  Let $\Bbb Z$ and $\Bbb N$ be the set of integers and the set of positive
integers, respectively. For $a,b,c,d,n\in\Bbb N$ let $N(a,b,c,d;n)$ be the
number of representations of $n$ by $ax^2+by^2+cz^2+dw^2$, and let
$t(a,b,c,d;n)$ be the number of representations of $n$ by
$ax(x-1)/2+by(y-1)/2+cz(z-1)/2 +dw(w-1)/2$ $(x,y,z,w\in\Bbb Z$). In this paper
we reveal some connections between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$.
