We present deep , high velocity resolution ( \sim 1.6 km sec ^ { -1 } ) Giant Meterwave Radio Telescope HI 21cm synthesis images , as well as optical broad band images , for the faint ( M _ { B } \sim - 10.9 ) dwarf irregular galaxy Camelopardalis B .

We find that the HI in the galaxy has a regular velocity field , consistent with rotational motion .
Further , the implied kinematical major axis is well aligned with the major axis of both the HI flux distribution as well as that of the optical emission .
Camelopardalis B is the faintest known galaxy with such relatively well behaved kinematics .

From the HI velocity field we derive a rotation curve for the galaxy using the usual tilted ring model .
The rotation curve can be measured out to galacto-centric distances > 4 times the optical scale length .
The peak ( inclination corrected ) rotation velocity v _ { o } is only \sim 7 km sec ^ { -1 } – the high velocity resolution of our observations were hence critical to measuring the rotation curve .
Further , the peak rotational velocity is comparable to the random velocity \sigma of the gas , i.e . v _ { o } / \sigma \sim 1 .
This makes it crucial to correct the observed rotation velocities for random motions before trying to use the kinematics to construct mass models for the galaxy .
After applying this correction we find a corrected peak rotation velocity of \sim 20 km sec ^ { -1 } .

On fitting mass models to the corrected rotation curve we find that the kinematics of Camelopardalis B can be well fit with a modified isothermal halo with central density \rho _ { 0 } \sim 12 M _ { \odot } pc ^ { -3 } .
This central density is well determined , i.e .
it has a very weak dependence on the assumed mass to light ratio of the stellar disk .
We also find that the corrected rotation curve can not be fit with an NFW halo regardless of the assumed mass to light ratio .

Finally we compile from the literature a sample of galaxies ( ranging from normal spirals to faint dwarfs ) with rotation curves obtained from HI synthesis observations .
The complete sample covers a luminosity range of \sim 12 magnitudes .
From this sample we find ( i ) that Camelopardalis B lies on the Tully-Fisher relation defined by these galaxies , provided we use the pressure support corrected rotation velocity , and ( ii ) a weak trend for increasing halo central density with decreasing galaxy size .
Such a trend is expected in hierarchical models of halo formation .