Differential that is. Both axles are out so it's a pretty good bet it's time to play with the gears. I never personally worked on a differential that old but I believe most had a drop-out third member. If so you pull both axles, disconnect the the drive shaft, undo the bolts or nuts securing the third member to the axle housing, out she comes. You then can take the whole unit to a place of your choosing and repair as necessary.

When I started working as a mechanic back in the 70s, a shop down the street was known mainly for selling tires. One of their older employees could change a tire using hand tools faster than I could with a Coats tire machine.

These were the days of valve jobs every 2-3 years, tuneups every summer and winter, carburetor chokes causing wintertime no-starts, oil leaks, front ends needing rebuilding every 4-5 years, brake fade, the list goes on.
Cars have become much more reliable and don't break down hardly at all if maintained. My 09 Toyota Avalon really doesn't need anything major done to it until about 90000 miles. This Buick probably had one tire in the junkyard at that mileage.

It is very difficult to tell if this is a Buick Century Convertible (Model 66-C) or a Buick Special Convertible (Model 46-C). But Buick built only 766 of the Century Convertible and just 1,650 of the Special Convertible in 1936.

The Century Convertible cost $1,135, had a 122 inch wheelbase, and weighed 3,775 pounds. The Special Convertible cost $820, had a 118 inch wheelbase, and weighed 3,190 pounds.

Buick would build its last rumble seat models in 1938.

The other car in the background looks like a 1936 Buick as well - most likely a Special 4-door Trunk Sedan, Model 41. It cost $885, weighed 3,360 pounds and was on a 118 inch wheelbase. There were 78,803 built.

The cupola in the background leads me to believe this is next door to the Park & Shop shopping center at Connecticut Avenue & Porter Street in Cleveland Park. It is said to be the first shopping center in the United States with parking in front. Here is a present day view with an Exxon still on the site.

http://goo.gl/maps/60gPO

The sedan in the background with the vent wings draws me back to better days. You could throw the wings wide open to clear out hot air from the car being closed. Also very good on a rainy day for a little ventilation without being soaked. These "modern" cars with A/C are good until it quits working.

I remember from not all that many years ago, you could buy a re-grooving tool (essentially a big soldering iron) from J.C. Whitney and do it yourself.

One is a milk crate, and the other is a chicken crate!

It makes me wonder if this mechanic saw retirement in the "fullness of time."

Joenotes, it IS possible to take a tire off of a wheel without a machine. It's just a VERY hard thing to do. My dad did this when his Vietnam surplus Jeep ambulance had a flat in Mexico. It was a split rim and a BEAR to change.

When you could have your bald tires regrooved!

I agree the Convertible Coupe is a 1936 Buick. The bumpers and taillights match.

1936 Buick, maybe. Not later than that because the tail lights start getting integrated more with the bodies. GM fer shure, though.

This situation feels very familiar, even the cardboard laid out on the pavement to save your semi-clean shirt as you hammer on things.

I got to do it on grass/mud on a rainy April weekend in Wisconsin.

Both axles are pulled, those circular objects in front of the crate on our left look rather like bearing races, and that box labeled 'Republic Gear Co.' is just about the right size to be a fresh set of differential gears.

I'm going to speculate that this is an employee's personal vehicle, setting pinion lash can be 'entertaining' enough on a workbench let alone lying out on pavement in the weather, it just doesn't strike me as the sort of workmanship a responsible business owner is going to warranty.

That's what we who worked there said that ESSO stood for.
I don't see a tire machine. I wonder how he got the old tire off and the new tire on?
Additional:
Looking at comments from loribl and working_fool, this poor guy had his work cut out for him. Geeez!

I was thinking Pontiac from the ribs on the bumper but I don't think so. Can anyone tell me what make and year the car is?

If the photo date is September 1940 then the license plate had expired 6 mos prior.

Wow, were the old milk crates tough or what?

Within a couple of years tires would become almost impossible to find as war rationing began.

I'll bet the nearby service station today doesn't use two crates to raise the tires for changing these days, as our busy (plus neat and clean) attendant does here.