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It seems relatively few ZC1s, if any, were issued complete with a watch.  Legend has it that these watches were considered to be highly attractive items and being small and portable were soon reported as "Lost".  The authorities were awake to such loses and issue of watches as standard ZC1 kit ceased and lost ones were not replaced.

That's the legend but the truth may be different.  Today no one seems quite sure what watches were issued or how many.  The watch holder fitted to the ZC1 radio is of a standard British design as fitted to many British radios, eg the 19 set, in pre and early War years.

The British had a number of standard type watches built to War Department specifications.   These watches were typically 9 jewel movements of robust design and capable of keeping reasonably good time for the day.  These movements could be fitted to different type cases dependant on intended end use.  The most common size case was 2 inches (50mm) in diameter in an "Open Face" style.  Large numbers of these watches had been made for the First World War, but after the war most of these had been destroyed in accordance with contractural agreements with the manufacturers.  They had supplied their products at heavily discounted prices for the duration of the war.  Understandibly they did not want the market flooded with good quality cheap watches after the war.

It could be expected that the military would have retained a stock of watches to meet peacetime requirements hence the watch holder was most likely designed to hold these watches.   Pocket watches from the late 1890s throught to around 1909 tended to have longer winding stems than WW2 vintage pocket watches.  This is an important factor in finding a watch today that will fit a watch holder as anyone who has tried will know.  Another important factor is the thickness of the watch case.   In many  watches of around 50mm diameter the case can be be quite thick because of the rounding of the back cover of the watch case.  This can prevent the front of the watch holder being screwed on as the winding stem is not set back far enough in the holder.     However in watches that fit, the back cover of the watch is flattened allowing the watch to sit much further back in the holder.

The diagram shows the profile and dimensions of a modern pocket watch manufactured in 2012 for the British Armed Service.  This watch looks as though it should fit a standard WW2 British watch holder.

Finding a watch that will fit your ZC1.  Ces Byrne in his talk on working at Radio 1936 states that Westclox pocket watches were used while others have suggested that Waltham watches ex NZ Railways were used. 
If either suggestion is correct or not  is hard to say but looking at available old catalogues few models of either make would fit without modification as supplied.  Railway watches were generally very good watches and capable of keeping excellent time.  A few pre 1909 Waltham  models would have fitted but not many.  One problem is that although movements were made in standard sizes, cases were often made by other manufacturers and no standard case sizes exist.

One last consideration is that in fitting watches to Military radios it was soon found that the watch case should not be made of steel as they rapidly became magnetised and affected the accuracy of the watch.

One of the best options is to look for a British GSTP (General Service Trade Pattern) watch which the British War Office purchased in large numbers, mainly from Swiss manufacturers but also others such as Waltham of America.    These were not Mil Spec watches but standard commercial quality movements which were fitted to heavier duty cases.  The cases are mostly to the same general case pattern but variation in case dimensions including diameter can be found.  Try and find one with a case diameter of 50mm and no thicker than 12mm.  Dependant on if you have a ZC1 Mk-1 or a Mk-2 you also need to think about the bow fitted to the watch.

For British GSTP watches the standard Bow is circular in shape and is fitted directly to the body of the Stem making a strong simple fitting.  Sadly on WW2 GSTP watches the distance on the stem between the case and Bow is about 1mm shorter than on the original watches.  The longer stems were found to be weak and stem lengths in many modern watches are now very short to almost non-existent.  WW2 GSTP watches will still fit the watch holder but the top edges of the slot in the holder have to be filed slightly to angle them back making a shallow V shape to accommodate the Bow on the watch.   Only a tiny amount of filing is required to make the watch fit well but its Bow cannot be folded down.  This is not a problem on a ZC1 Mk-2 but on a ZC1 Mk-1 the upright Bow prevents the lid being fitted to the set meaning the watch has to be removed from the set.

One simple solution to the problem is to remove the Bow from the watch.  After all if it's to be mounted in a holder it doesn't really need a Bow.  In fact some batches of watches were supplied without Bows for this reason.

Another approach is to find a so called Military pattern watch which is a normal commercial watch using the same basic movement but fitted to a commercial case but looking like a Military GSTP watch.  The cases are usually of lighter metal and with hinged front and back covers.  The Bows on these cases are often of a different style and make the effective stem length longer allowing the Bow to be folded down.
Cyma GSTP watch
Commercial Military style watch
A Waltham GSTP watch
Updated June 2014