I remember a few years ago a similar thread, but here goes anyway.
The principal reason that coins sink is gravity...the force of gravity does not end at the earth's surface, otherwise we would not fall down a mineshaft. That is the principal force at work, making coins sink, gravity.
There are other factors at work which vary the rate at which coins sink...one of those is the density of the soil.e.g. se what happens when you drop a coin on loose sand at the beach...the coin disappears quite quickly...disturb the sand and it sinks even further.
Another factor which affects the rate of sinking in soils is the creatures in the soil, not \just worms, but other tiny creatures which burrow their way through the soil leaving tiny cavities behind them as they go..this makes the work of gravity a bit easier.
Other factors include pressure from people or vehicles walking over the dropped coin (or other article), particularly when the soil is wet, thus making it easier for the pressure exerted from the top to affect the descent of the coin.
With respect to the theory of the build-up of soil through mulch, consider this: just the othre day I was detecting on a footpath near a park. The footpath had grassed soil between the kerb and a metre-wide concrete path with grassed dirt on the other side of the concrete as well. Suffice to say I was detecting on the grass, which was exactly the same level as the concrete path. The coin I found was a 1960 coin which went out of circulation here about 50 years ago, ie there was a currency conversion, and this particular coin was taken out of circulation between 1966 and 1968. The coin was about 5" below the surface of the dirt. Now, if that coin was at that depth due to a build-up of mulch, the top of the soil should have been 5-6" higher than the concrete path....it wasn't, it was still level, and because I grew up in this area, I know that that concrete path has been there for over 60 years, maybe much longer.
One post mentioned the loamy soil round a big tree whre the soil away from the tree was clay...this is not an unusual phenomenom. Over years, if clay is continually mulched, good loamy soil will be produced...thus, something lost in this good soil will sink faster and further than a coin dropped onto clay.
A coin will only sink as far as the density of the coin is greater than the density of the matrix where it is lying, i.e. if it sinks as far as a rock, it will sink no further, as the desnsity of the rock prevents the coin from sinking further.
With respect to the difference to coins of the same density, but of different sizes, the relative rates of sinking should depend on the density of the matrix where they are. eg, in loose sand, I would expect a larger heavier coin to sink faster than a relatively lighter smaller coin, whereas, in a more dense matrix, the smaller coin, due to its size should have an easier passage through the compacted soil, particularly considering the impact on their descent of worms and other creatures. Remember, the force of gravity is the same on both coins, no matter what the size. It is the other factors which will vary the rate of descent. HH
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