What is this set of sieves used for?

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My guess would be for flour with baking tins attached.
No, it's nothing like that at all! These are engineering seives, used for grading all manner of crushed, dry materials.

The label specifies the applicable British Standard:
Seive set.jpg

Here are the bodies responsible for drawing up that standard:
Seive set2.jpg
 
classifying sieves for panning gold, some people go to a lot of trouble to pan gold, the claim is that everything goes into the course sieve at the top and everything of various sizes is captured as it's works it way to the bottom sieve, and then each sieve is panned separately and nothing else in that particular sieve competes with any gold that is in there.
 
The proper way was to use them in gold mining is to find out what the different sizes you will need to Classify Placer to to recover the 80-90% of the total.
Say if your gold is all 20 mesh minus then you could eliminate the 20+ faction and only process the smaller faction through what ever your recovery process is. If 80% of your gold is 100 mesh minus then you have to decide if the other 20% is worth trying to recover or just stockpile it till you get enough to process economically by what ever method you/engineer decides to.

In hard rock mining you would use them to find out how small you would need to crush and grind the rock to release the particles of gold for what ever process you were using to extract the gold. This could be a chemical(cyanide), or water gravity sluices, or Mercury Amalgamation.
If the particle of gold is not released from its matrix then it cant be touched by the chemical process or the wet process won't work as the Quartz will change the Specific Gravity of the particle and the gravity system will loose it.
 
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