OP THE UNITED STATES. 407 



the projection under the above condition, whether the geo- 

 centric radius oi' the hititude, tlic railiiis of curvature of the 

 meridian at the tangent jwint, or the radius of the sphere tan- 

 gent to the spheroid at the point. Further than this I had 

 not proceeded, when I abandoned tlie subject, by tlie inter- 

 ruption of my work. 



It is at all events necessary that these projections go off 

 from different points of hititude, and be all of equal extc?it 

 from the central meridian and parahcl, in order tluU the de- 

 viations fiom tlie real magnitude may never become so 

 great as to require the application of correction for the plane 

 table operations, whicli determine of course the details in 

 the neigiibourhood of any point of a triangle from the posi- 

 tion of these points, as laid down by tlie projection, — and 

 that in bringing the different parts together, their points on 

 the edges may meet again completely, being equally aHected 

 by the projection. 



In each of these sheets? it was intended to liring tlie results 

 of several parallels, so that the central meridian alone should 

 become a straight line, and all the other meridians and jja- 

 rallcls broken lines, nearest the curve, to which they belong; 

 the angular points of the trapezium being transferred to pa- 

 per by their rectangular ordinates, from the middle right 

 angle, calculated from the angle at the centre of the projec- 

 tion, in the protracted axis of the earth. 



The papers to be given to the detail surveyors should lie 

 divided differently : viz. they nmst always contain tliose 

 points, and extend over such parts as may, l)y the nature and 

 configuration of the country, be best ada|)ted to be surveyed 

 together. But the points must be laid down upon them ac- 

 cording to the place whicli they would occupy in the al)ovc 

 regular disfiihution of the projections. 



This distribution of the projection, in an asseml)lage of 

 sections of surfaces of successive cones, tangcrUs to or cutt- 

 ine; a regidar succession of parallels, and upon rci;;idiuly 

 changing central meridians, appeared to me the only one 



