OK Roger, here is exactly what to do:

Go to this Sears parts website:
http://www3.sears.com/
Enter in your number 315.34160 for your electric chainsaw in field number
2 entitled "Type in your model number. Click on "go". Then click on
"Continue" on the next screen which verifies that you are looking at the
right machine. On the next page click on the View Diagram radio button,
then continue, and another window opens with every part on your machine
shown with a part number in an exploded view. Now back on the original
window click on the View Part List radio button, then continue, and you
see the name for each one of those parts. Now just switch back and forth
between these two windows and you can identify every single part on your
electric chainsaw. Easy as cake. (I have been doing this recently as I
have been fixing up our Kenmore washer, dryer and fridge...)
Hope this helps,
Tomes
Thanks for the pointer. Excellent.
Yes, that diagram ID's the silver button as the pump, as I expected, and the
cap as the filler cap, so that indeed must be for the oil. On the mystery
knob, it is still not clear what it does, it is just called an "adjustment
knob". Just *What* it adjusts is not clear. Next time I go into the
chainsaw repair shop, I'll ask the guy there. Thanks again. Roger