Diverted handle screw

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Hi,
Not sure if the title is correct name for item in question.
Basically I’ve got bath taps with overhead shower connected.
There is a lever / handle which when operated left or right directs water into bath or the shower.
The screw that passes though the lever / handle has snapped.
I’ve removed it but asking are these a specific plumbing thread or metric etc.

If I measure the diameter of it does that then advise what thread it will be.

Currently can’t see anything about & the taps fitted are about 17 years old & don’t see this part listed on any spares listings.
 

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1. Measuring the diameter of the thread will NOT tell you what thread it is, although it may point you in the right direction.
2. Most, but not all, plumbing threads are British Standard Pipe (BSP) threads. These are broadly specified by:
2.1 Outside diameter, which is not the actual measurement of a male thread, but rther the internal bore diameter of the pipe they were originally intended to fit.
2.2 The included angle of the thread. They are all Whitiworth form threads of 55 degrees included angle.
2.3 The number of threads per inch. This is standardised across the range, being for example 19TPI for 1/4" BSP, 14TPI for 1/2" BSP and 11TPI for 1" BSP.
2.4 There are two "flavours" of BSP, parallel threads (BSPP) and tapered threads (BSPT). The tapered threads are mostly used for screwed low carbon steel pipe and fittings where a water tight seal is made by interference of the threads.
3. From your photograph that looks like a 1/4" BSP (parallel). If you measure (accurately, not a ruler) the outside diameter of the thread and it is about 13.2mm and the length of the threaded section is about 8 mm, it is most probably a 1/4" BSP.
4. If it's not 1/4 BSP you'll need to work out what it is. For that you will need something like a vernier caliper or micrometer for the diameter and a set of thread gauges for the thread pitch.
5. If the threaded part has broken from the hexagonal cap, then you need an equivalent sized hexagon headed machine screw to replace it. Idoubt you'll get a chrome plated one, by https://www.spaldingfasteners.co.uk/PARENT4760 has a stainless steel one which could perhaps be cut down to suit.
 
It’s a fancy bolt with a large head.
Don’t grub screws have an Allen key down the middle.

The item in photo is the broken item in two pieces
 

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1. It's a Deva Attersall Coronation 1902 bath shower mixer (Model CR23) . Discontinued and there appear to be no parts available.
2. Your photograph 9053.JPEG shows a brass collar above the screw thread and below the hesagon head. If this is essential, you aren't going to find a replacement.
 
1. See post #3 item 3. Looks like 1/4 BSP but can't tell from a photogrpah.
2. See post #3 item 4. Can't tell what thread it is without measurements.
3. To measure diameter (with reasonable accuracy but without verniers / micrometer):
3.1 Get a strip of paper with a straight edge.
3.2 Wrap around thread.
3.3 Put a pin through the paper into a "valley" in the threads.
3.4 Unwind paper, measure between pin holes.
3.5 Diameter is distance between pin holes divided by Pi. Distance multiplied by 7 divided by 22 is probably accurate enough.
4. A more accurate measure of thread pitch is to measure in a straight line between the crests of as many threads as possible. If you publish number of threads and distance between first and last crest its possible to calculate a reasonable approximation of pitch.
 
From a rough guide a 1/4 bsp bolt what diameter is it in mm

I ask as I’m out at present and earlier I did measure it using a vernier & it was 4.8mm the pitch between each thread seemed coarse
In my head 1/4 BSP is much larger.
 

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