ON THE SPIN-DOWN OF PSR-B1509-58

The pulsar PSR B1509 - 58 is associated with the supernova remnant G32 0.4 - 1.2 (MSH 15 - 52) and has the largest pulse period derivative an d the second smallest characteristic age after the Crab pulsar. Althou gh PSR B1509 - 58 is the second youngest known pulsar, it has not glit ched during an 11 yr data span and shows little timing noise, permitti ng an accurate study of its slowdown. We have measured its braking ind ex to be n = 2.837 +/- 0.001 and its frequency third derivative to be nu = (-1.02 +/- 0.25) x 10(-31) S-4. The third derivative is consisten t with the value expected for a constant braking index and magnetic mo ment, although we cannot rule out models in which these quantities var y.