The first argument was completely undermined after taking into account the amount of heat generated by radioactive decay.
The second depended on highly dubious theories of formation of the earth and moon and plays relatively little role in this compilation.
They assumed that current rates—of sediment deposition and of salt transport by rivers—were the same as historical rates, despite the evidence they had that our own age is one of atypically high geologic activity. The rock cycle, as we now know, is driven by plate tectonics, with sedimentary material vanishing into subduction zones.
The first of these referred to the rate of heat loss from the earth and the length of time it would have taken to form its solid crust.The most famous came in 1654, when Archbishop James Ussher of Ireland offered the date of 4004 B. Within decades observation began overtaking such thinking.In the 1660s Nicolas Steno formulated our modern concepts of deposition of horizontal strata.And we should resist the temptation to blame them for their resistance. Different methods of measurement (such as the decay of uranium to helium versus its decay to lead) sometimes gave discordant values, and almost a decade passed between the first use of radiometric dating and the discovery of isotopes, let alone the working out of the three separate major decay chains in nature.The constancy of radioactive decay rates was regarded as an independent and questionable assumption because it was not known—and could not be known until the development of modern quantum mechanics—that these rates were fixed by the fundamental constants of physics.