We discuss H -band ( 1.65 \mu m ) near-infrared photometry of the central 9 \ > h ^ { -2 } Mpc ^ { 2 } of Abell 1644 to a limiting M _ { H } \sim M ^ { * } _ { H } +3 ( throughout this paper H _ { 0 } = 100 \ > h km s ^ { -1 } Mpc ^ { -1 } ) .
There are 861 galaxies in the photometric survey region .
We also measured radial velocities of 155 galaxies ; 141 of these are cluster members within 2.44 \ > h ^ { -1 } Mpc of the cluster center .
The completeness limit of the spectroscopic survey is H \sim 13 ( M _ { H } \sim M ^ { * } _ { H } ) .
The cluster velocity dispersion of \sigma \sim 1000 km s ^ { -1 } remains constant out to the limiting radius .
We find no evidence for substructure in the cluster .
The cluster mass within R = 2.4 \ > h ^ { -1 } Mpc is 7.6 \pm 1.3 \times 10 ^ { 14 } \ > h ^ { -1 } \ > M _ { \odot } .

We compute the cluster luminosity function ; the Schechter parameters \alpha = -1.14 \pm 0.08 and M ^ { * } _ { H } = -24.3 \pm 0.2 ( with h = 0.5 ) agree well with other H -band luminosity functions .
From the virial theorem and the caustic method we compute one of the first mass-to-light ratios at H ; the result is M / L _ { H } = 82 - 127 \ > h\ > M _ { \odot } / L _ { \odot } within 1.5 \ > h ^ { -1 } Mpc .
This ratio corresponds to 374 - 579 \ > h\ > M _ { \odot } / L _ { \odot } at R .
The agreement of our IR measurement with previous M / L determinations indicates that at low redshift dust and young stellar populations may produce only negligible systematic errors in optical mass-to-light ratios .