Newer versions of Java will not allow an applet to run unless it is either digitally "signed" or you allow a security exemption for NineChime. Furthermore, Chrome no longer allows Java applets to run, and Firefox may have issues sending data when using the Java Plugin.
The only effective option is to use Internet Explorer (Windows) or possibly an older version of Safari (OSX), and make sure to grant NineChime a security exception.
To enable Java on NineChime, open up the Java control panel. On Windows 7 and older versions of Windows, this means clicking the Start Menu and then Control Panel. On newer versions of Windows, click the Start Menu and do a search for "Control Panel". One you find the Java control panel, click the "Security" tab, and click the "Manage Site List" button.
Once there, you will have to add direct paths in the Exception Site List. You will need to add two to this list:
This only allows Java to run applets from specific parts of NineChime, and will not allow potentially insecure applets to be run from other sites on the Internet.
This procedure will work with any oekaki on which you want to draw, or any of those nice science applet sites.
Return to DTP or perhaps to Coonikaki
Starting with Java 7, update 51, Oracle had decided to block all Java applets that do not have a signed security certificate issued by a Certificate Authority. In other words, developers are required to formally identify themselves and digitally “sign” their applets, and this requires a fee.
This is part of Oracle's plan to tighten security and improve safety shift legal liability away from Oracle's security sandbox. The idea is that if the computer is compromized due to a security flaw in Java, the blame would be placed on the owner of the applet or web site, rather than the vulnerabilities in the Java sandbox. This pretty much defeats the whole purpose of Java, but... whatever.
I cannot sign the applets myself as I do not have a CA certificate (plus, my site doesn't support HTTPS just yet). The only way around this issue at the moment is for users to give NineChime.com (plus any other oekaki hosts you visit) a security exception.
As for the web browsers, Chrome has removed support for NSAPI plugins, and therefore the Java plugin will not work. Firefox still supports the NSAPI plugin, but it may still block Java from sending data correctly, resulting in the annoying socketPermission() error. I do not yet know of a workaround for this issue other than to use Internet Explorer to run Java (Edge does not support Java, either).