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GRADUATION, in mathematics, the act of graduating or di-viding any thing into degrees or equal parts.

GRAFF, or GRAFT, [greffe, Fr.j a small branch insertedinto the stock of another tree, and nourished by its sap, but bear-ing its own fruit; a young cvon.

GRAFTING , or ENGRAFTING, in gardening, the takingof a shoot from one tree, and inserting it into another, so that theymay closely unite, and form one trunk. Grafting has been prac-tised from the most remote antiquity ; but its origin and inventionare differently related by Naturalists. The great aim of this use-ful art is, to propagate any curious sorts of fruit-trees, to insurethe growth of similar kinds, which cannot be effected by any othermethod : for, as all the good species of fruit have been acciden-tally obtained from seeds, many of these, when sown, will degene-rate, and produce bad fruit. But, when shoots are taken fromsuch trees as bear good fruit, they will never change their kind,whatever be their stock, or the tree on which they are grafted.Mr. Bradley observes, that the stock grafted on, is only to beconsidered as a fund of vegetable matter, which is to be filferedthrough the cyon, digested, and brought to maturity, as the timeof growth in the vessels of the cyon directs. A cyon, therefore,of one kind, grafted on a tree of another, may be rather said totake root in the tree it is grafted, than to unite with it: for it isobvious that the cyon preserves its natural purity, though it be fedand nourished by a mere crab. The grafts or eyons with whichthis operation is effected, should be of the last summer’s growth,from the outside branches ; firm and well-ripened ; and selectedfrom healthy' trees. The graft is always the middle part of eachshoot, cut to five or six inches in length, or so as to nave four orfive good eyes, or buds, but should be preserved at full length,till grafting time. The proper tools and other materials used ingrading, are: 1. A strong knife for cutting off the heads of thestocks, previous to the insertion of the graft; also a small hand-saw, for occasional use, in cutting off the heads of large stocks ;2. A common grafting knife, or strong sharp penknife, for cuttingand shaping the grafts ready for insertion ; also to slope and formthe stocks for the reception of the eyons; 3. A flat grafting-chi-sel, and small mallet for defting large stocks, in cleft-grafting; 4.A quantity of new bass-strings for bandages, for securing (lie grafts,and promoting their speedy union with the stock ; and 5. A quan-tity of clay, for applying closely round the grafts after their inser-tion and binding, to defend the parts from the influence of the sun,winds, and wet weather, or from being affected by cold. For thispurpose a kind of stiff loamy mortar may be prepared of strongfat loam ; or any other tough clay may be substituted; to whichmay be added a fourth part of fresh horse-dung, free from litter,and a small portion of cut hay, with a little water, well mixed :the whole should be properly beaten with a stick, ami thus incor-porated. This operation should be repeated, according to thenature of the clay, and performed several times during the firstday ; the composition being still moistened with water tor six orseven flays successively, at the end of which time it will be lit foruse. There are various .other modes of engrafting, w hich aretermed whip-grafting, or tongue-grafting, cleft-grafting, crown-grafting, root-grafting, cheek-grafting, side-grafting ; and, lastly,grafting bv approach, or inarching. The following are most com-monly and successfully practised:

1 . Whip-grafting, or Tonguf.-grafting, is generally per-formed in nurseries, upon small stocks, from a quarter of an inchto half, or a whole inch in diameter. The stock, and exons orgrafts, should in every instance be of the same size or ap-proach as nearly to the same size as possible. They areboth to be sloped off a full inch, or more, and then tied closelytogether. This method may be much improved, by performingwhat gardeners call tongm ing, or tipping; that is, by making aitincision in the hare pari of the stock, downwards, and’a similar slitin the cyon, upwards; after which they are to be carefully joinedtogether, so that the rinds of both may meet in every part, whena ligament or bandage of bass is to be tied round the cvon, to pre-vent it from being displaced ; and the whole is to be coveredover, or coated, w ith the clay above described.

