From Nainfa's Costumes of Prelates:
2. The "usual" clerical hat is familiar to all persons who have travelled in countries where clergymen wear the full ecclesiastical dress outside of their houses, such as Italy, France, Belgium and Spain. Although, according to local customs, it may slightly vary in some of its features, yet its shape and general appearance make it quite different from a layman s hat.
In the eighteenth century, it had assumed the triangular shape of the cocked hat... and it generally retained this shape until the middle of the nineteenth century; but it has nowadays reverted to its earlier form of a round, broad-brimmed, low-crowned hat. In strict etiquette, it should be made of beaver hair; but, for reasons of general economy, and also for greater comfort in summer, it is frequently made of ordinary felt.
The usual hat is uniformly black for all ecclesiastics, except the Pope and Cardinals, as will be noted hereafter; but the crown is encircled with a silk band or cord, the color of which is indicative of the wearer s dignity. The cord seems now generally preferred to the band, it ends in two tassels which slightly hang in back a little to the left. That band or cord is red and gold for Cardinals; green and gold for Patriarchs and Archbishops; green for Bishops and the Regent of the Apostolic Chancery; amaranth red for the first three classes of Protonotaries Apostolic; purple for the Domestic Prelates and, outside of Rome, for the Prelates di mantellone; black for Titular Protonotaries and all other ecclesiastics. We may add that, strictly speaking, the lining of the hat should be of the same color as the band or cord; but it is not always easy to make hatters comply with this last regulation.
3. The Pope, when riding or walking in his gardens, wears a red felt hat adorned with a gold band or cord ending in gold tassels; this hat is of the general form above described, but the brim is raised and held on both sides by small gold strings.
4. Cardinals, besides the usual black hat which they wear like all other Prelates, have another one of red felt [See NLM note below in "Of a Cardinal"] to be used only when they wear the purple or red cassock; but the reader must note that this red hat is different from the Cardinals pontifical hat which is bestowed upon them as one of the principal insignia of their high dignity.
5. The clerical hat, as here described, rather than the biretta, is the proper head-dress for a Prelate wearing his official costume outside of church ceremonies...
Here are a few images of the cappello Romano.
First that of the simple cleric:
(Image credit: Orbis Catholicus)
Next, that of a Monsignor:
(Image credit: Orbis Catholicus)
Of a Bishop:
(The tassles look different on this one only because, if you look closely, the cappello is actually being hung and this is the view looking upwards)
(Image credit: Orbis Catholicus)
Of a Cardinal:
As a point of note, the cappello of a Cardinal, like that of the pope, was red in the time of Nainfa, but this was abolished by Pope Paul VI in Ut Sive Sollicite. Since that time, the cappello of a Cardinal is much like that of a bishop, black but with red and gold cords instead of green and gold.
Present cappello of a Cardinal:
(Image credit: Dieter Philippi)
I believe this would have been the pre-Paul VI cappello:
(Image credit: Dieter Philippi)
Of the Pope:
(The cappello of Pius XII)
