We discuss H-band (1.65 mum) near-infrared photometry of the central 9 h(-2
) Mpc(2) of Abell 1644 (A1644) to a limiting M-H similar to M*(H)+3 (throug
hout this paper H-o = 100 h km s(-1) Mpc(-1)). There are 861 galaxies in th
e photometric survey region. We also measured radial velocities of 155 gala
xies; 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 similar to
13 (M-H similar to M-H*). The cluster velocity dispersion of sigma similar
to 1000 km s(-1) remains constant out to the limiting radius. We find no e
vidence for substructure in the cluster. The cluster mass within R = 2.4 h(
-1) Mpc is 7.6 +/- 1.3 x 10(14) h(-1) M-.. We compute the cluster luminosit
y function; the Schechter parameters alpha = -1.14 +/- 0.08 and M-H* = -24.
3 +/- 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-./L-. within 1
.5 h(-1) Mpc. This ratio corresponds to 374-579 h M-./L-. at R. The agreeme
nt of our IR measurement with previous M/L determinations indicates that at
low redshift dust and young stellar populations may produce only negligibl
e systematic errors in optical mass-to-light ratios.