Known as Typo Script, which started out as metal type (p. 402, American Type Founders Specimen Book, 1923) and moved into the phototypesetting era:
http://library.rit.edu/cary/typo-script-extended-specimen

It seems to have been digitized for math typesetting, of all things, but by a hobbyist, not a foundry (not putting down hobbyists, just making a distinction in case licensing or web fonts are needed):
http://levien.com/type/myfonts/ofl.html

No one seems to have revived it commercially. These faces are very similar (essentially the same font, just different foundries):

http://www.myfonts.com/fonts/bitstream/english-111/ [Adagio]
http://www.myfonts.com/fonts/linotype/shelley-script/ [Pro or Andante]

Thanks Kevin for the ATF Typoscript match.
Note that the alphabet in Levien's version has only 23 capital letters and 11 lower case. No numbers.
A complete alphabet of the capitals can be found in Ralph Smith's Formal Script, a math symbols font for LaTex, at http://www.ctan.org/pkg/rsfs The files are type1, a format where you need to put the .pfb and .pfm files in the same folder to view the font. Best practice is to repackage it in an .otf wrapper. This is a fairly coarse version, based on a smaller point size.
Shelly script is indeed a fairly good substitute. Most readers would not notice the differences such as the closed loop where the upper and lower stokes come together on _B_, _k_ and other letters, rather than the open loop in Typo Script as clearly shown in Levin's digitization.
Don