Vinegar

I removed the floating gunk off the top of our apple mixture, strained the remaining product through an old pillowcase, and now...

We have vinegar!  Now, I do not claim to be scientifically "sound" in my concocting.  I basically threw a few things in a pot and waited.  However, I am glad that I was able to utilize left over apple remnants that would have otherwise been wasted.  We will not consume this product, but I will use it to clean and disinfect. 
I welcome any advice concerning how to "formally" make vinegar.