When you deal with something like compassion for physical pain, which we know is very, very old in evolution - we can find evidence for it in nonhuman species - the brain processes it at a faster speed. Compassion for mental pain took many seconds longer.
When we talk about emotion, we really talk about a collection of behaviors that are produced by the brain. You can look at a person in the throes of an emotion and observe changes in the face, in the body posture, in the coloration of the skin and so on.
Emotion consists of a very well orchestrated set of alterations in the body that has, as a general purpose, making life more survivable by taking care of a danger, of taking care of an opportunity, either/or, or something in between.
The mechanism of primary emotions does not describe the full range of emotional behaviors. They are, to be sure, the basic mechanism. However, I believe that in terms of an individual's development they are followed by mechanisms of secondary emotions, which occur once we begin experiencing feelings and forming systematic connections between categories of objects and situations, on the one hand, and primary emotions, on the other.
I got interested in the emotions after studying patients who had lost the ability to emote and feel under certain circumstances. Many of those patients also had major impairments in their ability to make decisions.
We may say that feelings have two kinds of intensity. One is the intensity of the feeling itself, by which loud sounds are distinguished from faint ones, luminous colors from dark ones, highly chromatic colors from almost neutral tints, etc. The other is the intensity of consciousness that lays hold of the feeling, which makes the ticking of a watch actually heard infinitely more vivid than a cannon shot remembered to have been heard a few minutes ago.
Action seems to follow feeling, but really action and feeling go together; and by regulating the action, which is under the more direct control of the will, we can indirectly regulate the feeling, which is not.
Dixxit 
