In tropical climes there are certain times of day
When all the citizens retire, to tear their clothes off and perspire.
It's one of those rules that the biggest fools obey,
Because the sun is much too sultry and one must avoid its ultry-violet ray --
The natives grieve when the white men leave their huts,
Because they're obviously, absolutely nuts --
I am partly English by background, and that probably explains why the mad dogs and I have been out in the summer heat these past two days, something that focuses the mind on dressing cool when there is no air conditioning. Our predecessors had it right so far as I could tell - air permeability and sweat absorption are the two things to focus on. Everything from hat (and there must be a hat to shade the face and keep the scalp from burning) to shoes should breathe. From a construction standpoint that means minimal or no lining in anything, again from shoes to hat. White bucks were traditionally unlined for just that reason, and Anthony Drexel's suit in the illustration is apparently so minimalist in its construction that it lacks even the extra layer of cloth required to make a breast pocket.
Sweat absorption is a good argument in favor of the cotton neckerchief by the way. My daily dress has been a straw hat, neckerchief, cotton polo under an unlined linen jacket (though mine has pockets), linen trousers and unlined shoes worn sockless or with linen socks. Sockless looks a little more casual, particularly when one's ankles are tanned, but linen or hemp socks actually keep the feet more comfortable. And the cotton polo acts as an undershirt, absorbing perspiration while the jacket keeps that particular condition hidden from view.
Mad dogs, Englishmen and Californians have something in common.