Well - my K&E Railroad Transit arrived yesterday in fully working order (pretty impressive for something that's over 100 years old). All parts seem fully operational (i.e. compass, levels, gears, etc.)! Having it "in hand" to really compare to the screen grabs, I can now say with 99.99% certainty that the transit used by Indy in ROTLA is, indeed, a K&E Railroad Transit (Model 5160).
There are a couple of minor variations from the one in my possession and the screen grabs (as noted below), but most of those can easily be accounted for by swapping the direction of the parts or (in the case of the levels) some parts that have been replaced over the years. (There could also be some variation in models year-over-year. Mine is from 1916 - confirmed by matching serial number ranges, but the production used transit was likely from a different model year.)
I've annotated a few key indicators on both the screen grabs and the actual K&E Railroad Transit, which I believe to conclusively prove that this is, in fact the correct model. Having searched exhaustively online to find this one and compared many other K&E and other manufacturers' transits, I believe these indicator points to also be the key differences between the correct transit and the many other vintage transits out there.
A - The level tube (the smaller horizontal tube) attaches to the main scope (the larger tube) about 1" in from the end of the eye piece.
B - The eye piece itself is a distinctive shape with a flared end that is slightly smaller than the "connector" where it attaches to the scope. Both the eye piece and the connector are "ribbed" on the sides.
C - The small wheel opposite where the level attaches (honestly, I have not been able to figure out what this wheel does) has a distinctive mounting bracket which is rectangular.
D - Just in from where the level attaches, there are two rows of rectangular "brackets" attached to the scope. The row closest to the eye piece is secured with flat head screws and the row next to it is secured with round "screw" connectors with little holes in them.
E & F - The "U"-shaped mounting brackets have no cross-beam connectors. One side has a round "screw" connector with little holes (E) and the opposite side has two flat head screws (F) which - on my version - is used to attach an angle indicator that appears to be part of the "wheel" which is missing/removed in the movie version.
G - There is an "A"-shaped bracket that appears to be used to make very subtle adjustments to the inclination (up/down movement) of the scope. The wheel, cross beam, and beveling of the bracket are distinctive.
H & I - The focus "knob" is ribbed on the sides with a distinctive horizontal line running around the middle. It attaches a little bit forward (about 1/2") of the level connector on the opposite side (I).
J - Twisting the focus "knob" (H) moves the entire "lens" (J) forward and backward (just like you can see in the movie). The lens piece is also a distinctive shape and length.
K - There is a small circular "connector" on the base (opposite one of the base levels) that is made up of 3 increasingly smaller concentric circles (almost like a pyramid) with a round "screw" connector with little holes on top.
L - There is a slightly raised glass and metal plate which displays the horizontal angle of the base. (There is another one on the opposite side, as well.)
M - There is a "cone" shaped screw with a flared (looks like a mushroom) head that separates in the middle. (Also not too sure what this does, but it seems to be a distinctive and unique identifier of this model.)
N - There are 2 bubble levels to level the base. They are both cylindrical and connected with either 2 round "screw" connectors with little holes (as in the movie version) or 1 round "screw" connector with little holes and 1 flat head screw (flush mount) (as in my version). One level is opposite the "cone" structure (M) and the other is opposite the circular connector (K).
The scope does, in fact, spin all the way around so that it can be used "upside down" like Indy seems to be doing in the movie. You can see in the movie, however, that the level tube is correctly oriented "up" (so the bubbles are visible from the top), which indicates that they must have slightly modified the transit. (There are 2 large round "screw" connectors with little holes which could be easily removed to reverse the level tube, so this seems like a fairly easy modification.) As has also been pointed out, the movie version did not have the "wheel" or angle indicator attachment. It's not clear to me if that indicates that it was simply removed for production (so it didn't block the camera view) or if that might have been an optional module when ordering (the catalog I have doesn't indicate any models without the wheel, leading me to believe that it was probable removed before production or for production).
The one fairly major difference between my model and the movie model seems to be that the "U" shaped brackets are reversed on mine. On the movie version the "U" bracket with the flat head screws mid-way up the side (F) are directly above the circle connector (K) and the "U" bracket with the screw connecting at the top (E) is directly above the side level. On my model, those "U" brackets are reversed. This could be a minor manufacturing difference (the guy at the factory just put them on differently) or it could be something that changed over the years.
One final point of interest is that, when looking through the scope, it does show the multiple horizontal and vertical lines like in the movie, but there are no numbers. It makes sense that the "effect" would have been added in the movie post-production, but also interesting to note that it's not truly authentic to the prop itself. (Unless that is another thing that changed over the years.)
Next up is the search for the tripod, which does not appear to match any vintage transit (K&E or any other manufacturer) tripods that I have found. It seems to be much heavier duty with much wider legs. I've been thinking that maybe they used a movie camera tripod (or studio light tripod) which might have been handy on the set, and although vintage movie tripods look closer, I still haven't found one that's an exact match.
