The Collaborative International Dictionary of English v.0.48:

Apportionment \Ap*por"tion*ment\, n. [Cf. F. apportionnement,
   LL. apportionamentum.]
   The act of apportioning; a dividing into just proportions or
   shares; a division or shares; a division and assignment, to
   each proprietor, of his just portion of an undivided right or
   property. --A. Hamilton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

apportionment
    n 1: the act of distributing by allotting or apportioning;
         distribution according to a plan; "the apportionment of
         seats in the House of Representatives is based on the
         relative population of each state" [syn: allotment,
         apportionment, apportioning, allocation, parceling,
         parcelling, assignation]

Bouvier's Law Dictionary, Revised 6th Ed (1856):

APPORTIONMENT, contracts. Lord Coke defines it to be a division or partition
of a rent, common, or the like, or the making it into parts. Co. Litt. 147.
This definition seems incomplete. Apportionment frequently denotes, not,
division, but distribution ; and in its ordinary technical sense, the
distribution of one subject in proportion to another previously distributed.
1 Swanst. C. 87, n.
     2. Apportionment will here be considered only in relation to contracts,
by talking a view, 1, of such as are purely personal and, 2, of such as
relate to the realty.
     3.-1. When a Purely personal contract is entire and not divisible in
its nature, it is manifest it cannot be apportioned; as when the subject of
the contract is but one thing, and there is but one creditor and one debtor,
neither can apportion the obligation without the consent of the other. In
such case the creditor cannot force his debtor to pay him a part of his debt
only, and leave the other part unpaid, nor can the debtor compel his
creditor to receive a part only of what is due to him on account of his
claim. Nor can the assignee of a part sustain an action for such part. 5 N.
S. 192.
     4. When there is a special contract between the parties, in general no
compensation can be received unless the whole contract has been actually
fulfilled. 4 Greenl. 454; 2 Pick. R. 267; 10 Pick. R. 209; 4 Pick. R. 103; 4
M'Cord, R. 26, 246; 6 Verm. R. 35. The subject of the contract being a
complex event, constituted by the performance of various acts, the imperfect
completion of the event, by the performance of only some of those acts,
cannot, by virtue of that contract, of which it is not the subject, afford a
title to the whole, or any part of the stipulated benefit. See 1 Swanst. C.
338, n. and the cases there cited; Story, Bailm. Sec. 441; Chit. Contr. 168;
3 Watts, 331; 2 Mass. 147, 436; 3 Hen. & Munf. 407; 2 John. Cas. 17; 13
John. R. 365; 11 Wend. 257; 7 Cowen, 184; 8 Cowen, 84; 2 Pick. 332. See
generally on the subject of the apportionment, of personal obligations, 16
Vin. Ab. 138; 22 Vin. Ab. 13; Stark. Ev. part 4, p. 1622; Com. Dig.
Chancery, 2 E and 4 N 5; 3 Chit. Com. Law 129; Newl. Contr. 159; Long on
Sales, 108. And for the doctrine of the civil law, see Dumoulin, de dividuo
et individuo, part 2, n. 6, 7; Toull. Dr. Civ. Fr. liv. 3, tit 3, c. 4, n.
750, et seq.
     5.-2. With regard to rents, the law is different. Rents may in
general be apportioned, and this may take place in several ways; first, by
the act of the landlord or reversioner alone, and secondly, by virtue of the
statute of 11 Geo. II., c. 19, s. 15, or by statutes in the several states
in which its principles have been embodied.
     6.-1. When there is a subsisting obligation on the part of the tenant
to pay a certain rent, the reversioner may sell his estate in different
parts, to as many persons as he may deem proper, and the lessee or tenant
will be bound to pay to each a proportion of the rent. 3 Watts, 404; 3 Kent
Com. 470, 3d. ed.; Co. Litt. 158 a; Gilb. on Rents, 173; 7 Car. 23; 13 Co.
57 Cro. Eliz. 637, 651; Archb. L. &. T. 172 5 B. & A. 876; 6 Halst. 262. It
is usual for the owners of the reversion to agree among themselves as to the
amount which each is to receive; but when there is no agreement, the rent
will be apportioned by the jury. 3 Kent, Com. 470; 1 Bouv. Inst. n. 697.
     7.-2. Rent may be apportioned as to time by virtue of the stat. 11
Geo. H., C. 19, s. 15, by which it is provided that the rent due by a tenant
for life, who dies during the currency of a quarter, of a year, or other
division of time at which the rent was made payable, shall be apportioned to
the day of his death. In Delaware, Missouri, New Jersey, and New York, it is
provided by statutes, that if the tenant for life, lessor, die on the rent
day, his executors may recover the whole rent; if before, a proportional
part. In Delaware, Kentucky, Missouri, and New York, when one is entitled to
rents, depending on the life of another, he may recover them notwithstanding
the death of the latter. In Delaware, Kentucky, Missouri, and Virginia, it
is specially provided, that the husband, after the death of his wife, may
recover the rents of her lands. 1 Hill. Ab. c. 16, Sec. 50. In Kentucky, the
rent is to be apportioned when the lease is determined upon any contingency.
     8. When the tenant is deprived of the land, as by eviction, by title
paramount, or by quitting the premises with the landlord's consent, in the
absence of any agreement to the contrary, his obligation to pay rent ceases,
as regards the current quarter or half year, or other day of payment, as the
case may be. But rent which is due may be recovered. Gilb. on Rents, 145; 3
Kent, Comm. 376; 4 Wend. 423; 8 Cowen, 727 1 Har. & Gill, 308; 11 Mass. 493.
See 4 Cruise's Dig. 206; 3 Call's R. 268; 4 M'Cord 447; 1 Bailey's R. 469; 2
Bouv. Inst. n. 1675, et seq.