We present a sample of 17 newly discovered ultracool dwarf candidates later than \sim \mathrm { M } 8 , drawn from 231.90 arcmin ^ { 2 } of Hubble Space Telescope Wide Field Camera 3 infrared imaging . By comparing the observed number counts for 17.5 \leq J _ { 125 } \leq 25.5 AB mag to an exponential disk model , we estimate a vertical scale height of z _ { scl } = 290 \pm 25 ( \mathrm { random } ) \pm 31 ( \mathrm { systematic } ) pc for a binarity fraction of f _ { b } = 0 . While our estimate is roughly consistent with published results , we suggest that the differences can be attributed to sample properties , with the present sample containing far more substellar objects than previous work . We predict the object counts should peak at J _ { 125 } \sim 24 AB mag due to the exponentially-declining number density at the edge of the disc . We conclude by arguing that trend in scale height with spectral type may breakdown for brown dwarfs since they do not settle onto the main sequence .