How to figure out an unknown reprojection of a old (18 century) map (raster)?

Question

Here is a map of the Russian Empire of the late 18th century and I want to know its projection system. Unfortunately, the map does not contain information, which latitude point is a basis/which coordinate system it uses.

Could you give me an advice, how to transform the unknown projection of the map into a commonly used ones (e.g. WGS84). I can georeference the raster but it is not a solution in my case because I need to know how to transform the values of the system for other maps, which use (apparently) the same projection system. Examples of the rasters to transform using the projection are below.

https://yadi.sk/i/LS45OGbswAACx

P.S. Updated a second link. Should work now.

Answer 1

The imprinted grid seems to use Ferro coordinates. So you could use EPSG:4805 as target SRS, and reference your map to it using the imprinted grid (not from canvas).

Alternatively, you could create a vector grid based on the Ferro meridian with EPSG:4805, densify it and reproject it to a Lambert conformal conic projection centered on 125° East of Ferro

+proj=lcc +lat_1=15 +lat_2=65 +lat_0=30 +lon_0=125 +x_0=0 +y_0=0 +ellps=bessel +pm=ferro +units=m +no_defs

With that, you now can reference on grid intersections or known points on the map and on the canvas.

Answer 2

It appears to be a simple conic projection. See Section 2 of this link (http://kartoweb.itc.nl/geometrics/map%20projections/mappro.html).

Now you can use the gratiucle on the map to plot each of the interecting coordinate pairs to your chosen conic projection. The process is spelled out in this paper but you basically map each coordinate pair on your map to the relevant one in the projection.

Hamilton, Stuart E., Alexander Angelov, Vladimir Atanasov, and Marco Millones. "Fluid Borders: Rethinking Historical Geography and Fixed Map Boundaries in Contested Regions." The Professional Geographer 68, no. 1 (2016): 115-128.

I can see this projection would likely work for you by looking at your map. http://spatialreference.org/ref/sr-org/8568/

Then just use raster reprojection tools to get to WGS 84. You could actually just use a WGS 84 grid to do this but it would be a bear and a high chance of error due to major scale mismatches. You'd likely have to use a high polynominal adjustment as well. I'd go via the conic route.