It's interesting to see how much the art's evolved in just six months, although admittedly here Bob Kane has Sheldon Moldoff helping with the pencils. (This is before the period when Moldoff became one of Kane's primary uncredited "ghost artists". Apparently they kept that secret from DC.) The main thing that's changed is how they draw Batman himself. The ears have evolved, the mask looks three-dimensional and he wouldn't look out of place in a modern Batman comic. He also now has a secret laboratory, "baterangs" (sic) and a batplane, although he still lives in Manhattan, New York. (Gotham City was introduced in Batman #4 in 1940.)
Anyway, this story was reprinted in the DC Comics Graphic Novel Collection of Batman Hush part 2, because it's the first telling of Batman's origin. That only takes two pages, but it's pretty much the same as all other versions. It's perfectly respectable and stands up to modern rereading.
After that, we're into a ten-page story about a DIRIGIBLE OF DOOM. It flies over Manhattan, shooting death rays on the orders of "another Napoleon". (Today, it feels weird to reflect that there used to be an age when Napoleon was the European dictator of choice for megalomaniac comparisons.) All this is cool, in an H.G. Wells's Martians kind of way. Skyscrapers explode and rain concrete down on the people below.
There's yet another deathtrap from which Batman escapes when the villain (Dr Carl Kruger) leaves the room. Of course. Naturally. The story gets startling, though, when Kruger kills Batman! I was impressed. The Case of the Chemical Syndicate is very much a period piece, but this is more exciting than your average modern Batman comic. (Albeit with far worse art.) Batman lives, of course, but his escape method is in itself surprising. He overpowered one of Kruger's guards, swapped clothes with him and let Kruger turn an unconscious man into a heap of ashes.
BATMAN (when the dirigibles return): "Those ruthless murderers, taking innocent lives!"
UNSPOKEN IMPLICATION: "...that's my job!"
Naturally, Kruger doesn't survive the adventure. These early Batman adventures are bloodthirsty. This one's also surprisingly good.