The instructions not found in the Jaguar service manual
Moss gearbox
How to correctly assemble the 3rd-4th gear operating sleeve
Doing it correctly, first time

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In his 1996 description of the problem of his XK120 gearbox jamming in first gear, Rob Reilly stated:

My 3rd/4th synchro sleeve has two plungers and two relieved teeth, one forward and one to the rear, and the 2 notches in the mainshaft are offset; thus it can go on the mainshaft six different ways but only one way is right. The manual says nothing about this little fact. It just says to assemble the sleeve to the mainshaft.

Here's an expanded description of how to assemble the operating sleeve and synchro sleeve in the correct way.

 

3-4-recesses

The forward end of the mainshaft spline has two recesses machined into the spline section for third and fourth gear plungers. These recesses are opposite one another on the mainshaft.

The recesses are longitudinally offset ~3.3mm (~1/8").

Looking at the forward side of the operating sleeve, locate the single relieved internal tooth visible from the front side. This is the relieved tooth which must be mated to the shaft so that plunger and ball associated with this relieved tooth mate with the forward recess in the main shaft.

The diagram shows a stylised version of the 3rd-4th synchro sleeve and operating sleeve, correctly assembled.

mainshaft-no-notes

In this version of the diagram, the way the plungers, balls, relieved teeth and mainshaft recesses act together when selecting third gear is explained.

The selection of fourth gear is similar.

Same information in a PDF file

mainshaft-with-notes