serve video from osx server

I'm running Apache as a web server on OSX Mavericks on a Mac mini, with a 100Mbps fibre network to the outside world.

Videos in the HTML5 <video> tag do not play on iOS devices. They do play on other devices (laptop, desktop, OSX, Windows, Firefox, …)

The required "AddType" directives are present in the .htaccess file at the root of the site.

The same videos with the same HTML do play on iOS devices if I put them on my hosting service, which also runs Apache.

The sample video in the W3Schools <video> tag also plays on iOS devices.

The only difference I can observe is that my Apache server runs on top of OSX Mavericks. I suspect a small tweak is needed in the configuration of the Mavericks Apache server, but what?

Any suggestions?