We may begin our investigation with a formula common in Derbyshire.
In M [place name] habuit K [man’s name] a car[ucatas] terrae ad geldum. Terra b car[ucarum or carucis]. Ibi nunc in dominio d car[ucae] et ... villani et ... bordarii habent e car[ucas].
The Lincolnshire formula is perhaps yet plainer. Instead of saying ‘Terra b car[ucarum],’ it says, ‘Terra ad b car[ucas].’ Still more instructive is a formula used in Yorkshire.
In M habuit K a car[ucatas] terrae ad geldum ubi possunt esse b car[ucae]. Nunc habet ibi K d car[ucas] et ... villanos et ... bordarios cum e car[ucis].
As a variant on the phrase ‘ubi possunt esse b car[ucae],’ we have, ‘quas potest arare 1 car[uca],’ or ‘has possunt arare b car[ucae][1340].’
The teams on the demesne (d) and the teams of the tenants (e) are enumerated separately. The total number of the teams (d + e) we will call c.
Now occasionally we may find an entry concerning which the following equation will hold good: a = b = c: in other words, the same number will stand for the carucates at which the manor is taxed, the ‘teamlands’ that there are in it (or to put it another way the number of teams that ‘can be there,’ or the number of teams that ‘can plough it’[1341]) and also for the teams that are actually to be found there. Thus:—
Terra Roberti de Todeni.... In Ulestanestorp habuit Leuricus 4 car[ucatas] terrae ad geldum. Terra totidem car[ucis]. Ibi habet Robertus in dominio 1 car[ucam] et 6 villanos et 3 bordarios et 8 sochemannos habentes 3 car[ucas][1342].
Here a = b = c. But entries so neat as this are not very common. In the first place, the number (c) of teams often exceeds or falls short of the number (b) of ‘teamlands,’ or, which is the same thing, the number of teams that there ‘can be.’ An excess of ‘teamlands’ over teams is common. In some parts of Yorkshire and elsewhere instead of reading that there are so many teams, we read ‘modo vasta est’:—there are no oxen there at all. But the reverse of this case is not very uncommon. Thus we may be told that there are 3 carucates for geld, that ‘there can be there 2 teams’ and that there are 4 teams[1343]; we may find a manor that contains land for but 3 teams equipped with as many as 7[1344]. As to the relation between a and b, this is not fixed. On one and the same page we may find that a is equal to, greater and less than b. Thus in Lincolnshire[1345]:
In Colebi habuit Siuuard 7 car. terrae ad geldum. Terra ad totidem car.