The opinion of the author below seems to be that it should be "tranquilizing the body-conditioner" rather than "tranquilizing the bodily formations aka bodily conditions".
I would like to take this opportunity to discuss all the meanings of
the term "sankhara." This is a very common and important word in the
Pali scriptures, but many people have problems with it due to its
different uses and meanings. Languages are like that, uncertain and
seemingly unreliable. The single word "sankhara" can mean
"conditioner," the cause that conditions; it can mean "condition," the
result of the action of conditioning; and it can mean "'conditioning,"
the activity or process of conditioning. We use the same word for the
subject of the conditioning, "the concocter," as well as the object,
"the concoction." We even use it for the activity, "the concocting,"
itself. This may be a bit confusing for you, so please remember that
"sankhara" has three meanings. The correct meaning depends on the
context. This knowledge will be valuable in your further studies. (74)
Study the three meanings of sankhara in this body of ours. There is no
need to study it in books or in a theoretical way. The body itself is
a sankhara. It has been conditioned by a variety of causes and by the
many things of which it is formed. Thus, it is a sankhara in the
meaning of "condition." Once this body exists, it causes the arising
of other things, such as thoughts, feelings, and actions. Without the
body these thoughts and actions could never happen. Thus, it is a
"conditioner" because it causes other actions. Lastly, in this
flesh-body sankhara of ours, there is the process of conditioning
going on constantly. We can discover all three aspects of the word
sankhara within this very body.
Study the meaning of sankhara in this
comprehensive way. Then you will find it easy and convenient to
realize more and more profound Dhamma as you go on. (75)
EXPERIENCING SANKHARA
In step three - "experiencing all bodies," experiencing both the
breath and this flesh-body - each of these three meanings is
practiced. First, we contemplate the flesh-body as the thing
conditioned by the breath. Then, we see the breath as the conditioner
of the flesh-body. Lastly, we observe the activity of conditioning
that always exists simultaneously between the two of them. Thus, in
the practice of step three we see the conditioner, the condition, and
the action of conditioning. This conditioning of the body is the
physical level of sankhara. We have not yet seen it on the mental
level. Step three is this work of seeing these three things together,
simultaneously and continuously, within the mind. Then, you will see
everything concerning the term "sankhara," especially as it relates to
the kaya and its activity, right here in step three. (76)
When we have studied this fact until it is plainly, obviously, and
universally understood as explained above, then we will be able to
experience all three of these facts together in one moment. Even for
the duration of just one in-breath, or for just one out-breath, we can
experience all three facts in just one stroke of the breath. If we are
able to do so, then we have "fully experienced the kaya-sankhara
(body-conditioner)" and step three is successfully completed. (77)
The essence of practicing step three is to know that there are two
kaya, and to be able to regulate one kaya through the other kaya. That
is, we can regulate the flesh-body through the breath-body. Once we
are certain or this, once we see it dearly, once we are convinced by
our experience of this fact with each in-breath and out-breath, then
we have realized success in our practice of step three. (78)
STEP FOUR: CALMING THE BREATH
After we know that we can regulate the flesh-body with the
breath-body, we begin to practice step four. The Lord Buddha described
step four as "calming the body-conditioner (passambhayam
kayasankharam)." We are able to do this once we know that we can use
the breath-body to control the flesh-body. (79)
The subject of step four is to calm the body-conditioner
(kaya-sankhara) while breathing in and calm the body-conditioner while
breathing out. This means we can make the body-conditioner. (breath)
calmer and calmer at the same time that we inhale and exhale. This is
the matter which we now will explain. (80)
Note the specific wording of this step. "Calming the
body-conditioner" refers to calming the breath-body. In step four,
the aim of our practice is to calm the breath. We make it fine and
peaceful using various techniques which are available to us. If we can
calm the breath, there will be very interesting and powerful results.
First of all, the flesh-body will become very gentle, relaxed, and
tranquil. Then there will arise a calming of the mind, also. There
will be other results as well, but they will be left alone until
later. The immediate lesson is to calm the breath. To manage the breath
is the first point to be considered in the practice of step four. (81)