Exercise Problem $5\mathrm{.}3.$ A level set up an extended line BA in a position $70$ meters from A and $100$ meters from B reads $1\mathrm{.}684$ on a staff held at A and $2\mathrm{.}122$ on a staff held at $B,$ the bubble having been carefully brought to the centre of its run before each reading. It is known that the elevation of the tops of the pegs A and $B$ are $89\mathrm{.}620$ and $89\mathrm{.}222,$ respectively. Find $($a$)$ the collimation error, and $($b$)$ the readings that would have been obtained had there been no collimation error.