Programming :: AWK - Combining Multiple Columns?

I have a folder with only 24 files named <number>.dat (i.e. 4.dat, 6.dat and so on) where <number> is between 0 and 256. Each file has just two columns of data and nothing else.

I'm trying to combine all the second columns ($2) together. I've been fiddling around with getline and so far have

awk '{ getline ln < "6.dat" ; print ln" "$2 }' 4.dat

which takes file 4.dat and adds $2 from 6.dat, but I want a single command to take each $2 from every file and add them to (for example) 4.dat (having $1 from 4.dat is no problem). A command that takes every file in the folder and grabs $2 and places them in a common file would be ideal. Frankly I can work around if you combine both columns from every file.