Let $P_4(x)$ be a rational quartic polynomial which is not the square of a quadratic. Both Campbell and Ulas considered the problem of finding an rational arithmetic progression $x_1,x_2,\ldots,x_n$, with $P_4(x_i)$ a rational square for $1 \le i \le n$. They found examples with $n=10$ and $n=12$. By simplifying Ulas' approach, we can derive more general parametric solutions for $n=10$, which give a large number of examples with $n=12$ and a few with $n=14$.