Is there a law establishing the procedure by which a U.S. senator resigns?
<p><a href="https://politics.stackexchange.com/questions/9256/the-law-on-addressees-of-u-s-senators-resignations">This question</a> on politics.stackexchange.com isn't getting any answers, so I'll try a similar question here.</p>

<ul>
<li>Is there some statute or provision of the Constitution of the United States or case law saying that the way a U.S. senator resigns is by submitting a letter of resignation to the <b>governor</b> of the state that the senator represents, rather than to some other person such as the president of the senate (who is also the vice-president of the United States) or other federal officer?</li>
<li>Is that considered the proper way to do it <b>only</b> because someone set a precedent and others follow precedent?  If so, when was the precedent set?  And might it be considered law if there is no Constitutional provision or statute or case law?</li>
</ul>

<p>Article I, Section 5 of the Constitution specifies that</p>
<blockquote>
<p>Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller Number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.</p>
<p>Each House may determine the Rules of its Proceedings, punish its Members for disorderly Behaviour, and, with the Concurrence of two thirds, expel a Member.</p>
</blockquote>
<p>It therefore seems likely that if there is any procedure specified for the resignation of a senator, it is specified in the Senate rules.  Since Senate rules are passed by the Senate only, not being voted on by the House of Representatives nor presented to the President for his signature, they are not laws.</p>
<p>My quick perusal of the rules, however, did not find anything.</p>

us-senate