county

Don't want to seem pedantic, but these ships are under construction on the ways (i.e. the slipways on which they are built above the water line prior to being launched and fitted out afloat). They are not in dock which suggests that they are either afloat in dock or in a drydock.

The red painted vessel on the left in this picture is probably the Type 12 Frigate HMS FALMOUTH YN1187. Regards Dave

Difficult to tell without a date and with the foreshortened view. That looks like Vickers. The Glamorgan was built there and launched in 1964. The slope of the main deck down to the poop looks like a County although proportions are not easy to judge.

That is the Walker Yard slip way.

en.wikipedia.org/wiki/Harry_Kendall_Thaw

Actually, not the courthouse, but instead the photo was taken in front of the Ludlow Street Jail, no longer standing. The sign by the front door reads "New York County Jail" (New York County is essentially Manhattan), and that is what the Ludlow Street Jail was.
Thaw, in 1915, was returned to New York City after escaping confinement at Matteawan State Hospital (He had been acquitted of the 1906 murder of architect Stanford White by reason of insanity). His lawyers successfully asked the court to move him from The Tombs to the Ludlow Street Jail, on the basis that he was not charged in a criminal matter, but that he was to have a jury trial only as to his present sanity.
query.nytimes.com/gst/abstract.html?res=F10916F93E5D16738...
In this old print, you can see that the door was near the corner of Ludlow and Essex Market Place. [Essex Market Place ran from Essex to Ludlow Streets between Broome and Grand Streets and was closed in 1926, around the time the jail was demolished.] You can see that there was a giant gas lamp over the door, whereas in Bain's 1915 picture just the bracket remained.
digitalgallery.nypl.org/nypldigital/dgkeysearchdetail.cfm...

knickerbockervillage.blogspot.com/2009/10/seward-park-aer...

This was probably taken when Thaw was due to be taken from the jail to court.
He and 5 others who helped him escape the state hospital were tried in March, 1915 and acquitted. He then had a second trial in 1915 to determine if he was presently sane. He was determined sane in this trial on July 14, 1915, which is presumably about when this shot was taken.
The New York Times account describes 2,000 people gathered at the courthouse, cheering thaw after the trial:
query.nytimes.com/gst/abstract.html?res=FA0E10FC3E5A15738...

See also:

And not to forget, the Thaw trials were about Evelyn Nesbit Thaw, or more exactly Thaw's shooting of her presumed lover, Stanford White.

Eccellente scatto!!