The gearbox as used by Norton was actually a design from Sturmey Archer which was bought by Norton but the boxes themselves were built by Burman. Modification of the SA design possibly done by Burman but the gear change mechanism was a Norton patent of 1935. (424,154. Controlling variable speed gearing. NORTON MOTORS, Ltd., and CARROLL, A.)

Drawings from the patent show the initial configuration of the ratchet lever with the swivel at the end for fixing the gearbox control rod. This version was replaced in 1937 by a straight ratchet lever without a swivel. From 1938 onwards, 2 additonal nuts were applied at the rear of the head to improve the fixing of the Stop Studs for Pawl Carrier to the dolls head housing. These additional nuts required a new ratchet lever to remain clear of the nuts. 

   
 evolution of ratchet levers, from left to right, pre 1937, 1937 and post 1937 version.

Further changes over time was the introduction of bushes on the return spring cover plate and the cam plate, an obvious attempt to improve the wear resistance of the support of the gear change lever. This was retrospectively applied on earlier machines, based on DME B.304 dated 7-9-1942. Not absolutely certain which solution in the picture of the camplate (steel bush or bronze bush) was the Norton applied change or the workshop version based on the DME.

The application of the bushes required a bigger hole in the gear change mechanism cover. Up to late 1939 there was no brass gear position indication plate on the dolls head. This was likelt introduced due to the influx of large numbers of non-experienced motorcyclists in the military. The cover of the earlier change mechanism showed a small vertical stripe in the bottom of the first "o" of the Norton name to indicate neutral only. The brass plate showed all 4 gears and neutral. 

Gear change mechanism covers at left early without brass indication plate and small hole, at right later with brass plate riveted to the top of the cover and larger hole to accommodate the bush in the return spring cover.

Gear change indicator at left used up to 1939 in combination with early cover, at right 1939 and up in combination with later cover.
no exact change date known. As covers were made before changes were introduced, early covers can be found having been modified with the brass plate.

Upper one is early production gear control rod, lower one a later production, unknown when latter was introduced as part number never changed.

Gearbox castings, identification and ratio's

The gear ratio's given in the Norton Maintenance and Instruction Manuals and as often found in various contemporary books are slightly confusing when looking for a proper gearbox for your bike. The ratio's given are basically the ratio's of the entire transmission system from engine sprocket to rear wheel drum mounted sprocket, and not of the gearbox itself. Civilian 16H and Big4, and WD16H gearbox shells were all identical. Most common casting numbers were N8001 and N8001-3, some deviations are observed which may have been production errors as internals were correct. Very early (1936) gearboxes did not have a drain plug at the bottom rear of the casting but it was standard from 1937 onwards.

Several serial number prefixes are observed, following explanation is conjecture but with logic. As Burman made gearboxes for other motorcycle manufacturers as well it is believed that the "N" in the serial number generically stands for Norton, the other letters for the specific application.

Especially for the Big4 restorers its difficult to find a correct bearbox because there are still loads of WD16H gearboxes around, but not many WDBig4 gearboxes.
It has to be kept in mind however that if you are restoring a prewar civilian Big4, the civil/military 16H gearbox is correct.
The military Big4 received a trials gearbox with a different, lower, gearing to haul the heavy sidecar through mud.
Unfortunately ratio's were not always applied making it difficult to ascertain if they were specific for military application, below some examples for WD16H en WDBig4.

Survey of gearbox internals showing identification numbers as given  on the individual gear wheels, number of teeths and Norton spare part number, usually engraved into the gear wheel by the N80xx number. (See also exploded view below)

Survey of gears for military and civilian 16H and Big4 MC's

Survey of Sprocket teeths on the various positions

According to EM Franks (see ref page), "For civilian purposes a 21 or 22 tooth engine sprocket should be fitted to the sidecar wheel drive outfit (W.D. B4), and a 19 tooth to the W.D.16H machine." 

Total transmission ratio’s between crankshaft and rear wheel drum

I calculated the overall transmission ratio's based on the actual numbers of teeths on all the gear wheels and sprockets.
From this I came to slightly different values than actually given by Norton. I guess the differences are caused by rounding off variations etc.
Being actual hard numbers its impossible to calculate other values, there are no 1/2 teeths possible.
I did not find any overall transmission values for the civilian 16H and Big4's.

Dismantling and re-assembly of the Norton 4 speed gearbox is generally relatively straight forward when following the instructions given in the Maintenance and Instruction Manual. There is no difference between the 16H and Big4 boxes apart from the gear wheels.

There are some points of attention.  The M&I Manual does not give any figures for the total wear allowed on the Bronze Clutch Thrust Washer. Additionally, the gearbox exploded view of the M&I Manual shows a dished washer at the end of the main shaft, which in many cases is missing in actual gearboxes, and the same exploded view does not give the Main Gear Wheel Sleeve Bearing Roller Retaining Washer, which is a crucial part in the gearbox! (I have drawn this washer into the original gearbox exploded view below, encircled by a red ring.)

