Here are some family members who were appointed as Mayors:

Family Member	Town	Year
Henry Boase (1763-1827)	Penzance	1816
William Boase (1785-1843)	Liskeard	1836
William Davey Boase (1818-1866)	Liskeard	1844 1849 1852
Francis Boase (1819-1888)	Penzance	1859 1864 1866 1867 1870 1873 1876 1880

In those days, the Mayor was not simply the Council Chairman and Honorary Chief Townsman, but was himself expected to take responsibility for running the town almost single-handed during his year of office. We are fortunate in having preserved the Diary kept by Henry Boase, Mayor in 1816-17, during a term of office in which a large volume of routine business was increased by the passage and implementation of the Act for settling the harbour dues, and by a great storm in January 18l7 which did much damage to the quay and other property. Boase, born in Madron parish, went to London in 1787 and became a partner in a bank there, returning to Penzance for reasons of health in 1809 and becoming a partner in one of the Penzance banks. He became an Assistant of the Corporation in 1814 and an Alderman two years later immediately prior to becoming Mayor. His Diary gives a vivid picture of the duties and responsibilities of the Mayor as the one authority of the Town, uniting in his person practically all executive power. Though never in good health, Boase continued membership of the Corporation after leaving office, until his death in 1827.
His grandson, George Clement Boase (son of the Alderman and Magistrate John Josias Arthur Boase) published the full text of the Diary, with many valuable notes, in Collectanea Cornubiensis (1890); the selections following have been chosen to illustrate the Organisation of the town business and, especially, the astonishing variety of the duties which the Mayor was expected to perform.
THE MAYOR'S DIARY - EXTRACTS FROM THE DIARY OF HENRY BOASE, MAYOR OF PENZANCE 1816-17

1816
20 Sept.	Unanimously elected an Alderman of Penzance, and put in nomination for the Mayoralty.
4 Oct.	Unanimously elected Mayor for the year ensuing.
5 Oct.	Sat at the Guildhall and determined appeals respecting the rates for the highways and other business.
6 Oct. (Sun)	At Church.
7 Oct.	Granted a warrant to Emma Chellew against her natural father John Quick, to show cause why he refused to maintain her.
8 Oct.	Adjudged John Quick to pay £6 for the clothing and return to Plymouth of his daughter Chellew. Refused a pass to James Flemingan, Irishman, not knowing him.
9 Oct.	Ordered notices to be painted on boards to avoid nuisances in the markets. Wrote Mr. Davies Giddy that the harvest of this county had failed to a great extent, more than half.
l0 Oct.	Paid sergeants and constables fees and gratuity on election as alderman and mayor. Granted William Cotton, Excise Officer, a search warrant against William Mayne for smuggled goods. Granted to Grace Smaller and child, a soldier's widow passed from Northampton, an order to the Overseers to supply with the means of passing to Scilly. Granted to Thomas Tresize permission to ask relief for the loss of a horse during a week, being recommended by several householders.
15 Oct.	Jane Penaluna complained of Robert Stevens about a pair of pattens, spoke to him and he promised to rectify the mistake. Gave Ann May permission to ask charity for one week, her husband having broken his leg.
I7 Oct.	Complaints of the corn market that millers etc. were buying up before the public was supplied. Enquired of the Town Clerk the law of the case, who informed me that so far as dealers purchased for the ordinary demands, they could not be hindered.
18 Oct.	Michaelmas Sessions. In the evening let the quay and market for the year ensuing, viz. the quay dues to Holmes and Pengilly for £1140, the market to Nicholas Richards for £461, being £14O for the quay, and £10 for the market above the rent of last year.
19 Oct.	Granted a pass to a sailor named Manton, landed sick from the Asp , the ship in which Capt. Richard Trevithick is embarking for Lima. Sent out a precept for a meeting of the Corporation on the 21st to consider about a capstem, light and counting house for the quay, and the market dues for butter, dried fish, oil etc. Gave notice of a general meeting of the inhabitants of the town at the Guildhall on the 22nd, to consider the expedience of an application to Parliament for paving, lighting etc.
20 Oct. (Sun)	To Madron Church, to qualify.
21 Oct.	Held a meeting of the Corporation who resolved to erect a capstern on the pier if it can be done for £25, a light if for £10, and to pave 50 feet in length with moor stones, also agreed to tax butter and salt fish one penny a baskett.
22 Oct.	Held meeting at the Town Hall to consider whether any application should be made to Parliament for a bill for improving the town. A noisy throng, adjourned to 5th November.
23 Oct.	Wrote Mr. Giddy informing him of proceedings and requesting the papers he promised relative to the bill for the town.
24 Oct.	Decided between pork sellers and buyers, in one case that the pork should be taken back, and in the other that the difference shall be divided. Agreed with Capt. Teague for purchase of the Delhi's capstern at five guineas.
25 Oct.	Held adjourned sessions and granted a highway rate of one shilling. Made the sacramental qualification.
26 Oct.	Granted to Francis Codd exciseman a search warrant on information against George Hemmings for smuggled goods.