2. Gi.eft-grafting, or Slit-grafting, as gardeners dif-ferently term it, is p rformed upon stocks from one"to two inchesin diameter. The bead of the stock being carefully cut off, in* asloping direction, a perpendicular deft, or slit, is to be made

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about two inches deep, with a knife or chisel, towards the back ofthe slope, into wliicl, a wedge is to be driven, in order to keep itopen for the admission of the cyon : the latter must now be cut ini perpendicular direction, and in the form of a wedge, so as to litthe incision in the stock. As soon as it is prepared, it should beplaced in the cleft, in such a manner that the inner bark of boththe stock and cyon may meet exactly together. It is then to betied with a ligature of bass, and clayed over, as is practised inwhip-grafting, three or four eyes being left on the cyon uncovered.The proper season for tins mode of grafting is the same as tor thepreceding, viz. the months of February and March : towards (lielatter end of May, or the beginning of June, the junction of thegraft and stock will be completed, and the latter begin to shoot;when the clav may be taken off, and, in the course of a fortnightor three weeks, the bandages may be removed.

3. Approach-grafting, or Inarching, is performed in Aprilor May, when the stock we would graft, and the tree we would pro-pagate, grow so near together, as to be conveniently in contact, andthe nearer the graft and the stock are of a size the better. This modeof propagation is esteemed the surest of all; and in truth, some thingscannot be so well propagated any other way. It is a method that is,or can be, seldom used foi common fruit-trees; but if anv one wishesto try the experiment, the stock or stocks must be planted at least ayear before, first making the soil good, as it may need it, beingso near another tree, for it of course must be close. Plants inpots or tubs, being easily brought together, are frequently propa-gated this way; so that inarching is used much in greenhousesand hot-houses for various things, as oranges, lemons, pomegra-nates, jasmines, and vines sometimes; oranges and lemons thustreated in May will be united by August. The method of inarchingis tliis, bend the best-situated young branch of the tree or shrub tobe propagated, to the stock to be grafted, and having determinedon the part at which most conveniently to (ix the shoot, cut thebark of that part of d ■ shoot off, with nearly Ijalf the wood (notto touch the p th) to the length of about three inches for a strongbranch, or less for a weaker. Then cut exactly so much of thebark and biancli of the stock off, as will receive the cut part ofthe branch or shoot, so as to bring bark and bark in contact inevery' part; and if tbe contrivance of lipping is used, it will securethem belter together. Bind and clay, and if in open ground,fix a stake to tie the work so that the wind may have no powerover it; a tie also to a neat stick may be proper for those inarch-ed in pots, Ac. By this kind of grafting may he raised almostany kind of tree or shrub, which is often done by way of curiosity,to ingraft a fruit-hearing branch of a fruit-tree upon any commonstock of the same genus, whereby a new tree bearing fruit is rais-ed in a few months. This is sometimes practised upon orangeand lemon-trees, &c. bv grafting bearing branches of a fruit-treeupon any common stocks raised from the kernels of any of thesame kind of fruit, or into branches of each other, so as to haveoranges, lemons, and citrons, all on the same tree.

GRAFTON, Richard, an English historian, born at Lon-don , in the reign of Henry VI11. lie published, t. An Abridge-ment of the Chronicles of England; and. 2. A Chronicle amilarge History of the Alfavre, England and Kings of tlie same,deduced from the Creation of the VVorld. He died in the reignof Queen Elizabeth.

Grafton, an extensive couiitv of New Hampshire , boundedon the E. by Maine District, S. by Stiaifnrd, Hillsborough , and.Cheshire counties; W. by Vermont, and N. by Canada .

Grafton, a township of the above county, 13 miles S. E. ofDar mouth, and 19 S. \V. of Plymouth.

Grafton, or Grafton Island, one of (he Bashee islands inthe East Indian Sea. I .on. 120. 5 j. F,. I/at. 21. i. N.

GRAHAM, Geo'rgk, clock and watch-maker, the most inge-nious and accurate artist in his time, was horn m Hi75. A'ter hisapprenticeship, Mr. Tompson received him into his family, purelyou account of his merit; and treated him with a kind ol parentalaffection as long as he lived. Re-ides his movers; ]|\ aikm"-ledged skill in his profession, lieu as a complete mechanic andastronomer: the great mural arch in the obseivatorv t Gr'cii-with was made by l)r. Halley, under his immediate inspection,and divided by his own hand ; and from this incomparable origi-nal, the best foreign instruments of (lie kind are copies made byEnglish artists. The sector, by which Dr. Bradley tirst discover-