What was the "high Commissioner of the Police in Scotland" in 1777?

The word 'police' is different in its meaning from the modern narrow definition we are likely to hold true for back then. In modern words: much more setting policy, thus mainly more legislative than purely executive. If it helps, think of pronouncing it more like 'policy'…

The word was adopted in English in the 18th century and was disliked as a symbol of foreign oppression. The first official use appears, according to the New English Dictionary, in the appointment of "Commissioners of Police" for Scotland in 1714. A police system has been devised for the purpose of preventing evils and providing benefits. In its first meaning it protects and defends society from the dissidents, those who decline to be bound by the general standard of conduct accepted by the larger number of the law-abiding, and in this sense it is chiefly concerned with the prevention and pursuit of crime.

It has a second and more extensive meaning as applied to the regulation of public order and enforcing good government.

— "Police", Encyclopaedia Britanncia, 1911 version; compare with the current narrowed entry in that Encyclopaedia of police as "police, law enforcement"

In an easier to read scan of the same passage:

Oct 1776. Preferments. From the Lordon Gazette.
[…]
The King has been pleased […]

16. to nominate and appoint James Earl of March to be First Commissioner of Police in Scotland, in the room of Charles Lord Cathcart, deceased.

— The Scots Magazine, Oct 1776, Deaths and Preferments, p 176, gBooks

Now the first person mentioned is

Lieutenant-General Charles Schaw Cathcart, 9th Lord Cathcart, KT (21 March 1721 – 14 August 1776)

And one of his biographies state:

Charles Schaw Cathcart, 9th Lord Cathcart (1721-1776) was Rector of the University from 1773 to 1775.

Born in Edinburgh, Cathcart served as an aide de camp to William Augustus, Duke of Cumberland, and was wounded at the Battle of Fontenoy in 1745. He subsequently held a number of senior military posts in Scotland; was a High Commissioner to the General Assembly of the Church of Scotland, and was Scotland's first Lord Commissioner of Police. In 1768 he was appointed ambassador to Russia and became a friend of Catherine the Great.

— University of Glasgow Story > People > Charles Schaw Cathcart 9th Baron Cathcart

As does this stub.

The word "police" is perhaps a bit confusing, as it does not necessarily mean just "'the police' force", as in the modern understanding, but rather:

police, n.
3. a. The regulation, discipline, and control of a community; civil administration; enforcement of law; public order. The early quotations refer to France, and other foreign countries, and to Scotland, where Commissioners of Police, for the general internal administration of the country, consisting of six noblemen and four gentlemen, were appointed by Queen Anne, 13 Dec. 1714. This was app. the first official use of the word in Great Britain. In England, it was still viewed with disfavour after 1760. A writer in the British Magazine, April 1763, p. 542, opines that `from an aversion to the French … and something under the name of police being already established in Scotland, English prejudice will not soon be reconciled to it'. (The name Commissioners of Police, or Police Commission, was in the 19th c. given to the local bodies having control of the Police force in Burghs and Police Burghs in Scotland.) […]

police, n.
(pəˈliːs, pəʊ-)Also 6 polyce, -yse, pollice. Also in reduced forms polie (Sc.), p'leece, etc. See also polis 2.[a. F. police (1477 in Godef.), organized government, civil administration, police, ad. med.L. polītĭa for earlier polītīa: see polity, policy, and -ice 1. In early use commonly pronounced (ˈpɒlɪs), as still often in Scotland and Ireland.]

police, n.

1. = policy n. 1 3, 4, 4b. public police = public policy. Obs. c1540: Surr. Northampton Priory in Prance Addit. Narr. Pop. Plot 36 “Steryng them with all perswasions, ingynes, and Polyce to dedd Images and Counterfeit Relicts.” 1547: Boorde Introd. Knowl. iv. (1870) 137 “My scyences and other polyces dyd kepe me in fauour.” Ibid. xxv. 186, “I werke by polyse, subtylyte, and craught.” 1632: Brome North. Lasse v. v, “The plot smells of your Ladiships police.” 1640: Nabbes Bride i. iii, “What more police Could I be guilty of?” 1766: Entick London IV. 208 “Assisted by the police and interests of the Roman see.” a1768: Erskine Inst. Laws of Scotl. (1773) I. 152 “If … the public police shall require that a highway be carried through the property of a private person.”

