



here. Besides this, the construction of the map is more simple than 

 that of the polyconic map ; the parallels being all concentric circles 

 and the meridians straight lines, while in the polyconic projection 

 ■each meridian must be constructed separately. But our projection 

 has still another advantage: it is the best among all the authalic 

 projections that are possible ; that is to say, the maximum of dis- 

 tortion cannot be made smaller than it is in our map. A study of 

 the map shows that the distortion reaches its maximum in the 

 extreme southern part of the United States, in latitude 25° north, 

 where it amounts to 1° 16'. Going north, it decreases rapidly, 

 until in latitude 28" 58' 49" it vanishes. Then it increases again 

 quickly, and in 37° 58' 16" again reaches its maximum of i* 16'. 

 Farther north it decreases, and on the parallel of 45° 58' 55" there 

 is no distortion. While in this zone (from 28° 58' 49" to 45° 58' 55") 

 the maximum of increase of length is in the direction of the merid- 

 ians, while the maximum of decrease is along the parallels, it is the 

 reverse north and south of it. From the northern line, on which 

 no distortion exists, it increases, and reaches 1° i6' on the 49th 

 parallel, the northern boundary of the United States. We have in- 

 dicated by various shading the regions of equal distortion on both 

 projections. The regions situated east and west of the line of l° 16' 

 distortion on the polyconic map are in every respect inferior to our 

 map. But it will be seen that the distortion of angles in the central 

 part of the polyconic map is slighter than in our map. The central 

 parts of our projection, on the other hand, are inferior to the poly- 

 conic projection so far as alteration of angles is concerned, while it 

 is superior for census purposes as being equivalent. We must not, 

 however, consider the central parts alone, as the map is intended 

 as one of the United States, not of parts of the States. For the 

 ■central parts alone, it would be necessary to adopt another equiva- 

 lent projection. In our map on the lines of maximum distortion the 

 lines whose lengths are increased are i.i per cent too long, while 

 those vertical to them are i.i per cent too short : therefore this is 

 the maximum error that can be made in measuring lengths. In the 

 polyconic projection this error is equal to the amount of deformation 

 of surface, being 6 per cent in the Eastern and Western States. 



The sketch-map on p. 62 shows the difference between the dis- 

 tortions of angles in these two maps. In the shaded portions the 

 polyconic projection has a slighter deformation of angles than our 

 projection ; in the dotted portions the reverse is the case. This 

 comparison shows that in 48 per cent of the area of the United 

 States the polyconic projection is superior to ours regarding defor- 

 mation, the maximum difference in its favor being 1° 16', while in 

 52 per cent of the area ours is superior, the maximum difference in 

 its favor being nearly 4°. A comparison between the amount of 

 deformation in both maps gives the following results : — 



From these remarks it appears that the conic projection excels 



the polyconic in every respect. 



It appears from our map, very clearly, that the polyconic projec- 

 tion has the valuable property of having very slight distortions on a 

 wide belt situated on both sides of the central meridian. This 

 property makes it valuable for maps showing narrow strips of land 

 only, such as coasts of the ocean and of lakes : therefore it is ser- 

 viceable for the purposes of the Coast Survey, particularly as the 

 alteration of surface is of little or no importance to the mariner. 

 The United States, hov/ever, have a wide extent in longitude, and 

 a far smaller one in latitude, which makes the projection not well 

 adapted for a map of the whole country. If the object were to 

 construct a map of the svhole territory of the United States on this 

 projection, we ought to make use of this fact. Our country is far 



more extended in longitude than in latitude. But by assuming a 

 system of parallels and meridians the pole of which is situated near 

 latitude 12" north, longitude 175° west from Greenwich, and using 

 this for a polyconic projection, the greatest distance from the new 

 central meridian will be 13" instead of 30*, and the greatest distor- 

 tion less than 1° instead of nearly 4°, while the increase of surface 

 will be less than two per cent in the outlying portions. This pro- 

 jection may be considered quite a good one, as the central part of 

 the country adjoining about the 40th parallel of latitude would have 

 hardly any distortion. From this line it would increase very slowly 

 northward and southward. 



We said, however, above, that, for the purposes of a census, 

 equivalence of surfaces must be the fundamental point of view for 

 the construction of a map, and, as even the oblique projection just 

 mentioned is not equivalent, it cannot be accepted. For the same 

 reason it is necessary to take into account the spheroidal shape of 

 the earth, which makes the computation of oblique projections dif- 

 ficult: therefore they will be only chosen if they offer great improve- 

 ments upon others. 



Assuming the central point of a circle circumscribed about the 

 United States as a zenith, and computing a conical projection that 

 is equivalent, and in which the alteration of angles is as slight as 

 possible, we shall find that the maximum alteration of angle is not 

 more than 58', the map including the whole territory of the United 

 States. We should recommend this map, if it were not for the 

 fact that there would be an open sector of 10° aperture running 

 from the centre near Omaha to the northern boundary. This is 

 produced by the development of the cone upon which the map has 

 been projected. The existence of this open sector is so serious an 

 objection, that the decrease of 18' in the deformation cannot be 

 considered an equivalent. 



By assuming an oblique conic projection the alteration of angle 

 might be reduced to 1° 9', but the difficulty of computing this pro- 

 jection for the spheroid induces us to discard it. A thorough inves- 

 tigation into the properties of all known projections leads us to the 

 conclusion that the projection we propose here is the best that is 

 possible for census purposes, and the only one that ought to be 

 used for it. The easiness of computation of the elements adds to 

 the properties that qualify it for an extensive use. Dr. F. Bo.^vs. 



JAMES STEVENSON. 



Ix the death of James Stevenson on Wednesday, July 25, the pub- 

 lic lost the services of one of the most active and indefatigable eth- 

 nologists of the time. Certainly, so far as knowledge of the aborigi- 

 nal American race habits and customs is concerned, he contributed 

 more than any predecessor, and by his keen appreciation of the 

 subject and tireless investigation he saved from irreparable loss 

 much of the evidence upon which must stand all we know of many 

 of the ancient peoples of this continent and their polity. 



From an article in a recent issue of the National Tribune of 

 Washington we get the following facts relating to the life and 

 labors of Mr. Stevenson. He was born at Maysville, Ky., in 1840, 

 and his life was devoted to the one passion of geographical and 

 ethnological research, except when interrupted by the war. 



He went West first when quite a boy, several years prior to the 

 Rebellion, with Professor Hayden, to the Missouri River country, 

 making unofficial observations of Indian customs, and learning their 

 dialects. Upon the breaking-out of the war. Professor Hayden en- 

 tered the service as a surgeon, and young Stevenson enlisted as a 

 private, and became a second-lieutenant of the Thirteenth New York 

 \'olunteers. He was at the second Bull Run, and was an impor- 

 tant witness in the famous Fitz-John Porter case. 



In 1866 he resumed his explorations, going to the Bad Lands of 

 Dakota with Professor Hayden, as his assistant in the Geological 

 Survey. Being a warm personal friend of the late Gen. John A. 

 Logan, young Stevenson aroused in him a deep interest in the sub- 

 ject of developing a better knowledge of our Western lands. Logan, 

 at Stevenson's suggestion, conceived the idea of establishing such 

 a sun'ey as a distinct and responsible branch of the general gov- 

 ernment, and from his place on the floor of the House, in the 

 winter of 1866-67, he offered .an amendment to the Sundry Civil 

 Bill appropriating the sum of five thousand dollars for such an in- 