Changes in Penzance in the 19th century were not limited to growth in extent and prosperity and the erection of all the public buildings; the period also saw the decline and disappearance of the town's most noteworthy ancient custom, the lighting of fires on St. John's or Midsummer Eve (23 June) and St. Peter's Eve (28 june). This Midsummer custom was not limited to Penzance ; it was in fact the ancient pagan festival of the Summer Solstice, the Longest Day. The proceedings were first described by Dr. Paris, but the best account is that of Courtney:
Pandemonium then seems to have broken loose on Penzance and its neighbourhood. As soon as the evening begins to gather in, the youths from the different parts of the town parade the streets with burning torches, which they swing around their heads with a peculiar circular motion. Some of these are of considerable weight, and they require much exertion and no small skill to keep them from approaching too near the body of the bearer. Thus twisting and wriggling along, with the fitful blaze of the torch reflecting on his or her features (for both sexes mingle in the sport) and you have, without much stretch of the imagination, a strong resemblance to one of the furies. With the increase of darkness there is also an increase in the number of torch bearers; tar barrels and bonfires then blaze in every direction, and as not only Penzance, but also Marazion and St. Michael's Mount on the one hand, and Newlyn, Mousehole and Paul on the other, participate in the amusement, the whole bay seems to be lit up and presents a most splendid and brilliant illumination. Meanwhile the central part of the town is filled with all classes of individuals who come out to enjoy the scene. Fireworks of every description are set off without intermission and a continued series of flight and chase continues for some hours, it being a principal part of the sport to steal as quietly as possible amongst a crowd and disperse them by the unexpected report of a cracker or the hissing fire of a serpent . . . About eleven o'clock the spirits of the greater number of those engaged in the sports begin to flag, the fires are also nearly burnt out, and then commences another part, principally enacted by the lads and lasses living in the vicinity of the quay. These form a line, and running through the street call out "An Eye ! An Eye ! An Eye !" and proceed to "thread the needle" ... The two individuals at the upper end hold high their hands and the whole of the party, beginning with the opposite extremity, rush quickly through; this of course reverses their position, and it is now the turn of those who at first held up their hands to be the leaders of the thread. Thus alternating, rush after rush takes place, with shouts and laughter, until weariness compels them to desist. Home is now the word, and soon after midnight all is so quiet that a stranger entering Penzance, could never imagine it to have been the scene of these noisy revellings, which an hour before had exhibited.
One feature of the festivities not mentioned by Courtney was the boring of "Midsummer Holes" , thus described by Richard Edmonds:
In St. Just and other mining parishes the young miners, mimicking their fathers' employments, bore rows of holes in the rocks, load them with gun-powder, and explode them in rapid succession by trains of the same substance. As the holes are not deep enough to split the rocks, the same little batteries serve for many years.
As this fire festival was celebrated in Penzance annually for centuries, it is remarkable that the town was burnt down only once, and then by the Spaniards and not by its own inhabitants. The fearful risk was appreciated by the authorities, who put guards on the powder magazines and took other precautions; as Courtney recorded, "The Mayor always causes a proclamation to be made against these proceedings, which is however entirely disregarded." Thus in 1817 Mayor Henry Boase planned to "prevent the mischief of the Midsummer Bonfires by making all arranged and orderly exhibitions on some proper ground out of the town," but the festival took place regardless, and the same occurred in 1868 when a similar prohibition was attempted by his namesake and successor Francis Boase, an event satirised in bogus 'Old English' verse by one John Barren in a pamphlet, published anonymously, called Ye Battel of Ye Bonfyres . It was not until 1877 that the celebrations were last held in the streets of the town.

Source: The History of the Town & Borough of Penzance, by P.A.S. Pool.