This section is from the book "The National Capitol. Its Architecture Art And History", by George C. Hazelton, Jr. Also available from Amazon: The National Capitol Its Architecture Art and History.
The President and Vice-President are not truly elected until the votes cast by the electors chosen by the people of the several States are counted, according to the Constitution, in the presence of the Senate and House of Representatives, and the Vice-President declares that each has received the requisite majority of ballots. This ceremony customarily takes place in the House Chamber. First, the Doorkeeper of the House announces the arrival of the Vice-President and Senate, preceded by a half dozen Capitol police and by a doorkeeper of the Senate, who bears two cherry boxes in which are the electoral votes still sealed just as they were delivered to the Vice-President by the special messenger of each State. The Secretary of the Senate escorts the Vice-President to the Speaker's chair. They are followed down the aisle by the two* Senators who are to act as tellers on behalf of the Senate, and by the remaining Senators, two by two, to whom are assigned the front rows of seats on the right of the Speaker. Two keys are then placed upon the Speaker's desk by the Secretary, with which the Vice-President opens the boxes. From these he takes long brown envelopes, each marked with the name of its State, and for the first time breaks their inner wrappers. The enclosed certificates are then read—that only, however, from Alabama, as it is the first in the alphabetical list, in full—and given to the tellers, of whom there are two also on the part of the House. When all are opened, the tellers announce the number of votes for each candidate, the Secretary gathers up the originals of the certificates and the duplicates taken from the second box, and the Vice-President declares the result. Then falls the gavel, and the electoral count is finished. In a few moments, the House resumes its session. An amusing incident occurred at the count in 1893. Vice-President Morton was unable to find one of the keys, and only after considerable search and much discomfiture at last discovered it in his own vest pocket.