On the Partition of an Odd Number into Three Primes in a Prescribed Proportion

We prove that, for any partition $1=a+b+c$ of unity into three positive summands, each odd number $n$ can be subdivided into three primes $n=p_a(n)+p_b(n)+p_c(n)$ so that the fraction of the first summand will approach $a$, that of the second, $b$, and that of the third, $c$ as $n \to \infty$.