Marshalling
One common reason for dividing the field in heraldry is for purposes of combining two or more coats of arms to express alliance, inheritance, occupation of an office, etc. This practice, called marshalling, initially took the form of dimidiation, or splicing together two coats of arms split down the middle (or sometimes, though rarely, split across the centre per fess or quarterly) so that half one coat was matched up with the opposite half of the other. As this would sometimes yield confusing or misleading results, the practice was supplanted by impalement, which kept both coats intact and simply squished them into half the space. According to Fox-Davies (1909), the practice of dimidiation was short-lived and had already reached its peak in the early 14th century, while impalement remains in practice to modern times. One important remainder of the practice, however, is that when a coat of arms with a bordure is impaled with another coat, the bordure does not continue down the centre, but stops short where it meets the line of impalement. Eventually quartering gained usage, and in the height of its popularity during the Victorian era, some coats of arms featured hundreds of "quarterings" (see the Grenville arms at right). More usually, however, a quartered coat of arms consisted of four parts, as the name suggests. The origin and underlying purpose of quartering is to express inheritance by female succession: when a female heir (who has no brothers, or whose brothers have all preceded her in death) dies, her son (only after her death) quarters her arms with those of his father, placing the father's arms in the first (upper left) and fourth (lower right) quarters and his mother's arms in the second (upper right) and third (lower left).
In the UK heraldries, complex systems of marshalling have developed, and continue to thrive, around heraldic expressions of inheritance. In many cases of marriage, the shield is impaled with the husband's entire coat of arms placed on the dexter side and the wife's entire coat placed on the sinister side; if the wife is an heiress, however, her arms are placed in escutcheon over her husband's (such usage is almost entirely English, Scots marshalling being impaling like any other marriage arms). If the husband is a knight of any order, however, the ensigns of that order belong only to him and are not shared with his wife. Two separate shields are then employed, the dexter shield bearing the husband's arms within the circle of his knighthood, and the sinister shield bearing the husband's arms impaled with the wife's usually encircled with a meaningless wreath of oak leaves for artistic balance. A male peer impales the arms of his wife as described above, but including the supporters, coronet and helmet of the peer; if he is also a knight of any order, the two-shield method is used. If a female peer marries a commoner, however, the husband places her arms inescutcheon, surmounted by a coronet of her rank, over his own, but the supporters of her rank cannot be conferred to him; the wife bears her arms singly on a lozenge with the supporters and coronet of her rank. Volumes may be written on all the endless heraldic possibilities of this convoluted system of marshalling, but it may suffice here to say that for various purposes, arms may be marshalled by four basic methods: dimidiation by clipping and splicing two coats (usually per pale), impalement by dividing per pale and crowding an entire coat of arms into each half, quartering by dividing the shield into usually four (but potentially innumerable) "quarters", and superimposition by placing one coat of arms inescutcheon over another. It is also worth noting that one common form in German-Nordic heraldry is "quarterly with a heart" (a shield quartered with an inescutcheon overall). This may have stemmed from the continental practice of sovereigns placing their own hereditary arms inescutcheon over the arms of their dominions.
The arms of Novohrad-Volynskyi, Ukraine, show an unusual form of marshalling quarterly with a heart, where one quarter is dimidiated while the others are not.
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Example of two coats of arms dimidiated
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The same two coats impaled
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Example of the quartering of two coats of arms
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Example of incorporating arms as an escutcheon
Read more about this topic: Division Of The Field