The officer who presides (be in position of authority) over the senate when the vice-president is not in attendance is called:

President Pro Tempore

Explanation:

In the absence of the vice president, the Constitution provides for a President pro tempore to preside over the Senate.

The President pro tempore has been included in the presidential line of succession with the exception of the years from 1886 to 1947.

A law of 1947 changed the order of succession to put the House Speaker in line following the vice president, followed by the president pro tempore, and then the Secretary of State and other cabinet officers in order to create their departments.

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