Working out the descent or succession of a peerage can be a complicated task in individual cases, but the general rules governing the normal cases are perfectly simple. (There are, of course, variations to which we shall come in due course.)
The normal course for many centuries has been to confine the descent of a peerage to the "heirs male of his (or her) body lawfully begotten". That is a quite simple position. Descent is confined to the male line, but so long as any descendants in the male line of the original grantee exist the peerage continues; though with the failure of one branch the line of succession may jump back centuries.
An excellent illustration of this is to be found in the Dukedom of Somerset, created in the reign of Edward VI. When the seventh Duke died in 1750 the succession had to be traced back again to the sixteenth century to the descendant of another son of the first Duke. Similarly, when the direct line of this new branch failed with the fifteenth Duke in 1923, the succession again was diverted to a cadet branch which traced descent to a younger son of the eighth Duke.
There are numerous instances of this kind in the peerage, but however much the succession may jump from branch to branch, the principle is the same, that descent can be traced in each case in unbroken male line to the original grantee.
This principle accounts for the statement one sometimes sees on the death of a peer that, say, "the earldom lapses but the barony passes to his kinsman so-and-so". The explanation is that the heir is descended not from any previous holder of the earldom but from an earlier generation still which possessed only the barony.
A case in point is that of the Earldom of Brownlow, which was conferred on the second Baron Brownlow in 1815. When the third Earl died in 1921 without issue the only possible heir to any of his titles was a kinsman who was descended from the first Baron. He thus had no claim on the earldom, which therefore became extinct, but inherited the barony.