police, n.
4. The department of government which is concerned with the maintenance of public order and safety, and the enforcement of the law: the extent of its functions varying greatly in different countries and at different periods.

and crucially:

police, n.
5. a. The civil force to which is entrusted the duty of maintaining public order, enforcing regulations for the prevention and punishment of breaches of the law, and detecting crime; construed as pl., the members of a police force; the constabulary of a locality.
Marine Police, the name given to the force instituted c 1798 (orig. by private enterprise) to protect the merchant shipping on the Thames in the Port of London. (The earliest use in this sense.) New Police (quots. 1830, 1831, 1884): the name by which the police force established for London in 1829 (Act 10 Geo. IV, c. 44) was for some time known.

— Oxford English Dictionary, 2nd edition

So Cathcart for example did not just oversee constables, detectives and inspectors, catching burglars, pickpockets and murderers. This was a more general posting.

For example, Cathcart is known in the annals of history of medicine — as Lord Commissioner of Police — for being important in disseminating methods for resuscitation:

Extract from the Journals of the Board of Police

This is, as it suggests, a very brief three page extract from the Journals of the Board of Police which is dated 11 August 1774. There were three people present at the meeting; Lord Cathcart (President), the Earl of Lauderdale and the Earl of Leven. Lord Cathcart presented a personal paper to the Board together with Cullen’s letter and the Board then ‘ordered’ that: The said paper and letter be printed; and that the clerk do send copies of it to all the Sheriffs of Counties, Magistrates of Royal Burghs, and Moderators of Synods and Presbyteries in Scotland; and that he do prepare a book for registering such communications as he may hereafter receive from any Sheriff, Magistrate, or Minister; and particularly such accounts of successful cases as may be transmitted to him.

It was also ‘resolved’ by the Board that the following articles constitute a proper apparatus for the recovery of drowned persons which could be obtained from Lawrie Jnr & Co., druggists, at the head of Niddry’s Wynd, Edinburgh at the following prices:

[List follows, example: 1 A fumigator; consisting of a small set of bellows, a brass box and handle, a flexible tube and ivory pipe … 10s … 6d … ]

Paper presented by Lord Cathcart

This is undated but bears an uncanny resemblance to the letter produced by Cullen. There is some extra detail of other resuscitation societies in Milan, Venice and Hamburg and a reference to the creation of the London Society, ‘this summer’ (this would again put the date at 1774).

He puts forward the case for such policies to be adopted in Scotland with great eloquence.

There is no country, which, from its situation, surrounded by the sea, and everywhere intersected by rivers, lakes, and bays, calls more loudly for effectual measures, for affording immediate relief to persons seemingly dead, from drowning, than Scotland; no nation more likely eagerly to adopt such measures, if proposed; nor any, where, from the nature of its government, such measures may so easily be carried into execution; and by the following steps: Let the Board of Police compose a proper advertis*m*nt, founded on the principles of those of other countries, containing the necessary advice to the public, and informing them of the reward offered by way of encouragement to those who shall follow it …

Cathcart explains that the adoption of this policy would be entirely optional on the various sheriffs, magistrates and clergy to whom the advertis*m*nt was to be sent but as there were few costs involved, except the initial purchase of the recommended equipment, he felt its adoption and implementation would not be a problem.

He provides an outline plan for the advertis*m*nt which has a series of recommendations:

1. The patient should be transported with great care to a nearby house.
2. The patient should be carefully dried and then gently warmed.
3. The lungs should be inflated either with expired air mouth to nostril or with bellows; at the same time tobacco smoke should be blown into the rectum.
4. If signs of life appear then the patient should be bled, given oral fluids and be encouraged to vomit.

Cathcart also outlines a set of rewards for initiating such resuscitation which were to be paid by the clerk of the county within two weeks of receipt provided such applications were supported by a certificate from a clergyman:

1. For the first person to alert a doctor or clergyman that someone had been taken out of the water —— 2s—6d […]

Cathcart also recommends that each parish should buy two sets of apparatus as previously described and that the notice should be fixed to every church door and market place in Scotland.