The Clutch Thrust washer is the washer taking up the reaction forces when the Clutch is operated. Its positioned on the main axle facing the hardened steel ring that keeps the rollers of the Main Gear wheel in place. (Main Gear Wheel Sleeve Bearing Roller Retainer Washer).
The Bronze washer has three grooves in one face, which to be correctly positioned should be facing towards the Main gear wheel (Clutch). When these grooves are worn away, the washer needs to be replaced. The Clutch Thrust washer has a thickness of approximately 7/32 inch (5,55 mm).  Maximum permissible wear of the Clutch Thrust Washer is 1,58 mm or 1/16th inch.
Investigation of the Clutch Thrust washer is indicated when the max end float of the clutch itself exceeds the 1,6 to 2,38 mm. This can be roughly inspected by pushing and pulling on the clutch in axial direction.
End float of the main axle should preferably between 0,254 and 0,508 mm (0,01 - 0,02 inch). If the end float is still outside this range while the Clutch Thrust washer is within the specified thickness, the main axle should be shimmed behind the Clutch Worm nut.

This is where the elusive dished washer may be become handy although flat shims will do the job as well.  The exploded view drawings of the gearbox in the Maintenance and Instrucion Manual as well as various books, show a dished steel spring washer at the end of the main axle. Its not given in the spare parts list of either old or newer contracts or postwar civilian lists. The dimensions are I.D. 5/8", O.D. 1 7/16", steel thickness 1/64" and dished height 1/16" (as measured from an actual washer). 

 Main Gear Wheel Sleeve Bearing Roller Retainer Washer and Felt Washer for Clutch Nut .
This hardened washer has the tendency to fracture. Two of the 3 gearboxes I have showed this to be the case. The washer is given in the spare parts lists (all) under spare part no 3598 (Main Gear Wheel Sleeve Bearing Roller Retainer Washer).  I have however not been able to find original replacements for them, and had them made from a cold work tool steel (AISI D2 or UNS T30402) and hardened to 59 Rc. Remains of the original were measured to be 60 Rc so I think I am close enough.
Felt Washer for Clutch Nut, part no. 9744 is also added to the exploded view below.

Below also some pictures of various gearbox parts, (source: Olav Jerzykowski)

      
Click to enlarge

One book showing the gearbox in very clear drawings was made by Niels Schoen, "Norton, Garden Gate Manx" (ISBN 978-90-9029193-2) who kindly gave permission to show (part off) his meticoulously made drawings of the gearbox to be replicated here. It is missing the kick starter but it does give a very detailed picture of the 1935 designed gearbox and gear change mechanism, still in use after the war.  Part numbers are in the post war style. Attached scanned copy is to be regarded as reduced quality version of this superbly illustrated book.

        click on picture to retrieve pdf file.

Unfortunately there are some confusions around the correct springs for the "Kickstarter Return Spring" (pn 9710)  and the "Return Spring for Pawl Carrier" (pn 3629).
Both items are different for pre- and wartime gearboxes versus most post war gearboxes. Pictures below show the differences.

           
Correct kickstarter spring at left, incorrect version at right.                    correct Pawl carrier spring at left, incorrect at right

Disengagement
A not uncommon problem encountered when using the MC is that at a certain moment it appears the clutch cable needs regular adjustment for a proper clutch release. This is usually caused by the loosening of the central clutch nut.  Contrary to the expectation in the Instruction and Maintenance manual, a clutch puller is not always required to remove it from the gearbox axle.  A side effect of a regular adjustment of the clutch cable length may be that at a certain point, the clutch bolts eat metal away from the outer primary chain case. The clutch itself is a fairly simple but effective part.
The original WD clutch back plate was a relatively thin pressed sheet metal part of even thickness. Post war AMC clutch back plates are much thicker parts with a chamfered outer edge. They do fit on the earlier machines as well but there will be even less clearance between backplate and the primary chain case.

Another source for disengagement problems can be caused by spring force differences and possible damages to (almost) sliding faces between cup and stud. The end plate disc should lift squarely from the plates.

New clutch plates
I hear many Norton riders complain about the bad working of the clutch after installing new clutch plates. New clutch plates made by/to fit AMC upto 1959 fit in WD and other pre-war Norton clutches.
It keeps dragging a lot. I found out years ago that the newer plates were slightly thicker than the older ones, resulting in a minimum play when pulling the clutch lever. This usually results in continuously dragging plates, leading to gear change problems, especially when trying to find the neutral position while standing still. My solution to the problem has been to just remove one steel and one fiction plate. The plates will get more "room" to disengage, reducing the drag to a minimum. With good springs there will not be any slippage, and the front wheel of the bike can still be lifted from the ground by a sudden clutch engagement.  
If the clutch does show some slippage, the springs could be replaced by longer ones or some washers can be added at the bottom of the spring cups, making up some of the thickness of the missing plates.

Clutch assembly
When looking at the exploded view of the clutch, it suggests that the Clutch Spring Studs (6) are mounted onto the Clutch Body Back Cover Plate (5) but in actual fact they are used to bolt the Clutch Body (7) down through the Clutch Body Back Cover Plate (5) to the Clutch Back Plate (2) where they are fixed with the hexagon flanged nuts (1).