Chapter Four of Book V of On War is titled “Relationship between the Branches of the Service.” This chapter, however, doesn’t really seek to explain the relationship between the branches (infantry, artillery, and cavalry). Instead, it seeks to explain the relative strengths and weaknesses of the three branches. The specific relationships between the branches are left for us to intuit.
Clausewitz explains the strengths right off:
“The engagement consists of two essentially different components: the destructive power of firearms, and hand-to-hand, or individual, combat. The latter in turn can be used for either attack or defense (words here employed in an absolute sense, for we are speaking in the broadest of terms). Artillery is effective only through the destructive power of fire; cavalry only by way of individual combat; infantry by both these means.
In hand-to-hand fighting, the essence of defense is to stand fast, as it were, rooted to the ground; whereas movement is the essence of attack. Cavalry is totally incapable of the former, but preeminent in the latter, so is suited only to attack. Infantry is best at standing fast, but does not lack some capacity to move.” (p.285)
Clausewitz then enumerates his thoughts on the combat arms:
“1. Infantry is the most independent of the arms.
2. Artillery has no independence.
3. When one or more arms are combined, infantry is the most important of them.
4. Cavalry is the most easily dispensable arm.
5. A combination of all three confers the greatest strength.” (p.286)
And so Clausewitz starts beating around the Combined Arms bush.