818 



ROTATION 



ROTATION OF CROPS 



will pas* continuously from position to position. 

 It will trace out cylindrical surfaces, one in space 

 and one in the body ; and at anv -m-n instant 

 these surfaces will touch along tlic line which is 

 for the moment the instantaneous axis. It is not 

 difficult to show tluit the complete motion of tlie 

 body may be represented liy the rolling of one of 

 these surfaces upon the other. In the simple case 

 of the carriage wheel the rolling surfaces are 

 evidently the circumference of the wheel and the 

 plane of the road. These theorems in uniplanar 

 motion have many interesting applications in the 

 kinematics of machinery (see Minchin's Uniplanar 

 Kiiirmatie*, Clarendon Press, 1882). 



If the motion is not uniplanar it in no longer 

 possible in general to represent it by a succession 

 of pure rotation*. There ia, however, a very 

 remarkable theorem, which can be proved with- 

 out dillirulty, but which is hard of apprehension 

 and even of acceptation. It is that after any dis- 

 placement whatever of a body in space there is, 

 in the body or rigidly connected with it, a line of 

 points which is simply shifted along its own line 

 in space. The whole displacement may then lie 

 effected by means of a sliding along this line to- 

 gether with a pure rotation about it in other 

 words, by a definite screw motion with reference 

 to this line as axis (see SCREW). Even in the 

 simpler case, when by fixing one point of a body 

 we quite exclude translation, it is not easy to 

 grasp the significance of the fact that after any 

 displacement there is always one row of points 

 which occupy exactly the same positions as liefore 

 the displacement. From this theorem it follows 

 that, however such a Ixxly may 1x3 moving, there is 

 momentarily a line which is at rest. This line is 

 the instantaneous axis of rotation. It always 

 passes through the fixed point, and will as it shifts 

 in time describe two conical surfaces, one in space 

 and the other in the body. Any given continuous 

 motion can then be effected by the rolling of one 

 determinate conical surface fixed in the body upon 

 another fixed in space. As a familiar example 

 take an ordinary spinning-top. Here to the eye 

 there is in general a rotation of the top alxiut its 

 axis of figure, while at the same time the top 

 executes a conical motion about a vertical line 

 through the point of support In reality, however, 

 at any instant of time the top is subject to one 

 rotation about an instantaneous axis, which coin- 

 cides neither with the axis of figure nor with the 

 vertical line. This instantaneous axis executes a 

 definite conical motion, both in the l>ody and in 

 space. Clerk-Maxwell (see his collected papers) 

 devised a very ingenious and simple optical metlnxl 

 for observing the position of the instantaneous axis, 

 and so studying experimentally its motions with 

 reference to the top. It should ! mentioned in 

 conclusion that infinitely small rotations are 



resolved and compounded ac ding to the sann 



laws as velocities and forces, so that we may 

 regard the ins^ntaneous angular velocity of a 

 rotating body as made up of component angular 

 velocities about any three chosen a\c~. It is thus 

 that the subject is usually treated analytically. 

 Such a treatment, however, is essentially artificial ; 

 and for a natural treatment we mart OO to geo- 

 metry or to the Calculus of Quaternions (q.v.). 



Rotation of Oops. In successful tillage- 

 farming it is a fundamental principle that tin 

 various crops shall lie grown in a well-considered 

 rotation. There are solid reasons for this. The 

 plants, like the animals, of the farm differ much in 

 their habits and in the different sorts of food upon 

 which they subsist. Although all plant* tend to 

 exhaust the soil, they do so in widely different 

 degrees ; they withdraw from the soil different 

 kiads and quantities of ingredients. Some of the 



'arm crops have long, penetrating roots, which 

 Iraw nourishment from the deeper la\ers of the 

 soil; others have short or spreading loots, which 

 minify near the surface. Certain crops occupy the 

 ground for a much longer |>eri<xl than others ; some 

 encourage the growth of weeds or interfile with 

 the proper cleaning of the land . others facilitate 

 the work of eradicating weeds ; and finally, 

 the ' crop residues ' of the various plants of the 

 farm differ greatly. A glance at the following 

 figures, giving the average weight of the principal 

 ingredients removed (per acre in Ibs.) from the soil 

 by the leading farm crops, will show the importance 

 of growing these crops upon a caref u 1 1 \ considered 

 system of rotation. 



Pbox 



NltnfW. Potuh. Lim.. phortc Silk*. 

 Add. 



Wheat (SO bluhela) 48 28-8 0-2 21 -1 96-9 



Barley (40 bushels) 48 867 92 20-7 88-6 



O*U(46buhels) SB 481 11'6 19'4 85 '8 



Swede* (21 torn.) 153 "8'8 83-6 82-6 10O 



Turaipn (17 tons) 112 148* 74-0 83-1 77 



Mngold.(22ton>) 147 8007 42'9 62-9 174 



PoUtow(6tons) 47 78-5 S'4 21-6 J-8 



Bean. (80 bushels) 99 67-1 29-2 29-1 78 



Clover W( 2 tons) 102 8S-4 90-1 24- 7-0 



Meadow by (1J tons).. 49 60-9 821 1-2-3 689 



It is thus obvious that bv alternating the root, 

 the cereal, and the gross and clover crops the pro- 

 ducing power of the soil is more easily maintained, 

 and its exhaustion longer deferred. With the 

 fuller knowledge which is now available both as to 

 the wants of the plants and the means of supplying 

 these wants, it is possible, and in certain cases also 

 practicable, for the farmer to grow with success the 

 same kind of crop on the same land year after year 

 for almoat any length of time. A more economical 

 method, however, is to alternate the crops, so that 

 the natural resources of the soil and the repairing 

 influences incident to a judicious rotation may l>e 

 utilised to full advantage. It was long ago demon- 

 strated in practice that when land lies for a few- 

 years under grass and clover it becomes enriched 

 with ash constituents and nitrogen. The grasses 

 and clovers not only increase the quantity of nitro- 

 gen in the surface soil by drawing supplies of it 

 from the subsoil and from the atmosphere, but 

 they have also the power of conserving that 

 accumulated nitrogen in a form in which it is 

 easily made available to a crop of grain. Points 

 often insufficiently considered in tillage-farming 

 are the period of growth and the season of the year 

 during which the crop occupies the ground. Judg- 

 ing from the table given almve, one would imagine 

 that turnips would require in the form of manure 

 far more nitrogen than is required for wheat. In 

 practice, however, it is well known that exactly 

 the reverse is the case. The difference in the points 

 just mentioned, that is in the period and sea 

 son of the growth of the two crops, is responsible 

 for this important peculiarity. Nitrification (q.v.), or 

 the formation of nitrates in the soil, is most active 

 during summer and autumn, and the cereal crops 

 thus occupy the ground at the time when the soil is 

 comparatively deficient in nitrates. The root-crop 

 on the other nand is in full growth in the autumn, 

 when the supply of nitrates in the soil is at the 

 maximum. Root-crops consumed on the farm are 

 therefore a good preparation for succeeding crops 

 of cereals. The precise form of rotation most suit 

 able for particular farms varies greatly, depending 

 upon various circumstances, and especially the 

 nature of the Boil, climate, markets, available 

 supplies of extra manures, amount of live-stock 

 kept, &c. That course of cropping is evidently 

 the most desirable which will economically secure. 

 with thorough cleanness of the soil, a high and in 

 (reusing state of fertility. 



Many rotations are based upon the Norfolk or 

 four-course system, which consists of ( 1 ) clover or 



