A study has been made of the feasibility of accurate numerical determinations of the transmission of gamma-rays through large thicknesses of materials. The first procedure investigated consists in regarding the total probability of photon transmission, $N_t$, as the sum of the probabilities $N_n$, where $N_n$ is the probability of photon transmission with exactly $n$ scatterings. The total expected transmitted energy, $E_t$ is similarly considered to be given by $\Sigma E_n$. A numerical calculation of $N_n$ and $E_n$ has been made for $n=0,1,2,3$ for a slab of uranium 20 cm thick, upon which photons are incident normally with energy $\alpha =10\mathrm{} m{c}^2$. The maximum value of $\frac{N_n}{N_0}$ occurs at $n=2\mathrm{}$ and of $\frac{E_n}{E_0}$ at $n=1\mathrm{}$. These calculations are also adapted to a slab of lead 35 cm thick. Consideration has been given to the behavior of $N_n$ and $E_n$ for large $n$, and estimates are thereby made for $N_t$ and $E_t$. The second procedure consists in deriving the transmission through a thick slab from a succession of transmissions through thin slabs. The transformation of an incident photon distribution into the distribution transmitted through a thin slab is conveniently expressed as a matrix, and the total transmission is then given by the iteration of the matrix on the successive transmitted distributions. Numerical results obtained by this procedure for particular incident photon distributions are presented.

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