Harvey:

To answer your questions about "Blow Negative" and "Negative Buoyancy" you
can read all about the U.S. Navy's Fleet Submarine at: [maritime.org]

When you open it up, scroll down to "Submarine Construction"....
then chapter #4B - "Water ballast Tanks". Now click on the blue #44 in the right
column. This should explain the use of the Special Ballast Tank called "Negative".
It's located just forward of the center of buoyancy of the boat.

Now for "Blow Negative"......

The order to "Blow Negative To The Mark" is given to the air-manifold operator (usually the auxiliaryman) by the diving officer when he sees that the boat is approaching his ordered depth, (either from the surface or at perisope depth.)
At the same moment the chief-of-the-watch is watching the Negative Tank liquidometer, with his hand open, and when he deems it appropriate, shuts his
open hand as a signal to the air-manifold operator to secure blowing Negative Tank. When the air has deen secured, the chief shuts the Negative Tank flood valve. With long experience standing this watch on the hydraulic manifold, the chief rarely misses the mark on the liquidometer. If he blows too much or too little water out, the diving officer will order the trim manifold operator to pump from or to sea to satisfy his trim.

The main purpose of the Negative Tank is to start the bow down in order to have
the bowplanes bite some water, as they are useless while the boat is on the surface.

I hope this has been helpful.

ROBERT M.