The techniques described in this pamphlet were very appropriate for the age and were a great improvement on many of the more injurious tech- niques described by previous authors. The adoption of expired air ventilation or the use of intubation and ventilation with or without bellows was sound and would have been quite practicable. Sadly there appears to be no information as to the implementation of these ideas. The pamphlet was published in London two years after it was written and there is no evidence that Cathcart’s notice was distributed to every town or that the advice was adopted.

Cathcart died the year that the pamphlet was published and so perhaps did not have time to promote the ideas it contained. Cullen was ‘busy’ teaching at the University in Edinburgh and seems not to have taken the concept further. Professor Anne Crowther from the Centre for the History of Medicine at Glasgow University has suggested that

"the Board of Police was a group of sinecurists with no great reputation for practical activity"

and further that the implementation required the local clergy to invest in the basic sets of apparatus for which there might have been little enthusiasm.

— David J. Wilkinson: "Resuscitation Greats: Dr. William Cullen and Lord Cathcart", Resuscitation (2006) 71, pp272–277, doi

That this Board of Police was just 'that' would of course not be correct, but should give you an idea of much more generalised this 'police' as 'policy' was.

The example shows however the word usage at the time:

PO’LICED. adj.
[from police.] Regulated; formed into a regular course of administration. Where there is a kingdom altogether unable or indign to govern, it is a just cause of war for another nation, that is civil or policed, to subdue them. Bacon's Holy War.

— Samuel Johnson: "A Dictionary of the English Language", 1755. (via LEME)

Or

Police: f.
Policie; politicke regiment, ciuill gouernment; or as a French Lawyer defines it, C'est le réglement de la Cité; or as another, C'est la forme, & le réglement estably aux choses necessaires à la vie humaine; whence; Droict de police. Power to make particular Orders for the Gouernment of all the inhabitants of a Towne, or Territorie; this Power (extending chiefely vnto three things, viz. small commodities (as victuals, &c.) Trades, or Occupations; and streetes, or high wayes;) though often challenged by the officers of the King (to whom all generall policie without question belongs) yet is (or should be) enioyed by euerie Lord in France, from the Chattelain vpwards.

— Randle Cotgrave: "A Dictionary of the French and English Tongues", 1611.

and

POLI’CED, adj.
[of police] regulated, formed into a regular course of administration. Bacon.

— Joseph Nicol Scott: "A New Universal Etymological English Dictionary", 1755. (via LEME)

POLICE,
the Regulation and Government of a City or Kingdom.

— Nathan Bailey: "An Universal Etymological English Dictionary", London, 1763. archive.org

The time inquired about falls right into the middle of the words introduction into English and its subsequent shift in main meaning towards our understanding:

A further problem arises with the word 'police'. The Greek πολιτεία (politeia) meant all matters affecting the survival and welfare of the polis. In Latin politia meant the state: an association which, unlike any other, had the right to enforce prescribed limits on public and private behaviour. […]

[…] within the tradition of Roman law the word 'police' gradually acquired the meaning of internal administration, welfare, protection and surveillance. By the early eighteenth century in France the word had come to mean the administration of a city and the harmony which this administration was expected to bring. In England however, with its common law tradition, the word was virtually unknown until the middle of the eighteenth century when the reforming Bow Street magistrates began to use it in a similar sense to the French; it gained something of its modern meaning and rather more currency as the century drew to a close.

Since neither England nor France had an organisation which contemporaries would have understood to be 'the police' during the eighteenth century, and since la police of nineteenth-century France included a much wider group of functionaries than the police of nineteenth-century England or the nineteenth-century United States, the question arises: who are 'the police' that I am proposing to compare in this book?

— Clive Emsley: "Policing and its Context, 1750–1870", Macmillan Press: London, 1983.

So another concrete example of what this Board of Police was doing on an everyday basis might be gleaned his involvement over the Crinan Canal building, or rather planning: — Marian Pallister: "The Crinan Canal", Birlinn, 2017 gBooks.

Similar general policy and administration duties are seen in the contemporary source:

Minutes Of The Adjourned Quarter Sessions Of Stirling-Shire. Stirling, 18Th October, 1773.

