The existing Legislature is independent of every thing except the Constitution of the United States; but while it is thus independent and may disregard those provisions, being the mere agent of the Federal Constitution, still it must necessarily act as a Legislature in the performance of that duty.
There must be a _legislative_ act.

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Whatever is done in relation to the election of a senator, must be done as a consequence of legislative action, otherwise it is no election by the Legislature.
They vote to form a convention for the purpose of choosing a senator, and when they meet in convention that choice may be made.