  The $B_N$-type Calogero-Sutherland-Moser system in one-dimension is shown to
be equivalent to a set of decoupled oscillators by a similarity transformation.
This result is used to show the connection of the $A_N$ and $B_N$ type models
and explain the degeneracy structure of the later. We identify the commuting
constants of motion and the generators of a linear $W_\infty$ algebra
associated with the $B_N$ system.
