Completed British 19th C, except portraits, Continental European after 1800, Dress and Textiles, Wales: Artists and Subjects 12 Could Naples be the Mediterranean Bay seen through this arch?

The mountain in the distance looks like Monte Faito and the exposed rock is present just before Vico Equense.

Yes I agree it is probably a view of Naples and under the arch we see the dome of a church and at the sea side a sort of castle which could be the Castel dell'ovo. If we accept these points it is probably the Vesuvio we see behind. The proposition of Santa Maria degli Angeli could fit if we see the dome, but if you draw a line from the church and Castel dell' ovo the vesuvio is not in the right place. At opposite if you draw a line between Vesuvio and castel dell'ovo you arrive with church like santa maria teresa which has a dome as you can see on google maps views I join you. I have been very interested with this picture from Penry Williams.
Jean-Pierre Cappoen Ph.D at Lille University (France) in 2021 with Henri Harpignies et les Salons (1819-1916). This landscapist had many works from Sorrento and Capri. Best regards.

I do not believe that this is a view of Vesuvius/Vesuvio, as the feature shown in the distance has none of the usually symmetrical features of a volcano. The mountain feature shares more of a similarity with Monte Faito, as suggested by Anselm Bassano above. (See attached). Given the artist's very high elevation it could have been painted from a suitable vantage point on the Castel Sant'Elmo fortress. The buildings at the shore line could be the Castel Nuovo, and not the Castel dell' ovo.

I think this is the Petraio, to the S of Castel Sant'Elmo. I have not found a shot from the uphill side but others may be more successful.
https://en.wikipedia.org/wiki/Petraio#/media/File:The_Petraio_Naples_Italy-02.jpeg

There is an image here from the uphill side. I rejected this view when I first saw it, early in the process, as there was no visible keystone in the arch, but it is clear that the buildings have been modified quite a bit. Note the semicircular top of an arch in the left-hand wall, under the major arch, which appears in Penry Williams' image also. Monte Faito is not visible in this photo but a line drawn (on Google Earth) from the very visible rock scar there past Castel dell'Ovo brings you to the Salita Petraio ...
http://salernocasamia.altervista.org/naples-petraio-walk/

Another view down the steps and through the arch, with the Monti Lattari on the Sorrentine peninsula visible on the far side of the Gulf of Naples, 15 miles or so away: https://bit.ly/3xcVxAP. Williams seems to have cheated the angle slightly (as well as the apparent distance), to bring Monte Faito (which it certainly must be) into the centre.

And here's a panoramic Google streetview across the gulf from Naples (at sea level, close to the Castel dell'Ovo) of the whole Lattari range, the backbone of the peninsula, Faito being the tallest. Vesuvius, which is much closer, is to the left.

I agree that Williams cheated about the angle and (mightily) about the distance; the latter was perhaps the most confusing aspect. Did he use a telescope to sketch Monte Fialto? Whatever, it greatly improves the composition. I hope, however, that his delicate balconies or sunshades did exist; they add to the joyousness of the scene - the signorina is surely singing - and contrast with the current shabbiness. (The crude coat of render that now masks the moulding on the arch does not help.) The church may be the Basilica di Santa Maria degli Angeli but, again, some shifting of the line of sight seems to have been contrived.

Could Naples be the Mediterranean Bay seen through this arch?

I come to this discussion late but having viewed the eight posts made in its first three days in June last year, it would seem that we can answer postively that it is indeed Naples viewed through the arch. And further that the arch still exists (the artist has taken a few liberties to enhance his appealing picture).

More to say?

A better title would therefore be either 'The Bay of Naples seen from the Scalinata della Discesa del Pietraio' or 'Naples: the bay seen from the Scalinata...etc'

'More information' could note that Wiiliams appears to have brought the dome of Santa Maria degli Angeli and distant Monte Faito into the view through the arch, although not actually in direct line of sight from his viewpoint.

This ought to close: we know artist and site, and how he adjusted the view. There is nothing else to add allowing title ought to adjust slightly as above.