However, it is best to separate this composite of scales into two main factors called principal scale and local scale (Pearson 1990).

For example, if the principal scale is to be 1:10,000,000 this means that if the projected surface area is obtained from a globe with diameter 1.274m it would coincide with the map sheet.

The projection models can be used to establish the parameters of modern projections that fit the map, test one projection against other possible projections, and establish principal scale. This is done by determining the relationship between image coordinates and coordinates in the projection plane.

Writing h for the (geometric) mean of [h.sub.x] and [h.sub.y] in metres, and psize for the equivalent (geometric) average size of a 'pixel' on the page in centimetres, the principal scale can be estimated as:

Alternatively, the principal scale can be obtained from the metric properties of the scanner or camera when they are known.

They had earlier been photographed at 300 dpi and some comparisons are made between these cases for accuracy of determining principal scale and projection parameters.

DPI is the dpi of the scanner or camera and in this case was estimated by using the principal scale and inverting the equations provided earlier.

Map RMS is the Total RMS error (above) scaled to centimetres on the map using the estimated principal scale.

Using the principal scale, the RMS variation at the crossing points in cm on the maps can be estimated at 0.043 cm.

Based on Jupp (2017), the Kangxi base province maps were all the same at near 1:1,940,000 principal scale, and according to Wang (1991), the principal map scale of the collated copperplate mosaic was 1:1,400,000.

However, using the Sinusoidal models it is possible to easily re-project the provinces and at the same time make them consistent in principal scale. Additional constraints can also be used to help the mosaic.

It was at an enlarged principal scale; the graticule was at 1[degrees] intervals for both parallels and meridians, rather than every half-degree; the mountains were more finely drawn with less clutter, mainly to show the catchments of rivers; the rivers were smoothly drawn with artistic balance; and the smaller drawn characters were excellent calligraphy.