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one form, and he isolated a, 13 and y varieties with specific rotations of 105°, 52.5° and 22°.

20Both hands rested in her lap as she studied it for two full rotations.

00The 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.

00It 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.

00Although 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.

00The 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.

00(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

00In 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.

00In 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.

00In 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.

00He loved gardening, experimented enthusiastically in varieties and rotations of crops and kept meteorological tables with diligence.

00Also, 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.

00II); 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.

0039~ the effect of three successive positive rotations 2A, 2B, 2C

00The 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.

00If 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.

00It 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 ..._ -- - -

00If the, A, B rotations are equal and opposite, FIG.

00From 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)

00Thus 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, ~, ~.

00We will briefly notice the case of two degrees, which involves an interesting generalization of the method (already explained) of compounding rotations about intersecting axes.

00We take these as axes of x and y; then if f, n be the component rotations about them, we have -

00For 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.

00The phenomenon is known as the Eulerian nutalion, since it is supposed to come under the free rotations first discussed by Euler.

00If 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.

00Epicyclic 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.

00The 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.

001906, 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.

00With two plates of equal thickness and of opposite rotations, the pattern consists of a series of circles and of four similar spirals starting from the centre, each spiral being turned through 90° from that adjacent to it.

00Poynting, is before analysation to impress unequal rotations upon the plane of polarization of the two parts of the field, either by means of an active medium, or by oblique transmission through glass plates.

00The former consists of two semicircular plates of quartz, perpendicular to the optic axis and of opposite rotations, placed so as to have a common diameter and having such a thickness that each rotates the plane of polarization of mean yellow light through the same multiple of 90°.

00This is made of two plates of quartz, cut normally to the optic axis and of opposite rotations, placed the one in front of the other: the thickness of the one plate is fixed, while that of the other can be varied, as it is formed of two equal prisms that can be moved over one another along their common face.

00Both hands rested in her lap as she studied it for two full rotations.

00chopper rotations elapsed since the requested start time.

00crop rotations results from Danish Institute of Agricultural Sciences of long-term rotational monitoring.

00spring linseed poses problems for harvesting because of its late maturity and therefore can be difficult to include in arable rotations.

00micrometers for translations and 2 milliradians for rotations (1 mrad for the tilts ).

00relator inversions and rotations are ` ` genuinely ' ' random.

00Shorter rotations, earlier winter drilling, lower seed rates and less total inversion tillage inevitably mean growing pressures from the weed.

00tillage techniques have become popular over the recent decades due to the benefits they can bring to farm rotations.

00If 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.

00The 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.

00In their cultivation he adopted Tull's practice of drilling and horse-hoeing, and he was also the founder of the Norfolk or four-course system, the first of those rotations which dispense with the necessity of a summer-fallow and provide winter-keep for live-stock (see below, Rotation of Crops).

00It 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.

00Although 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.

00The 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.

00Soc. 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.

00one form, and he isolated a, 13 and y varieties with specific rotations of 105Ã‚°, 52.5Ã‚° and 22Ã‚°.

00(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

00(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.

00In 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.

00In 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.

00In 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.

00He loved gardening, experimented enthusiastically in varieties and rotations of crops and kept meteorological tables with diligence.

00And it is obvious that the same process applies in all cases in which we deal with quantities which may be regarded as of one directed dimension only, such as distances along a line, rotations about an axis, &c. But it is essential to notice that this is by no means necessarily true of operators.

00Also, 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.

00II); 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.

00rotation will bring a point from C to C and that the second will bring it back to C; the result is therefore equivalent to a rotation about OC. We note also that if the given rotations had been effected in the inverse order, the axis of the resultant rotation would have been OC, so that finite rotations do not obey the commutative law.

0039~ the effect of three successive positive rotations 2A, 2B, 2C

00The 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.

00If 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.

00It 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 ..._ -- - -

00If the, A, B rotations are equal and opposite, FIG.

00From 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)

00Thus 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, ~, ~.

00We will briefly notice the case of two degrees, which involves an interesting generalization of the method (already explained) of compounding rotations about intersecting axes.

00We take these as axes of x and y; then if f, n be the component rotations about them, we have -

00For 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.

00The phenomenon is known as the Eulerian nutalion, since it is supposed to come under the free rotations first discussed by Euler.

00If 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.

00Epicyclic 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.

00The 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.

001906, 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 290Ã‚°-300Ã‚°, and then distilling.

00With two plates of equal thickness and of opposite rotations, the pattern consists of a series of circles and of four similar spirals starting from the centre, each spiral being turned through 90Ã‚° from that adjacent to it.

00Poynting, is before analysation to impress unequal rotations upon the plane of polarization of the two parts of the field, either by means of an active medium, or by oblique transmission through glass plates.

00The former consists of two semicircular plates of quartz, perpendicular to the optic axis and of opposite rotations, placed so as to have a common diameter and having such a thickness that each rotates the plane of polarization of mean yellow light through the same multiple of 90Ã‚°.

00This is made of two plates of quartz, cut normally to the optic axis and of opposite rotations, placed the one in front of the other: the thickness of the one plate is fixed, while that of the other can be varied, as it is formed of two equal prisms that can be moved over one another along their common face.

00Notes: The relator inversions and rotations are ` ` genuinely ' ' random.

00The added bonus of adding cereals to our rotations has been the arrival of skylarks on the farm.

00Minimum tillage techniques have become popular over the recent decades due to the benefits they can bring to farm rotations.

00LP (long-playing) standard records that play up to 30 minutes per side, are 12" in width, and spin at about 33 1/3 rotations per minute.

00Special moves using complex quarter or half-circle rotations of the joystick also made their debut in Street Fighter II.

00Even if you can only cycle through two rotations, you'll build strength with regular practice.

00Participants in rotary sports such as tennis or golf can warm up by performing torso, hip and shoulder rotations.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.