The posts above cover the Hesse-Kassel, Hesse-Hanau and Brunswick quite well.
The period of the American War of Independence was a transition for the Royal artillery. In addition, there were various approaches used during the period 1775 to 1783 as well as in the northern, mid-Atlantic and southern theatres of war.
In organizational terms, the British battalions (regiments) did not have battalion pieces. The Royal Artillery and pieces from the artillery park were allocated to battalions at various points during the war, certainly through 1777 in Howe's army.
The artillery park system was used by the Royal Artillery, meaning their men were in companies while the hardware, the various artillery pieces, were assigned out of the park. Thus, the pieces for the task had men detailed for serving them.
The war saw the use of (what we call today) batteries, termed "brigades". Howe had "brigades" or artillery in the 1776 and 1777 campaigns, yet used them for the larger cannon (6-lbers and 12-lbers). Lighter pieces (6-lbers and 3-lbers) could be assigned to infantry brigades (at times four to a brigade with the brigades having 3 or 4 battalions) and similar formations (Guards, Light Infantry, Grenadiers). The comments above are not "fixed" for some infantry brigades also have 12-lbers attached to them.
The most explicit order for artillery assigned to the infantry brigades (though without artillery brigades) is from Howe in June 1777. See pages 448-449 of the Kemble Papers published in 1884 by the New York Historical Society
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One can go through the order books in the Mackenzie's Diary for example of orders issued at Rhode Island (I do not think this two-volume work is on line). For example, see volume 1's page 303, where the defenders are getting ready in June 1778 and two 6-lbers are attached to the 54th Foot with the additional direction: "They are to remain attached to them until further orders." Later, in August 1778 (page 384), he writess: "The Battalion Guns were posted in the most convenient situation near their resepective Corps."
It was very much an alloction as needed and as seen necessary.
Howe formed three artillery "brigades" for the heavier pieces for the march from Elk's Head on to Brandywine and Philadelphia (see Kemble, volume 1, page 477 or 484 or 488-9 or). On page 484, the orders note that for each Brigade in motion should have two field pieces. Page 489 orders the 40th Foot to have two 3-lbers with it. The composition of the artillery "brigades" themselves appears to have varied, though one did have six 12-lbers and four howitzers at the Brandywine battle.
Burgoyne was very clear about artillery "brigades" for his force. In his narrative, page 14, he said, "The forming artillery into brigades, in perference to detaching two guns to each battalion, has been constantly practised in most services during last war under the ablest men, it is productive of many advantages, as the brigades means, either singly or united, fall under the command of a proporionable number of officers. The service is carried on with greater rgulatity, and the effecct of the fire becomes much more formidable than when scatterd along the front of the line. This mode of service was recommended by Major.general Phillips, and adopted without hesitation by me, my own judgement being confirmed by an officier of his great skill and experience."
This said, the number of pieces in each artillery "brigade" in Burgoyne's force varied during the campaign. Hadden's Journal includes detailed information at various dates.
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At some points, an artillery "brigade" might have four 6-lbers (Jones Brigade) or four 6-lbers & four 3-lbers (Pauch's Hesse Brigade) because the English sent two of each to Pauch (page 110). Later, Pauch's Brigade is six 6-lbers and two 3-lbers (page 155). On the next page, 156, the artillery park itself was divided into three artillery "brigades" with a mix of pieces (note that not all pieces are distributed as some are still on a boat), thought two (Hosmer's and Mitchelson's each have two 12-lbers, two 6-lbers, one 8inch howitzer and 1 5&1/2 inch howitzer) while one (Blomfield's) has just two heavy pieces (24-lbers)
After Clinto takes overall command and matters become shift to the south, the use and allocation of artillery changes.
As an over generalization, the light troops (whether Jäger or Legion or Light Infantry) each have one or two light pieces with them, the German battalions retain their traditional two battalion pieces, and the British park tends to be employed in pairs of pieces for or with each British infantry brigade. There are exceptions. For the most part, the troops at Camden, reflects this generalization; see the previously referenced order of battle.
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A word on manning: the pieces were served by the Royal Artillery, though addional manpower could be sent from infantry units (often from the Provicial troops) to help the specialists in moving the pieces.
In accounts, there is no consistency of mentioning (or not noting) when individual infantry battalions have "battalion guns" with them. This is especially true for the Hessian and other German troops (who generally did have their pieces with them), but it is also true for British and Provincial battalions/regiments (who generally did not; except the Grenadiers, Ligh Infantry or Guards, who did) and also for the movement of British Infantry Brigades (who in 1776 and 1777 in Howe's army often did have pieces with them).
Trust this helps. – R
