On July $23$ of the current year, Dakota Mining Company pays $$6,745,200$ for land estimated to contain $8,760,000$ tons of recoverable ore. It installs and pays for machinery costing $$788,400$ on July $25.$ The company removes and sells $451,750$ tons of ore during its first five months of operations ending on December $31.$ Depreciation of the machinery is in proportion to the mine's depletion as the machinery will be abandoned after the ore is mined.

Required:

Prepare entries to record the following.

$($a$)$ The purchase of the land.

$($b$)$ The cost and installation of machinery.

$($c$)$ The first five months' depletion assuming the land has a net salvage value of zero after the ore is mined.

$($d$)$ The first five months' depreciation on the machinery.