Congratulations on finding a deposit Alex. I'll try to give you the efficient version.
Placer claims should be located by the aliquot parts of the PLSS. That means you need to follow the north/south east/west trend of the Public Land Survey. If you had discovered a lode deposit you could follow the direction of the strike but with placers you are going to have to describe your claim by the regular portions of the survey. That's all in the
Mining Act of 1872.
That does not mean you have to follow the
lines of the survey it means you make your claim based on the regular divisions (
aliquots) of the survey. For instance if you were making a 20 acre claim you could describe it as the south half of a quarter quarter section (NWNW or SESW etc). That would make the claim 1320 feet on the east/west and 660 feet on the north/south dimensions (20 acres). Describing the claim as the west half of a quarter quarter would put the 1320 foot long dimension on the north/south and the 660 foot short dimension on the east/west.
As I said you don't have to follow the lines themselves but the smallest division of the survey you can describe the claim by would be the quarter quarter quarter or 10 acres. Since placer claim descriptions can not join on a corner on your 20 acre claim that would mean you could move 10 acres (1/2) of the claim or the whole claim off the quarter quarter line east/west or north/south by 330 feet.
Now I know you are thinking why not just stack those regular portions so they follow the creek? There is a limit to the maximum long dimension of a 2 person 40 acre claim. That limit is 1320 feet - the same as a 20 acre claim. It's the policy of the United States to prevent claims that break the mineral estate into long strips. If you really want to follow that creek you will need to file however many 20 acre claims it takes to cover your deposit with the claims following the PLSS grid and being offset by increments of 330 feet.
Ah! Now you are thinking it might just be easier to make a lode claim so you can follow that creek without making a boatload of placer claims. That's a no go unless you discovered a mineral in place - a hardrock vein or ledge. A lode claim legally can't be located where there is no lode.
Are you confused yet? Luckily there is a source to help you straighten this out with some diagrams etc. Nevada (the Silver State) is serious about encouraging mining so they put out a booklet to help you visualize these claim restrictions as well as a bunch of other stuff you probably haven't even thought of yet. Of course Land Matters has a good copy for free in their Library.
Mining Claim Procedures is just 58 pages long but it's the best resource from any state. Study that and I'm sure my convoluted explanation will make perfect(?) sense.
About those state location requirements... Congress described the basic requirements for a mining claim location to make it valid under federal law. Then they left it up to the states and the miners to refine those requirements to meet their needs. (It's all there in the
1872 Mining Act)
The states and the miners are allowed to make any additional regulations about mining claims as long as they don't step on the federal regulations. So the states set the actual procedures needed to make a location. That often includes things like the type of monuments, what has to be on a location notice, where the location notice is recorded and what the cost is, and deadlines for recording your public mining notices and performing labor. If an organized mining district exists they are allowed to make even more regulations as long as they don't contradict the State or Federal regulations. This is the basis of American government hierarchy and you will find the same thing when dealing with water rights, land rights and many other aspects of substance in law.
Often this means claims are staked, monumented and recorded differently from state to state. The reason it matters if you follow the state regulations for mining claims is because if you have a mining contract, lease, association or mineral rights dispute it's going to be settled in a state court regulated by state laws. If you don't already have your state required ducks in a row (location requirements) you won't have a solid basis for legally protecting your claim to the minerals.
A lot of people are saying to themselves right now - hey! mining claims are a grant from Congress, not some state stuff so your mineral rights should be in a federal court under federal law.
You would think that would be the case except in the very first federal mining law Congress said - not our problem, and ducked out of the whole thing leaving it up to the miners and the states to settle things their own way within a pretty tight requirement. Here's that first 1865 mining law in it's entirety:
That no possessory action between individuals in any of the courts of the United States for the recovery of any mining title, or for damages to any such title, shall be affected by the fact that the paramount title to the land on which such mines are, is in the United States, but each case shall be adjudged by the law of possession.
To "possess" your claim you must follow the laws of location - all of them including and especially the State laws. Otherwise how would a state court rule for
possession in your favor?
Read the two documents linked here along with your state's location laws and I'm sure with a little study you will answer your questions. If not just wander back to this thread and ask any questions that come up.
Heavy Pans