Green’s Dictionary of Slang

a transparent blouse of muslin and lace with next to no collar and thus, for some puritan contemporaries, a shockingly low neckline.

1903		Hull Dly Mail 23 Apr. 2/6: Doctors are busy reaping the benefits arising from the wearing of the ‘pneuomania blouse’.
1903		N.-Y. Tribune 12 Sept. 8/4: [from Punch] And now, to match the low cut wear, / That Eve to Eve allows. / Behold by day the open air Pneumonia Blouse!
1905		S.F. Call 5 Nov. 2/4: Look at the way women go about [...] with bare chests and shoulders. Look at the ‘pneumonia blouse’.
1906		E. Godfrey Bridal of Anstace 137: After ten minutes or so a small person drifted, as it were, casually into the room, looking very chilly in a skim-milk blue ‘pneumonia’ blouse.
1910		R. Dehan One Braver Thing 79: Womanly anxiety throbbed in the bosom not too coyly hidden by the pneumonia blouse.
1915		R. Dehan Off Sandy Hook: And Other Stories 213: And she dressed herself in her best, with a large lace collar over a cloth jacket, and the once fashionable low-necked pneumonia-blouse.
1920		H.H. Johnston Mrs. Warren’s Daughter 182: Braces that really braced and held up the nether garment of trousers; a waistcoat buttoning fairly high up (no pneumonia blouse).
1921		N.W. Putnam West Broadway 11: A pussyfoot-silk street dress with no neck or sleeves or very much skirt [...] that latest cruelty of style known as a robe pneumonia.

(US) an open-topped car.

1921

N. Putnam West Broadway 16: I told Rollo the chauffeur, to take the pneumonia car home for a rest and I would walk.