How is the classic Gunmakers of yesteryear get their markings onto the barrels as shown in the picture especially their wording Special 470 Bore big game rifle!! Hand Engraved ???

Hand engraved, or more usually, roll marked. Look at the letters with at least a 10x magnifying loupe and you can usually tell the difference; if the bottoms of the letters are smooth and show no cut marks, then they were roll marked. If they are not perfectly smooth in the grooves and show cut marks, then they were hand engraved. A third possibility is pantograph engraving; again you will see tiny milling marks in the bottoms of the letters. For standard markings like company names and addresses on a quarter rib, the best and cleanest way is a roll mark.

Most European lettering I have run across have the wide part of the letter cut with a flat graver. Very easy to see.

On the barrels it is engraved in your picture. There are still people working here in the gun trade in Britain WHO DO NOTHING BUT engraving.

The "John Rigby" bit on the rib I don't know.

Engraving by the calibre and charge etc. hand is nice but also all that was "wrong" about the British gun trade.

Wrong because it sows a lack of ivestment in machinery and failure to move to modern machine methods for all but "the last draw of the file".

Eventually making English guns unaffordable for most and opening the floodgates to lower priced imports from Spain....where labour cost where cheaper

That is very accurate in almost any industry.
There is always a trade off between cost, quality and function. Engraved lettering is nice but adds zero to function while increasing cost.
Where there is enough volume to pay for the capital equipment and engineering modern processes can produce significant cost and quality advantages. But one caveat is the product should designed from production for best results.

quote:

Wrong because it sows a lack of ivestment in machinery and failure to move to modern machine methods for all but "the last draw of the file".

The bbls and the rib are all hand engraved lettering on the Rigby shown. Standard in the trade on anything that didn't come off of a production line.
It's what the customer that ordered it would expect.

A quick glance can tell you if they are hand cut or roll marked (die marked). No real mystery to that. Good eyesight and/or glasses helps of course. But 2 or 3X will reveal everything you need to see.

Roll dies and hand stamps used to be hand cut by the engravers also.
A specialty within the trade that probably kept more engravers working for and in production shops than firearms engraving alone ever did.