[Radioroslyn]

Well there are two ways. One is to whip out your handy dandy 1940 tube manual and look it up. Nowdays I look  it it up online. Some schematics have the pin numbers indicated on them some not.

I think you maybe be asking how do I count pins on the bottom of a tube?

Older standard base tubes: 4, 6, and 7 pin tube are simple. Find the two fat pins looking  from the bottom. Face them towards you. The pin on the left is pin#1 count clockwise to determine the others. For instants a 4 pin tube pin 1 is the fat pin to the left. Pin 2 is the thin one above it. Pin 3 is the thin pin to the right of pin 2. And pin 4 is the other fat one.
On the 5 pin tube two of the pins are closer together. Pin 1 is the one on the left of two that are closer together, pin 5 is the one to the right of pin1.
Schematics that don't pin numbers doesn't mean that the connections are layed out in the order in which they appear on the schematic.

I see I'm late to the party! Slow typer.

Thank you for the education on this. Are you saying with your last sentence that if the schematic, like the one I posted, doesn't have the pins numbered that I can't necessary refer to that layout? Stated another way. If the two fat pins is for the heater and the one thin one to the left of the heater on the schematic shows it connecting to a grid that the socket sitting in my chassis might actually be something like the plate? I suppose I should refer to the materials shared above as the "gospel" truth for that tube pin layout. - This could be why I am second guessing the circuit.

You got me there. General on a schematic the heater pin are in the proper place. Most of the it doesn't matter cause one side is at 6.3vac and the other is a chassis ground. But when you have a transformerless set (ac/dc) the heaters are in series then it can be important to know which pin is which.
[Image: http://www.philcoradio.com/phorum/attach...?aid=10253]
This  was a problem child I was working on a few months ago. The tubes at each end the the volt was too high and in the middle it was too low. The 1LN5 had only .5v and was inoperative, the 1LE3 and !LB4 had too much @ 1.75v. As you'll notice 1 pin is on the left and 8 is on the right as it should be. This makes it easier to troubleshoot.

Schematic are drawn to have the least of wires crossing to avoid confusion ( unless it's a Crosley). This doesn't necessarily correspond actual arrangement of the pin placement on the tube base. Notice that your 610 doesn't show any caps on the tube that have them.

I think I answered your question.