[…]

The Meeting taking under consideration the commerce of the Country above Stirling, and the great benefit that would accrue by water-carriage, they unanimously have agreed to request of Lord Cathcart, as President of the Board of Police, to move the Board to give orders for making out a plan, first with regard to the navigation of the river Forth up to Stirling, in what manner it shall be improved to the greatest advantage, and with the least expence. And, secondly, to examine how far, by a navigable canal joining the Upper Forth, commerce can be opened to the country above, and the navigation carried up the river as far as it can be made navigable; and to favour this meeting with such lights on these questions, and on the expence and model of execution, as may enable them to form a plan for those purposes, and to apply to Parliament for authority to execute it. His Lordship being present, undertook to move the Board accordingly.
(signed) Henry Home.

— Reports to the Lords commissioners of police relative to the navigation of the rivers Forth, Gudie, and Devon, M.DCC.LXXIII, 1773 ([By James Watt, the egineer], Robert & Andrew Foulis, 1773, gBooks.)

On financial administration for construction purposes on roads/bridges:

Royal warrant dated Hampton Court for a letter of gift to be passed under his Highness's privy seal in Scotland to Sir James Hall of a Few Duty for building a bridge at Coldbrane's Path [Cockburnspath]: the sheriffs of Haddington and Berwick having represented to the Lords Commissioners of Police in Scotland that the said shires have already advanced a considerable sum for building the said bridge and find that the finishing thereof will require a much greater sum of money than the Justices of Peace were empowered by law to raise from the said shires and consider that it properly belonged to the said Commissioners of Police to enquire into the condition of highways and bridges and that it were a great hardship the said work should entirely stop after so considerable an advance, and that Sir James Hall of Dunglass, bart., upon whose ground the said bridge doth stand, and who pays a yearly Few Duty to his Majesty, was willing to undertake to finish the said bridge and to uphold the same in all time hereafter upon his getting right to the said Few Duties; and the said Commissioners of Police have represented that the path of Coldbrands path is on the public road from Berwick to Edinburgh and is at present only passable with difficulty and in all probability will soon become impassable and that there is no way to avoid the said pass of Coldbrands path without turning out of the highway many miles to the great inconveniency of travellers and that the said Hall, whose loyalty and good affection to his Majesty's person and government was sufficiently known, had proposed as above to complete the bridge and to preserve it and the entries to it on both sides in repair in all time coming, at the sight of the Commissioners [sic for Justices] of Peace of the said two shires as a real burden on his estate of Coldbrandspath on his getting right to the said Few Duties: on which request of the said Commissioners of Police the King is hereby pleased to grant to him the Few Duties payable to the Crown out of his lands and estate of Colbrandspath and Old Cambus lying within the sheriffdom of Berwick amounting to 5l. 18s. 4½d. sterling, eight chalder of wheat, eight chalder of beer for the crops and years bygone resting unpaid, to wit from and including the year 1713 onwards for the term of his Majesty's life; on his being bound to complete and finish the buildings of the bridge with all proper and convenient expedition to the satisfaction of the Justices of the Peace of the said two shires and to uphold and preserve the same as above. Out Letters (North Britain) IV, pp. 157–9.

— 'Treasury Warrants: August 1717, 6-10', in Calendar of Treasury Books, Volume 31, 1717, ed. William A Shaw and F H Slingsby (Originally published by Her Majesty's Stationery Office, London, 1960), pp. 489–507. British History Online [June 2022].

For the bonus of exactly when 'the police' (force) of Scotland started to be — as in: as what we recognise as 'the police', we are at a loss, since that field suffers neglect, and as it would mean: 'in the English style', and 'of years later than 1776':

[…] to synthesise recent work on crime and English society from roughly the middle of the eighteenth until the close of the nineteenth century. There is a reference to crime in Wales where the legal system was indistinguishable from that of England; but Scotland, with a different legal system, and Ireland, with its rural and nationalist rebels together with a paramilitary police, receive little attention. […]

Policing in Edinburgh developed under a series of acts of parliament establishing lighting and watching commissioners. By the early nineteenth century the Edinburgh Police – one superintendent, or captain-lieutenant, three lieutenants, a sergeant-major, two dozen sergeants and about two hundred watchmen – seem closer to a Parisian-style police than anything English. […]

There is no detailed modern study of how what appears by 1900 to be a largely English model of police came to predominate in Scotland.

