From The Collaborative International Dictionary of English v.0.48:

Shall \Shall\, v. i. & auxiliary. [imp. Should.] [OE. shal,
   schal, imp. sholde, scholde, AS. scal, sceal, I am obliged,
   imp. scolde, sceolde, inf. sculan; akin to OS. skulan, pres.
   skal, imp. skolda, D. zullen, pres. zal, imp. zoude, zou,
   OHG. solan, scolan, pres. scal, sol. imp. scolta, solta, G.
   sollen, pres. soll, imp. sollte, Icel. skulu, pres. skal,
   imp. skyldi, SW. skola, pres. skall, imp. skulle, Dan.
   skulle, pres. skal, imp. skulde, Goth. skulan, pres. skal,
   imp. skulda, and to AS. scyld guilt, G. schuld guilt, fault,
   debt, and perhaps to L. scelus crime.]

   Note: [Shall is defective, having no infinitive, imperative,
         or participle.]
   1. To owe; to be under obligation for. [Obs.] "By the faith I
      shall to God" --Court of Love.
      [1913 Webster]

   2. To be obliged; must. [Obs.] "Me athinketh [I am sorry]
      that I shall rehearse it her." --Chaucer.
      [1913 Webster]

   3. As an auxiliary, shall indicates a duty or necessity whose
      obligation is derived from the person speaking; as, you
      shall go; he shall go; that is, I order or promise your
      going. It thus ordinarily expresses, in the second and
      third persons, a command, a threat, or a promise. If the
      auxillary be emphasized, the command is made more
      imperative, the promise or that more positive and sure. It
      is also employed in the language of prophecy; as, "the day
      shall come when . . ., " since a promise or threat and an
      authoritative prophecy nearly coincide in significance. In
      shall with the first person, the necessity of the action
      is sometimes implied as residing elsewhere than in the
      speaker; as, I shall suffer; we shall see; and there is
      always a less distinct and positive assertion of his
      volition than is indicated by will. "I shall go" implies
      nearly a simple futurity; more exactly, a foretelling or
      an expectation of my going, in which, naturally enough, a
      certain degree of plan or intention may be included;
      emphasize the shall, and the event is described as certain
      to occur, and the expression approximates in meaning to
      our emphatic "I will go." In a question, the relation of
      speaker and source of obligation is of course transferred
      to the person addressed; as, "Shall you go?" (answer, "I
      shall go"); "Shall he go?" i. e., "Do you require or
      promise his going?" (answer, "He shall go".) The same
      relation is transferred to either second or third person
      in such phrases as "You say, or think, you shall go;" "He
      says, or thinks, he shall go." After a conditional
      conjunction (as if, whether) shall is used in all persons
      to express futurity simply; as, if I, you, or he shall say
      they are right. Should is everywhere used in the same
      connection and the same senses as shall, as its imperfect.
      It also expresses duty or moral obligation; as, he should
      do it whether he will or not. In the early English, and
      hence in our English Bible, shall is the auxiliary mainly
      used, in all the persons, to express simple futurity. (Cf.
      Will, v. t.) Shall may be used elliptically; thus, with
      an adverb or other word expressive of motion go may be
      omitted. "He to England shall along with you." --Shak.
      [1913 Webster]

   Note: Shall and will are often confounded by inaccurate
         speakers and writers. Say: I shall be glad to see you.
         Shall I do this? Shall I help you? (not Will I do
         this?) See Will.
         [1913 Webster]

From The Collaborative International Dictionary of English v.0.48:

Should \Should\ (sh[oo^]d), imp. of Shall. [OE. sholde,
   shulde, scholde, schulde, AS. scolde, sceolde. See Shall.]
   Used as an auxiliary verb, to express a conditional or
   contingent act or state, or as a supposition of an actual
   fact; also, to express moral obligation (see Shall); e. g.:
   they should have come last week; if I should go; I should
   think you could go. "You have done that you should be sorry
   for." --Shak.
   [1913 Webster]

   Syn: See Ought.
        [1913 Webster]
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