Can someone tell me what the purpose is of the small pipe coming from this resonator box?

 

As in the one bottom right!

 

the one that appears to be snapped short??
its the bleed return from the boost solenoid

 

What's this do then? Also what does the larger pipe do? Thanks :-)

 

the larger pipe connects to a steel pipe that flows under the inlet manifold to feed your idle control valve

as mentioned the other pipe is simply the "bleed" off the boost controller, but as long as its blanked on the air box resonator it doesn't strictly need to vent here it can simply vent to atmosphere