We report new high precision data on the velocity of second sound clos
e to the lambda transition of He-4 at the saturated vapor pressure. Th
e second sound wave is detected by a powdered salt pill of copper ammo
nium bromide in direct contact with the liquid helium. With a thermome
ter noise of less-than-or-equal-to 10(-10)K/square-rootHz we are able
to make measurements in the linear regime to within 20 nanokelvin of t
he lambda point. We have obtained reasonable agreement with renormaliz
ation group theory predictions after allowance for the effect of gravi
ty. The results are also compared with previous experiments.