  We demonstrate a new technique for measuring the absolute frequencies of
atomic transitions. The technique uses a ring-cavity resonator whose length is
calibrated using a reference laser locked to the D_2 line in {87}Rb. The
frequency of this line is known to be 384 230 484.468(10) MHz. Using a second
laser locked to the D_1 line of Rb, we measure the frequencies of various
hyperfine transitions in the D_1 and D_2 lines with a precision of 30 kHz. We
obtain the following values: 120.687(17) MHz and 406.520(25) MHz for the
5P_{1/2} hyperfine constant A in {85}Rb and {87}Rb; 377 107 385.623(50) MHz and
377 107 463.209(50) MHz for the D_1 line in {85}Rb and {87}Rb; and 384 230
406.528(50) MHz for the D_2 line in {85}Rb. This yields the fine-structure
interval and the isotope shifts. The precision obtained is a significant
improvement over previous measurements.