— Clive Emsley: "Crime and Society in England, 1750 –1900", Pearson Longman: Harlow, London, ³2005. p1, p248.

That means for certain definitions of 'the police', and a quite English-coloured perspective, the watershed year would be 1829:

The establishment of the Metropolitan Police in 1829 has transfixed historians of the police. For some the new police emerged as a means of restoring the social cohesion that was claimed to have been lost through urbanization and industrialization. The police was, therefore, depicted as one of the nineteenth-century inventions which underpinned modern civilization and democracy […]

Discussion of the period before 1829 has, therefore, been dominated by that date. People and events only acquire importance in so far as they can be linked to the establishment of the new police and earlier models of police are set up to be unfavourably compared with what comes later. Critchley promised A History of Police in England and Wales 900–1966, but sped through the first 929 years in 57 pages, while dallying over the next 137 years in the remaining 265 pages. His purpose in writing about the first period is made clear at the outset where he talks about finding the ‘origins of the English police system’ in the law and customs of the Danes and Anglo-Saxons and claims that ‘the nearest equivalent to the modern policeman is the Saxon tythingman’:

The history of the first 1,000 years of police in England, up to, say 1729, is mainly the story of how the tythingman changed into the parish constable, and latterly of the constable’s slow decline; that of the next 100 years, in London at least, is the story of the way in which a medley of local parish officers and watchmen came to be replaced by a single body of constables embodied into a police force, the governing principles of which were unity of control and professional excellence.

— Pilip Rawlings: "Policing: A Short history", Routledge: Leondon, New York, 2002, p1–2,

Should indeed the history of 'police as law enforcement in Scotland' be the prime target of the question, then one accessible dissertation on that — which also starts with differentiating the meanings of 'police' — on that would be:

The wider sense has been traced back to the Greek word 'politeia' which linked all matters affecting the survival and well-being of the State. Following the more restricted meaning of 'internal administration' under Roman law, it has been noted that the word 'police' was used in Scotland much earlier than in England. Even at the beginning of the 19th century the so-called Commissioners of Police first appointed by Queen Anne in 1714, continued to function in advisory capacity to the Lord Advocate in matters pertaining to the central Government of Scotland.

— John McGowan: "The emergence of modern civil police in Scotland: a case study of the police and systems of police in Edinburghshire 1800–1833", PhD thesis, The Open University, 1997. PDF

Or a summarising:

The Beginnings of Modern Scottish Policing
From a relatively early date a number of both Scottish burghs and counties began to show an interest in developing the police idea in institutional form. In the burghs, this interest took the form of private Police Acts which proliferated in the early decades of the century. Among the major urban centres, for example, private Acts were obtained by Aberdeen in 1795, Glasgow in 1800, Edinburgh in 1805, Paisley in 1806 and Dundee in 1824.

— W G Carson: "Policing the periphery: The development of scottish policing 1795–1900: Part I", Journal of Criminology, Vol 17, Issue 4, 1984, pp207–232. doi

The more general descriptions might be found in a classic similar in title to the one mention in the question:
— Nicholas Phillipson & Rosalind Mitchison: "Scotland in the Age of Improvement", Edinburgh University Press: Edinburgh, ²1996 (1970). With the author Mitchison summing up the problem of this question in one short sentence as:

With surprising speed, the whole English machinery of rewards for the faithful was applied to Scotland. The most conspicuous example was the Commission of Police,[1] originally the Commission of Chamberlainry. This started as an attempt to provide a channel for political control, but soon became simply a method of transferring a few thousand pounds a year to Scotch politicians of the right alliances.

[1] ‘Police’ here means government.

and she explains again in a later footnote (same number, as they are per page):

[1] ‘Police’ here and elsewhere in Scottish legislation meant the general provision of public services.

— Rosalind Mitchison: "A History of Scotland", Routledge: London, New York, ³2002 (1970), p246, p288.