The X-ray source known as GRS1915+105 belongs to a group dubbed 'microquasa
rs'(1,2). These objects are binary systems which sporadically eject matter
at speeds that appear superluminal, as is the case for some quasars. GRS191
5+105 is also one of only two known binary sources thought to contain a max
imally spinning black hole(3). Determining the basic parameters of GRS195+1
05, such as the masses of the components, will help us to understand jet fo
rmation in this system, as well as providing links to other objects which e
xhibit jets. Using X-ray data, indirect methods(4,5) have previously been u
sed to infer a variety of masses for the accreting compact object in the ra
nge 10-30 solar masses (M-circle dot). Here we report a direct measurement
of the orbital period and mass function of GRS1915+105, which allow us to d
educe a mass of 14 +/-4 M-circle dot for the black hole. Black holes with m
asses >5-7M(circle dot) challenge the conventional picture of black-hole fo
rmation in binary systems(6-9). Based on the mass estimate, we interpret th
e distinct X-ray variability of GRS1915+105 as arising from instabilities i
n an accretion disk that is dominated by radiation pressure, and radiating
near the Eddington limit (the point where radiation pressure supports matte
r against gravity). Also, the mass estimate constrains most models which re
late observable X-ray properties to the spin of black holes in microquasars
.