ROT 



ROT 



one competent to the production of a motion of the particle 

 round an axis with a certain angular velocity, and the other 

 competent to the production of a rotatory motion about 

 another axis with a certain velocity, the combined effed of 

 all thefe impulfions, will be a motion of the whole fyflem 

 about a third axis, given in pofition, with an angular ve- 

 locity which is alfo given ; and this motion will obtain, with- 

 out any feparation or difunion of parts, except fuch as may 

 be occafioned by the adion of the centrifugal forces refulting 

 from the rotation. 



Hence, alfo, if a body be turning round any axis, and 

 every particle, in one initant, get precifely fuch an impulfe 

 as is competent to produce a given angular velocity round 

 another axis, the body will turn round a third axis given in 

 pofition, with a given angular velocity. 



Laftly, when a rigid body acquires a rotation about an 

 axis, by an impulfe on one part of it, and either at the fame 

 time, or afterwards, receive an impulfe on any part which 

 alone would have produced a certain rotation about another 

 axis, the joint effed of thefe impulfes will be a rotation 

 about a third axis, in conformity with this propoiition. 

 For when a rigid body acquires a motion about an axis, not 

 by the fimultaneous impulfe of the precifely competent 

 force on each particle, but by an impulfe on one part, there 

 has been propagated to every particle, (by means of the 

 cohefive forces, ) an impulfe precifely competent to the pro- 

 duction of that motion which the particle adually acquires ; 

 and when a rigid body already turning round an axis A a, 

 receives an impulfe which makes it actually turn about 

 another axis C c, there has been propagated in each particle 

 a force precifely adequate to the production, not of the 

 motion but of the changes of motion which takes place in 

 that particle ; that is, a force which, when compounded with 

 the inherent force of its primitive motion, produces the new 

 motion, that is, by the propofition a force which alone would 

 have caufed it to turn about a third axis B b, with a rotation 

 making the other component of the actual rotation about 

 Cc. 



This elegant theorem, the enunciation of which is due 

 to P. Frifi, is very important, and gives a great extenfion 

 to the dodrine of the compofition of motion. It is of 

 great ufe in many curious problems, and particularly that of 

 the preceffion of the equinoxes. Thofe who wifh for 

 farther information on the fubjed of rotatory motion, may 

 confult Gregory's " Mechanics," from which we have 

 taken the three laft propofitions ; Simpfon's "Trails;" 

 Frifi's " Cofmographia ;" " Philofophical Tranfadions," 

 1780 ; Landen's " Memoirs ;" Atwood " On the Rotatory 

 Motion of Bodies ;" Lagrange's " Mechanique Analy- 

 tique ;" and a memoir "Sur le Mouvement de Rotation," 

 by Francais, Paris, 18 13 ; in which latter work the fubjed 

 is treated with all the generality it feems to admit of, and 

 which method we fliould have adopted in this article, but 

 for the reafons ftated in the commencement of it, that is to 

 fay, the length to which we muft have extended it, in order 

 to have rendered it intelligible to the Englifh reader. 



Rotation is alfo fynonimous with Rolling, which fee. 



Rotation, in Geometry, the circumvolution of a furface 

 round a line, called the axis of rotation. 



By fuch rotation of planes, the figures of certain regular 

 folids are formed or generated. 



The method of cubing folids, generated by fuch rotation, 

 is laid down by M. de Moivre, in his fpecimen of the ufe of 

 the dodrine of fluxions. For the fluxions of fuch folids 

 take the produd of the fluxion of the abfeiffa, multiplied 

 by the circular bale, and fuppofe the ratio of a fquare to 



9 



the circle inferibed to be as — ; the equation exprefling the 

 nature or property of any circle, whofe diameter is d, is 



y y = d x — xx. Therefore 4 — is the fluxion 



of a portion of the fphere, and confequently the point it- 

 felf 4 , and the circumfcribed cylinder is 



4 — — ; therefore the portion of the fphere is to the 



circumfcribed cylinder as 5 d — 5 x to d — x. Phil. Tranf. 

 N° 216. 



For other inftances of this kind, and a view of t!-.e appli- 

 cation of the dodrine of fluxions, to find the contents of 

 folid bodies, fee Solidity. See alio Cestrobaryc 

 Method. 



Rotation, Revolution, in AJlronomy. See Revolu- 

 tion. 



Rotation, Diurnal. See Diurnal, and Earth. 



Rotation, in Anatomy, the adion of the mufculi rota- 

 tores ; or the motion which they give to the parts they are 

 fixed to. 



There are two mufcles, the great and the little obliquus, 

 ufed to perform the rotation of the eye. The obturator in- 

 ternus and externus effed the rotation of the thighs. 



Mr. Winflow has given an account of this, as well as of 

 pronation, and other "circulatory animal motions. See 

 Mem. de l'Acad. des Sciences, 1729. See alfo Extre- 

 mities. 



Rotation of Crops, in Agriculture, the feveral means of 

 cropping lands of the arable kind in luch a manner as to pre- 

 vent their being exhaulted as much as poflible, and at the 

 fame time to preferve them free from weeds in the mod com- 

 plete and perfed mode. The proper alternation of different 

 forts of crops in this intention, is a matter of va(t importance 

 to the intereits of agriculture, and in which immenfe im- 

 provements have been made in this and other countries with- 

 in this laft half century, but which is ftill far from any thing 

 like perfedion. See Courfe of Crops. 



In addition to what has been ftated under the head referred 

 to above, it may be obferved, in this place, that the nature 

 and ftate in which the manure is, when applied to the lands, 

 fliould likewife be attended to in fixing the rotations of the 

 crops, in order that the firft and all the fucceeding ones may 

 be fupported in the beft and molt effedual manner by the 

 changes that are always taking place afterwards in fuch 

 materials, when united and incorporated with the foils ; and 

 in this way, thofe parts of them which are not fitted to or 

 fuitable for one kind of crop, may be converted to the nou- 

 rifhment and fupport of the next, and fo on in the fame 

 manner. Thus, where the turnip is the firft crop in the ro- 

 tation, and manure of the frefli dung kind is ufed, which 

 diredly affords it the neceffary fupply of foluble matter, 

 while the heat which is generated in its decompofition affifts 

 the fprouting and growth of the feed, it fliould be fucceeded 

 by barley, or fome other fimilar fort of grain crop, with 

 fuitable grafs feeds, as the land will have been but little 

 robbed of its fertility by the preceding turnip crop, and of 

 courfe will plentifully fupply the foluble portions of the 

 gradually decompofing fubftance of the manure to that 

 crop ; while the graffes that remain on the land, which, in 

 many cafes, draw only a fmall portion of the matter of 

 which they are compofed from the earth, and in all probabi- 

 lity take up the gypfeous fubftance contained in the ma- 

 nure, which would be of little utility to other forts of crops, 



and 



