Finder said:
Enlargement factor does not alter the change and so it does not matter about cropping
Take a picture of a diagonal row of telegraph poles, sticks, pencils, trees, whatever, at a low aperture, on high-resolution film. Print to 8x10". Crop the central 10% and print to 8x10". View from the same distance. DOF will look different. The enlargement factor is important because you project the negative's circles of confusion when creating a print from a given negative. If you enlarge them more, DOF behaviour will be affected.
Of course if you step back by the same amount as your enlargement factor grows, DOF is not affected, but if you enlarge more to a print of the same physical size - such as when cropping - DOF behaviour changes.
Finder said:
Keep the relationship the same between the viewing distance and print area and the print DOF remains constant. The practical upshot is that changing print size does not affect print DOF...
...assuming that as your prints get larger, the viewer steps backwards. Nobody is denying that, but it's an assumption which is highly dependent on how and where the images are viewed.
For example, Soviet lenses have comparatively generous DOF scales. At f/16 my 35/f2.8 Jupiter-12 indicates DOF from infinity to 1m, my Skopar 35/f2.5 roughly from infinity to 1.3m, that's a 1 stop difference. My 1949 Kiev has a DOF scale for 50mm lenses (which might well be a German part) that, at f/16, indicates infinity to 1.7m; my 1984 Canon 50/f1.4 lens has a DOF scale which gives the same range only for f/22. The reason is precisely because the typical Soviet picture was a 7x10 in an album held in your lap. After the war viewing behaviour changed - primitively speaking the average print size got bigger, so DOF was becoming more critical, but peoples' albums and laps were still at the same distance because people didn't grow as their prints did.
It's true of course that the two are interrelated, but judging from my own viewing habits I find it not very useful to use viewing distance as my metric and much more useful to use print size and enlargement factor (which again are interrelated of course). I can do so precisely
because they are interrelated. Also this approach makes it much easier to compare DOF behaviour between 35mm and medium or large format prints.
Philipp