As ever stirling work by David Porter on the Territorial numbering system (yes there was definitely one).

In this case the TF Training schools were tasked to produce a number of Howitzer Batteries. These were numbered in the 500 series (which Frederick's Lineage records as New Army units), however as david has found out the men from these Batteries were brought under the administration of the Territorial County Associations.

In my research into T.F. Artillery renumbering I discovered blocks of six figure numbers allocated to individually numbered Howitzer batteries which I was under the impression were just regular. The majority were in the 500 series of Howitzer batteries formed in 1916. The conclusion I came to was that some must have been given T.F. affiliation. Finally, last weekend, I managed to look up what I thought relevant Army Council Instructions that were mentioned in documents found within Service Records. This is what I uncovered:

ACI 1298 of 1916, dated June 29, 1916, shows that 41 Howitzer batteries were formed, 12 of them at T.F. Artillery Training Schools (3rd Line Units).

ACI 1717 of 1916, dated September 4, 1916, gives the titles of the raised batteries in the T.F. as 529 to 540 along with the offices dealing their administration. This means that numbers 500 to 528 were allocated to those batteries raised at the listed regular reserve brigades.

ACI 2063 of 1916, dated November 1, 1916 shows that some establishments had difficulty in raising their batteries and 2nd Line T.F. batteries were withdrawn from their Divisions to fill the gaps in both regular and T.F line up. It can be seen that these too retain T.F. affiliation along with the 4 newly raised Home Service replacements, namely 541 to 544. The 6 regular batteries were replaced by 545 to 550. It is also interesting to note that certain batteries had already proceeded overseas.

Unfortunately, most of this numbering quickly disappeared as the batteries joined other brigade formations. By February 1917 most had been broken up and divided between other brigades in their group. It is also worth pointing out that 504 Bty & 505 Bty were subsequently armed with 6 x 18pdr each under ACI 2403 of 1916, dated December 22, 1916, and grouped with 465 Bty & 466 Bty at Bordon in 65th Army Brigade

Source: The 500 series Howitzer batteries raised in 1916