Because hydrogen appears in so many different kinds of compounds (hydrides, hydroxides, acids, alcohols, sugars, ketones, amines, paraffins ... srsly, it gets around, it occurs in literally millions of described compounds), it is uncommon to encounter the phrase “hydrogen derivatives” in a chemistry context.
To me, the text implies that hydrogen derivatives are women: “No; he never travels with the hydrogen derivatives. You generally see him alone or with another man”.
So what’s the connection between women and hydrogen? Two thoughts:
The story starts as follows: “It took me two weeks to find out what women carry in dress suit cases. And then I began to ask why a mattress is made in two pieces. This serious query was at first received with suspicion because it sounded like a conundrum. I was at last assured that its double form of construction was designed to make lighter the burden of woman, who makes up beds. I was so foolish as to persist, begging to know why, then, they were not made in two equal pieces; whereupon I was shunned.”
So we start by discussing that something is made in lighter pieces so that it can be lifted by a woman: then we (possibly) describe women as hydrogen derivatives. What would the average reader have known about hydrogen in the waking years of the 20th century? That it is flammable, and that it is lighter than air. I mean I am reaching on tippy-toes here. Women ... lightness ... hydrogen.
O Henry was a pharmacist before he was a writer and it is possible that hydrogen had different connotations for him than it would for the average reader. Here are two other examples of the use of “hydrogen” by O Henry.
In No Story
“I tell you, she’s a beauty that would take the hydrogen out of all the peroxides in the world.”
Such a strange metaphor. Clunky but baffling.
In The Higher Abdication
“The saloon was small, and in its atmosphere the odours of meat and drink struggled for the ascendancy. The pig and cabbage wrestled with hydrogen and oxygen.”
This one is more straightforward: the food smells are competing with alcohol smells.
He makes fairly frequent reference to peroxide (meaning hydrogen peroxide as a hair changer or perhaps a tooth whitener).
Nemesis and the Candy Man
“I’ve been up against peroxide and make-up boxes before”.
“Chorus girls are inseparable from peroxide, Panhards and Pittsburg.”
The Gold that Glittered
“but you mean a peroxide Juno, don’t you?”
So perhaps by hydrogen derivatives, O Henry just means a peroxide blonde woman, which would carry certain connotations in that time.
P.S. “odour”? Noah Webster must have been rolling in his grave.