Scale: 1/350
 
Set includes 2 directors (no radar antennas).
 
This set of models represents the US Navy's Mark 37 "square-back" Fire Control Director as configured to carry the Mk.4 radar antenna.  Unlike the director configured for Mk.12 and Mk.22 radar antennas, this director did not have two small boxy extensions fit to the rear shield. 

The US Navy Mark 37 Director was used to control the fire of the 5”/38 caliber dual purpose batteries against both aircraft and surface targets, to direct the fire of starshells for the illumination of surface targets and to position the searchlights.  

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Mk.37 directors were commonly installed on many classes of US Navy and US Coast Guard ships during World War II through the Cold War.   Here is a short summary of Mk.37 directors from noted naval historian and researcher Rick E. Davis:

Mk.37 "Angle-Back" director (available separately): the early Mod versions, called "taper-back" or "angle-back", were installed on the NORTH CAROLINA class battleships, SOUTH DAKOTA class battleships, USS Iowa BB-61, USS New Jersey BB-62, USS Saratoga CV-3 (from 1943), USS Hornet CV-8, SIMS-BENSON-GLEAVES class destroyers, and early completed cruisers and battleships like the first four ATLANTA class light cruisers. It appears in about 1941 the US Navy switched to the “square-back” Mk 37 directors for all ships being built (and modified), and continued to be made throughout WWII.
 
Mk.37 "Square-Back" director for Mk.4 radar (this set of models): the first version seen had a plain backside with only hand grip rails (this is the director top that comes with the Tamiya and Trumpeter FLETCHER class kits). Some FLETCHER’s ended the war still equipped with the Mk 4 radar. Units with Mk 4 radar that were recommissioned for the Korean War never had the Mk 12/22 radars installed, having the newer Mk 25 radar installed.  
Mk.37 "Square-Back" director for Mk 12/22 radar (available separately): these are the same directors as above with two extension boxes added to the back to house the electronics of the new radars.  As an aside, the Mk 12 radar was available and installed without the Mk 22 radar on a few destroyers in mid-1944.  Most of those destroyers had the Mk 22 installed before going to the war zone however during post-shakedown availabilities.

Mk.37 "Square-Back" director for Mk 12/22 radar, with commander's cockpit (available separately): the commander's cockpit was added as a mod to existing and new directors starting in early 1945.  Several of the Anti-Kamikaze Mod FLETCHER’s got the cockpit.  But, oddly, not all destroyers got the cockpits.  Reports indicate that many gun director Captains didn’t like it (too hot in the South Pacific).  It is believed that the cockpit-equipped directors are more common on the GEARING class.

Mk.37 director, Cold War-configuration (available separately): during the Cold War, the directors were enlarged to the front, receiving a very boxy-shaped housing.  These were commonly fit to the IOWA class battleships and ESSEX and MIDWAY class aircraft carriers from the 1950s onward.
 
Mk.37 Directors are known to have been carried by the following ships and classes but check your sources to know for sure which director type you need for your project:
USS Enterprise CV-6, late-war
USS Hornet CV-8
USS Pennsylvania (rebuilt)
USS Maryland (rebuilt)
USS Nevada (rebuilt)
USS California (rebuilt)
USS Tennessee (rebuilt)
USS West Virginia (rebuilt)
HMS Vanguard
Alaska class
Atlanta class
Baltimore class
Benson class
Buckley class
Butler class
Cleveland class
Essex class
Fletcher class
Garcia class
Gearing class
Gleaves class
Iowa class
Midway class
Montana class
North Carolina class had "angle-backs"
Sims class
South Dakota class had "angle-backs"
Sumner class
many others as well as various auxiliaries