336 Notes on Map Projections. 
same ratio as the corresponding projected meridional degrees. 
This condition would determine a new polyconi¢ projection, 
whose scale, from point to point, (an element which in Bonne’s, 
and the simple polyconic projection, is a function both of the 
central meridian distance, and azimuth) would become a function 
of the central meridian distance only, and would increase alike in 
all directions on receding from this line. Such a projection would 
reduce distortion of local configuration, to an absolute minimum, 
and the areas in projection would be proportional to the squares 
of their local graphic degrees. This would enable us to take 
strict account of those irregularities of scale which now lurk in 
disguise. But it would be a great labor to prepare the tables 
requisite for its ready use, and there would be some valid objec- 
tions to its results. In a large topographical map thus projected, 
the scale of each sheet could be derived and engraved on its 
plate, making the sheet quite homogeneous on that scale, and 
perfect in the preservation of its configuration. Were a topo- 
graphical map of the United States to be undertaken on a liberal 
scale, this projection might be found superior to any other, as 
each sheet areas, dimensions, relations, and rectangular intersec- 
tions, would be well preserved according to its own scale, giving 
it the greatest local perfection, while it would also combine cor- 
rectly in its proper place. It should be stated that this projection 
is novel and untried. 
The method of projection in common use in the Coast Survey 
office for small’ areas, such as those of plane-table and hydro- 
graphic sheets, may be called the equidistant polyconic. This 
ought to be regarded rather as a convenient graphic approxima: 
tion, admissible within certain limits, than as a distinct projection, 
though it is capable of being extended to the largest areas, a0 
with results quite peculiar to itself. In constructing such a pro- 
mediate ones to determine the meridians with proper correctness, 
are constructed by the tables, and the meridians are drawn. 
on the meridians in like manner, and the tabular auxiliary va 
allels are, all except the central one, erased. In fact, as only yee 
points of intersection are required, the auxiliary parallels pit 
not be actually drawn. From this process of construction sat a 
a projection in which equal meridian distances are every wher 
intercepted between the same parallels. 
