About the year 1720, a globular chart was published, said to be constructed by Mr. Henry Wilson; the errors in which were obviated by Mr. Thomas Haselden, in a letter to Dr. Halley; who at the same time exhibited a new scale, whereby distances on a given course may be measured, or laid off, at one extent of the compasses, on Wright’s projection; and was intended to render the same as easy in practice as the plane chart.
The above chart was published in opposition to Mr. Wright’s, which that author charged with imperfections and errors, and that it represented places bigger than they are upon the globe.
It is true, the surface is apparently enlarged; but the position of places, in respect to one another, are in no wise distorted; and it may be asserted, with the same parity of reason, that the lines of sines, tangents, and secants, are false, because the degrees of the circle, which are equal among themselves, are thereupon represented unequal.
Yet if a map or chart was so constructed, as to shew the situation and true extent of countries, &c. primâ facie (if I may be allowed the expression), and yet retain all the properties, uses, and simplicity, of Wright’s construction, it would be a truly great improvement; but this seems to be impossible.
The method exhibited by the Rev. Mr. Murdoch, in his paper, read before the Royal Society on the 9th of February last, shews the situation of places, and seems better calculated for determining superficial and linear measures, than any other that has occurred to me.
This Gentleman illustrates his theory with examples justly intended to point out the quantity of error, that will happen in a large extent.
For instance; Between latitudes 10° and 60° N. and containing 110 degrees difference of longitude, Mr. Murdoch computes the distance at 5594 miles; which, upon the arc of a great circle, is found to be 5477, or by other methods 5462; so that the difference is only 117, or at most 132 miles in so great an extent, and to an high latitude; and the higher the latitude the greater the error is like to be, where-ever middle latitude is concerned.
His courses also agree very nearly with computations made from the tables of meridional parts.
In example the first they are the very same:
In example the 2d they agree to half a minute: