Meridians and parallels not meeting perpendicularly is a dead give away that it does not intend to be a stereographic.
You are right Strebe, I did not look at the projection angles so minutely. Bonne is surely the closest match with standard parallel set pretty high at 40. Though David is already done with it, I was exploring it for a bit of learning.....
I was wondering how you do the comparison with least squares. You will need the distances at various points, say the graticule crossings from a fixed point. Do you have a software or some ready made methodology to do such analysis? Please do educate us on it when you find time. Thanks, it was a good learning.
Sorry to get back to this so late. I have a lot of hacky functionality on top of Geocart for my own research purposes that is not refined enough for release to others. One of those is a least-squares analysis. I preprocess the image to reduce biases caused by linear distortions (stretch, affine, rotation), insofar as they are clearly due to inaccuracies in image reproduction or warpage in the medium. Thus rectified, I state the cartesian coordinates of the graticule intersections. Then I just let Geocart churn through a large list of plausible candidate projections. For each, I use a root-finding algorithm to let Geocart adjust the scale of the candidate projection until its least-squares deviation from the image projection reaches a minimum. The candidate projection whose best least-squares deviation is the smallest of the lot wins.
That's the gist of it, but many projections are themselves able to be parameterized, and so this turns into more of a global minimization process, depending on what it is I am really trying to achieve. Usually there is a historical context attached to the image whose projection you are trying to identify, so if you are interested in the intent of the mapmaker (as opposed to just finding a projection that best fits the map), you would not add a projection developed in 1920 to the list of candidates if you know the map is from the 19th century. While I can come up with closer fits for this particular map through parameterizing, transforming, and mathematically distorting arbitrary projections, the historical context and the otherwise close fit of the Bonne clinches it. Also, the graticule deviates from the geography, so you'd have to decide which was more important to preserve if you were trying to reach a best fit, as opposed to reaching the mapmaker's intent.
-- daan Strebe