Objectives are a pain when mix n matching, B&L brass, very short, lomo 33, Jena 35, Beck and Wild.. 38? DIN 45. All 160 and all different. I had to mod my Zeiss to work with them all. Luckily the worst mismatch I made was a Leitz 170. Many Lomo's are 190.
I'm pretty sure, objectives over 170mm tube length will be metallurgical objectives. There were a whole slew of different lengths, 190mm being one of them. There are some odd tube lengths, such as 135mm for some hobby biological scopes. For almost all diascopic microscopes of a fixed tube length, though, the tube length will be either 160mm or 170mm. This is not always marked on the objective and it sometimes requires a bit of historical info., to determine the tube length or direct measurement. Irregardless of other corrections, an objective's tube length can be determined by measuring the magnification using a reticle or stage micrometer, by screwing the objective into a stand that has a known tube length. Using an eyepiece originally corrected for the test objective gives best results but probably any eyepiece will cough up enough of a result. A 160 objective will give roughly 6% greater magnification in a 170mm tube and a 170mm objective roughly 6% less in a 160mm tube.
However, with the complicating factor of parfocal distance and the distance to the intermediate image in the mix, not only does the magnification go askew using the wrong tube but also parfocality when mixing objectives becomes a pain, spherical aberration can be enough to reduce resolution,and as well, poor colour correction can flood the periphery of the field with lateral ca.
If the measurements are pretty close, there shouldn't be much of a problem but closing the gap between a 160mm tube and a 170mm tube with an adapter, is unlikely to provide an image that does not suffer from some degradation.
It wasn't really until the D.I.N. 45mm parfocal objective system with a 160mm tube came along and became almost ubiquitous that systems became somewhat theoretically interchangeable. This was however thwarted, by the invasion and necessity of W.F. eyepieces. Previously, the common use of Huygens eyepieces meant that eyepiece correction was somewhat consistent across brands. With W.F., proprietary designs were everywhere, so objective/eyepiece compatibility became the rule of the day, rather than parfocal/tube length compatibility.
The idea that fixed tube microscopes had interchangeability across brands is a myth. Maybe PZO and Zeiss West?....but mixing objectives is generally difficult and for sure you can put any other objectives on a compatible tube length stand, as long as you change to the correct eyepieces as well, so there is limited mix and match.
Even the short objective Nikon and Olympus systems were at odds with each other and as well the J.I.S. J.I.S. was a 170mm tube with 36mm parfocal. Nikon was 160mm with 35mm or less parfocal( I don't know exactly what it was) and Olympus was 160mm with 36.65 mm parfocal. The 3 companies, Shimadzu Kalnew ( once a major player in Japanese microscopes), Tiyoda and Olympus were all spawned out of the Japanese commercial microscope progenitor, M & Katera. M & Katera used 37mm parfocal and a 170mm tube. Shimadzu Kalnew spun off, using J.I.S., Olympus developed their own 36.65 and 160mm system and I am not sure about Tiyoda but it was probably J.I.S. Other Japanese makers , Carton, Kyowa were most likely J.I.S.