## Rotations Sentence Examples

- If the primary wave be represented by = e-ikx the component
**rotations**in the secondary wave are '1'3= P (- AN y) N r2 ' cwi= r x D y N 'y)' lw2=P (- AD + 6,N z2 - x2 ' D r N r2 where ik3T e-ikr _ P - 4 r The expression for the resultant rotation in the general case would be rather complicated, and is not needed for our purpose. - The Emilian region is one where regular
**rotations**are best observeda common shift being grain, maize, clover, beans and vetches, &c., grain, which has the disadvantage of the grain crops succeeding, each other. - It seems certain that success in any system involving a more extended growth of leguminous crops in
**rotations**must be dependent on a considerable variation in the description grown. - Although many different
**rotations**of crops are practised, they may for the most part be considered as little more than local adaptations of the system of alternating root-crops and leguminous crops with cereal crops, as exemplified in the old four-course rotation - roots, barley, clover, wheat. - The
**rotations**extending to five, six, seven or more years are, in most cases, only adaptations of the principle to variations of soil, altitude, aspect, climate, markets and other local conditions. - Soc. Trans., p. 1013) considered in detail an octahedral form, and showed how by means of certain simple
**rotations**of his system the formulae of Kekule and Claus could be obtained as projections. - One form, and he isolated a, 13 and y varieties with specific
**rotations**of 105°, 52.5° and 22°. - (b2V2 + n2) (a2 - b 2) = - z It will now be convenient to introduce the quantities a l, a 2', 7731 which express the
**rotations**of the elements of the medium round axes parallel to those of co-ordinates, in accordance with the equations Ty - 1 = dz ' 3= - dy 2 = dx - In terms of these we obtain from (7), by differentiation and subtraction, (b 2 v 2 + n 2) 7,3 = 0 (b 2 0 2 +n 2) .r i = dZ/dy (b 2 v 2 +n 2)', , 2 = - dZ/dx The first of equations (9) gives 3 = 0 (10) For al we have ?1= 47rb2, f dy e Y tkr dx dy dz - (This solution may be verified in the same manner as Poisson's theorem, in which k=o.) We will now introduce the supposition that the force Z acts only within a small space of volume T, situated at (x, y, z), and for simplicity suppose that it is at the origin of co-ordinates that the
**rotations**are to be estimated. - In most
**rotations**barley is grown after turnips, or some other " cleaning " crop, with or without the interposition of a wheat crop. The roots are fed off by sheep during autumn and early winter, after which the ground is ploughed to a depth of 3 or 4 in. - In these circumstances the number of
**rotations**made by the armature in a given time is proportional to the product of the strength of the current flowing through the armature and that flowing through the field-coils, the former being the current to be measured. - In a direct competitive test the presence of 3.25% of nickel increased nearly sixfold the number of
**rotations**which a steel shaft would endure before breaking. - He loved gardening, experimented enthusiastically in varieties and
**rotations**of crops and kept meteorological tables with diligence. - Also, everything relating to change of systems of axes, as for instance in the kinematics of a rigid system, where we have constantly to consider one set of
**rotations**with regard to axes fixed in space, and another set with regard to axes fixed in the system, is a matter of troublesome complexity by the usual methods. - II); and let J11, Jfs, Jis be the positions in space of the j,~ centres of the
**rotations**by - which the lamina can be brought from the first position to the second, from the second .li_s to the third, and soon. - 39~ the effect of three successive positive
**rotations**2A, 2B, 2C - The composition of finite
**rotations**about parallel axes is, a particular case of the preceding; the radius of the sphere is now infinite, and the triangles are plane. - If AB, AC represent infinitesimal
**rotations**about intersecting axes, the consequent displacement of any point 0 in the plane BAC will be at right angles to this plane, and will be represented by twice the sum of the areas OAB, OAC, taken with proper signs. - It is easily inferred as a limiting case, or proved directly, that two infini tesimal
**rotations**a, j3 about c u parallel axes are equivalent to a ..._ -- - - - If the, A, B
**rotations**are equal and opposite, FIG. - From the equivalence of a small rotation to a localized vector it follows that the rotation ~ will be equivalent to
**rotations**E,ii, ~ about Ox, Oy, Uz, respectively, provided = le, s1 = me, i nc (I) and we note that li+,72+l~Z~i (2) - Thus in the case of fig 36 it may be required to connect, the infinitesimal
**rotations**f, i1, l about OA, OB, OC with the variations of the angular co-ordinates 0, ~, ~. - We will briefly notice the case of two degrees, which involves an interesting generalization of the method (already explained) of compounding
**rotations**about intersecting axes. - We take these as axes of x and y; then if f, n be the component
**rotations**about them, we have - - For example, we can assert without further proof that any infinitely small displacement may be resolved into two
**rotations**, and that the axis of one of these can be chosen arbitrarily. - The phenomenon is known as the Eulerian nutalion, since it is supposed to come under the free
**rotations**first discussed by Euler. - If in (21) we imagine that x, y, I denote infinitesimal
**rotations**of a solid free to turn about a fixed point in a given field of force, it appears that the three normal modes consist each of a rotation about one of the three diameters aforesaid, and that the values of in are proportional to the ratios of the lengths of corresponding diameters of the two quadrics. - Epicyclic Trains.The term ep-icyclic train is used by Willis to denote a train of wheels carried by an arm, and having certain
**rotations**relatively to that arm, which itself rotates. - The comparative motions of the wheels and of the arm, and the aggregate paths traced by points in the wheels, are determined by the principles of the composition of
**rotations**, and of the description of rolling curves, explained in ~ 30, 31. - 1906, 39, p. 2486) showed that the difference in the
**rotations**of the natural and synthetic d-conine is not due to another substance, iso-conine, as was originally supposed, but that the artificial product is a stereo-isomer, which yields natural conine on heating for some time to 290°-300°, and then distilling.