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The American commander Brigadier-General Morgan indicated that the British force at Cowpens was comprised of 1,150 men (see How Many Fought at Cowpens?). I assume that this number included both the men (of all ranks) that fought at the battle and the detachment that was left behind to guard the British baggage train.
Rank and file totals for most British units can be found in a British report dated January 15, 1781. This includes the detachment of the 16th Foot (44 men), the 7th Foot (167 men), the 1st Battalion of the 71st Foot (249 men), the light infantry companies of the 71st Foot (69 men), and the British Legion (451 men).
I also reviewed the rolls for the Prince of Wales American Regiment (PoWAR) light infantry company, and determined that there were as many as 1 officer and 28 rank and file of this company present at Cowpens.
Finally, Lieutenant Roderick Mackenzie recorded the number of officers present in most of the units at Cowpens, including the 7th Foot (7), the 71st Foot (16 between the battalion and light companies), the PoWAR light infantry company (1), and the detachment of the 17th Light Dragoons (2).
Some assumptions had to be made fill in the gaps in the records.
Rank and File Estimates
The two 3-pounders that the British had at the battle had a crew in the neighborhood of 22 men and no officers (an estimate based primarily on John Moncure's estimate in The Cowpens Staff Ride and Battlefield Tour and Lawrence Babits' estimate in A Devil of a Whipping: The Battle of Cowpens).
Tarleton's account implies that the 17th Light Dragoons had around 50 men, but he was speaking very loosely. The other numbers he gave are demonstrably wrong, such as his statement that his total force was 1000 men, and that the 7th Foot, and 1st battalion of the 71st Foot both had 200 men. A U.S. intelligence report of Jan 6, 1781 gives 35 men for the 17th (see excerpt, below). This is also not entirely trustworthy. However a number between 35 and 50 men is probably accurate. For this reason, the 17th Light Dragoons are assumed to have had around 40 men.
The British report does not indicate how many of the rank and file in the British Legion were infantry and how many were dragoons. Tarleton's account implies that there were 250 dragoons, which would leave about 200 infantrymen. The US intelligence report, mentioned above, indicates that the infantry and cavalry components were of equal size (this is not shown in the excerpt above). An annotation on the Pigee Map (Babits, page 71) lists 280 men for Tarleton's cavalry. This number also appeared in a New Jersey newspaper account of the battle. My assumption is that the cavalry had around 240 men (280 rank and file total - 40 rank and file for the 17th light dragoons); this leaves about 210 rank and file for the infantry.
Using the number of officers listed by Mackenzie, and the rank and file numbers indicated above, it is possible to determine for some units the ratio of officers to rank and file. There were 9 officers for 167 rank and file in the 7th Foot (1:19), 16 officers for 318 rank and file in the 71st Foot (1:20) 2 officers for 40 rank and file in the 17th Light Dragoons (1:20), and 1 officer for 28 rank and file in the PoWAR light infantry (1:28). The average ratio is 1:20. By extension the number of officers in other units can be estimated.
British companies at the Cowpens were badly understrength. I'm assuming that there was not more than 1 musician per company. Following Babits, I'm further assuming that the detachment of the 16th Foot was organized as a single company, and that the 7th Foot was organized into four companies. The number of infantry and dragoon companies in the British Legion are based on records found on Marg Baskin's Banastre Tarleton website.
16th Foot: ~44 men (41 rank and file, 2 officers, and 1 musician).
7th Foot: ~180 men (167 rank and file, 9 officers, and 4 musicians).
71st Foot (1st battalion): ~269 men (249 rank and file, 12 officers, and 8 musicians)
71st Foot (light infantry companies): ~75 men (69 rank and file, 4 officers and 2 musicians).
17th Light Dragoons: ~43 men (40 rank and file, 2 officers, and 1 musician).
Royal Artillery detachment: ~ 22 men (all rank and file).
British Legion Infantry: ~226 men (about 210 rank and file plus about 10 officers and 6 musicians).
British Legion Dragoons: ~258 men (about 241 rank and file, 12 officers and 5 musicians)
Prince of Wales American Regiment light infantry: ~29 men (28 rank and file, 1 officer, and 0 musicians).
Total: 1,146 men of all ranks (1,067 rank and file, 52 officers, 27 musicians)
This total almost exactly matches the total of 1,150 men Morgan named.
Morgan said that the British claimed to have "fought" 1,037 during the battle. I'm assuming that this number was the total number of rank and file with Tarleton, minus the baggage detachment. The size of this detachment is unknown, however Mackenzie said that it was under the command of Ensign Fraser of the 71st. If the detachment was comprised of Ensign Fraser and 30 men then the total number of British present during the battle would be as follows:
Revised Total: 1,115 men of all ranks (1,037 rank and file, 51 officers, 27 musicians).
Tarleton and Mackenzie said the British force had 1,000 men. They were probably counting only rank and file that were on the battlefield.
American Lieutenant-Colonel John Eager Howard wrote that at the climax of the battle, his 350 men were confronted by 800 Bitish. I show he was facing 814 men (1146 for the British overall - 31 men for the baggage detachment - 258 men for the British Legion dragoons - 43 men for the 17th Light Dragoons = 814) minus whatever losses the British sustained earlier in the battle).
American Major-General Nathanael Greene estimated that there were 50 Loyalist militiamen accompanying Tarleton's baggage train and presumably serving as drivers and/or guards. Tarleton probably also had a number of African Americans serving as drivers. Morgan recorded, in his after action report, the capture of "ten negroes." Tarleton mentioned having the service of Loyalist guides, but they were probably very few in number. Of these, South Carolina militaman Thomas Young encountered the Loyalists "Littlefield and Kelly" after the battle. Loyalist Captain Alexander Chesney scouted for Tarleton and participated at least during the late stages of the fighting.
The British Force in Miniature
(click to enlarge)
7th Foot (left) and 71st Foot (right)
British Legion infantry (left) and British Legion dragoons (right)
17th Light Dragoons (left) and light infantry companies (right)
Royal Artillery detachment (left) and baggage guard (right)
John Moncure's online history of the battle, The Cowpens Staff Ride and Battlefield Tour, includes a transcription of statements by Morgan, Mackenzie, Tarleton, Howard, and Greene.
Marg Baskin's Banastre Tarleton website has transcriptions of Tarleton's account, Mackenzie's Strictures, and other records pertaining to the British Legion.
François-Jean de Chastellux's (1787) Travels in North-America, in the Years 1780, 1781, and 1782 is one place to find a copy of the British rank and file returns.
Lawrence Babits' 1998 A Devil of a Whipping: The Battle of Cowpens is available through amazon.com.
Theodorus Bailey Myers' 1881 Cowpens Papers has Morgan's account of the battle as it appeared in a New Jersey newspaper.