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.
When quenched as far as possible by rotation of a nicol prism, it exhibits a residue of a more intense blue colour; and further it is found that the direction of the most nearly complete polarization becomes inclined to the direction of the primary rays.
Thus the smallest rotation of either head communicates to the corresponding slide motion, which, if the screws are accurate, is proportional to the amount through which the head is turned.
The center passed through the axis of rotation.
Such rotation can obviously be controlled within limits that need not be further considered.
Rotation of the box round CC is prevented by downward pressure of the spring Z on a projection attached to the side of the box.
He also carried out many experiments in magneto-optics, and succeeded in showing, what Faraday had failed to detect, the rotation under the influence of magnetic force of the plane of polarization in certain gases and vapours.
Already anxieties appear as to the theological verdict upon two of his fundamental views - the infinitude of the universe, and the earth's rotation round the sun.
In the case of the Gulf Stream, which is not much impeded by the land, this descending motion is relatively slight, being perhaps largely due to the greater specific gravity of the water; it ceases to be perceptible beyond about 500 fathoms. On the European-African side the descending movement is more marked, partly because the coast-line is much more irregular and the northward current is deflected against it by the earth's rotation, and partly because of the outflow of salt water from the Mediterranean; here the movement is traceable to at least 1000 fathoms. The northward movement of water across the Norwegian Sea extends down from the surface to the IcelandShetland ridge, where it is sharply cut off; the lower levels of the Norwegian Sea are filled with ice-cold Arctic water, close down to the ridge.
The cups are placed symmetrically on the end of the arms, and it is easy to see that the wind always has the hollow of one cup presented to it; the back of the cup on the opposite end of the cross also faces the wind, but the pressure on it is naturally less, and hence a continual rotation is produced; each cup in turn as it comes round providing the necessary force.
This cone is driven by gearing from the wire drum, so that it rotates at the speed of the outgoing wire, the direction of rotation being such as to cause the nut to travel towards the smaller end of the cone.
Preserved for any length of time, a means is provided whereby the rate of vibration of either of the forks can be slowed down, so as to retard the rate of rotation of one or other of the arms. This is effected by means of " correcting " segments, of which there are six sets containing three each.
The instrument consists of two cams, the form of which regulates the components of the curbed signal, one cam being for the dot element and the other for the dash element, which by their sequence give the letter signals; these cams, by means of clutches controlled by the relay, are mechanically rotated by clockwork, the speed of rotation being approximately adjusted to the rate of transmission of a single element, so that the requisite number of consecutive elements is transmitted corresponding to the duration of contact of the relay arm with the side controlling that particular element.
In the rotation of crops there is an amazing diversityshifts of two years, three years, four years, six years, and in many cases whatever order strikes the fancy of the farmer.
The metropolitan of Athens is president, and there are four other members appointed by the government in annual rotation from the senior bishops.
The diurnal rotation of the earth furnishes two fixed points or poles, the axis joining which is fixed or nearly so in its direction in space.
The rotation of the earth thus fixes the directions of north and south and defines those of east and west.
Another important consequence of rotation is the deviation produced in moving bodies relatively to the surface.
In the form known as Ferrell's Law this runs: " If a body moves in any direction on the earth's surface, there is a deflecting force which arises from the earth's rotation which tends to deflect it to the right in the northern hemisphere but to the left in the southern hemisphere."
A similar rotation and dislocation occurs in various petrels, in correlation with the indigestible sepia-bills, &c., which these birds swallow in great quantities.
Speed to 60 fathoms for 20 knots, the pull of the line and rotator is borne by coned rollers, having their outlines tapering to a common point in their rotation, thus giving a broad rolling surface.
In whatever form energy is produced and distributed to the train it ultimately appears as mechanical energy applied to turn one or more axles against the resistance to their rotation imposed by the weight on the wheels and the motion of the train.
This gigantic nebulous mass, of which the sun was only the central and somewhat more condensed portion, is supposed to have a movement of rotation on its axis.
In fact a little consideration of the theory of probabilities will show it to be infinitely probable that such an object should really have some movement of rotation, no matter by what causes the nebula may have originated.
The rotation of the planets on their axes is also explained as a consequence of the nebular theory, for at the time of the first formation of the planet it must have participated in the rotation of the whole nebula, and by the subsequent contraction of the planet the speed with which the rotation was performed must have been accelerated.
Repetition of one crop in the field exhausts the ground; but rotation of the crops is good for the soil.
By small tenants on the old common-field system, which made it impossible for the individual to adopt a new crop rotation and hindered innovation of every kind.
Under the old Norfolk or four-course rotation (roots, barley, clover, wheat) land thus seeded with clover or grass seeds was intended to be ploughed up at the end of a year.
Whilst much grass land has been laid down with the intention from the outset that it should be permanent, at the same time some considerable areas have through stress of circumstances been allowed to drift from the temporary or rotation grass area to the permanent list, and have thus still further diminished the area formerly under the dominion of the plough.
Under hay are included the produce of clover, sainfoin and rotation grasses, and also that of permanent meadow.
Wheat 26ï¿½08 bushels, barley 2 9.3 o bushels, oats 38.14 bushels, beans 19.61 bushels, rotation hay 23.55 cwt., permanent hay 20.41 cwt.
The hay made from clover, sainfoin and grasses under rotation generally gives a bigger average yield than that from permanent grass land.
The greater freedom of cropping and the less close adherence to the formal system of rotation of crops, which characterize the early years of the 10th century, rest upon a scientific basis.
In the case of plants the method of procedure was to grow some of the most important crops of rotation, each separately year after year, for many years in succession on the same land, (a) without manure, (b) with farmyard manure and (c) with a great variety of chemical manures; the same description of manure being, as a rule, applied year after year on the same plot.
Experiments on an actual course of rotation, without manure, and with different manures, have also been made.
But the average produce over forty years of continuous growth of barley was, in all cases where nitrogenous and mineral manures (containing phosphates) were used together, much higher than the average produce of the crop grown in ordinary rotation in the United Kingdom, and very much higher than the average in most other countries when so grown.
Remarkable as Hellriegel's discovery was, it merely furnished the explanation of a fact which had been empirically established by the husbandman long before, and had received most intelligent application when the old four-course (or Norfolk) rotation was devised.
Thus the cereal crops, when grown in rotation, yield more produce for sale in the season of growth than when grown continuously.
The opportunities which rotation cropping affords for the cleaning of the land from weeds is another distinct element of advantage.
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.
Whatever the specific rotation, there may in practice be deviations from the plan of retaining on the farm the whole of the root-crops, the straw of the grain crops and the leguminous fodder crops (clover, vetches, sainfoin, &c.) for the production of meat or milk, and, coincidently, for that of manure to be returned to the land.
The benefits that accrue from the practice of rotation are well illustrated in the results obtained from the investigations at Rothamsted into the simple four-course system, which may fairly be regarded as a self-supporting system.
Of phosphoric acid, the cereal crops take up as much as, or more than, any other crops of the rotation, excepting clover; and the greater portion thus taken up is lost to the farm in the saleable product - the grain.
Of potash, each of the rotation crops takes up very much more than of phosphoric acid.
But much less potash than phosphoric acid is exported in the cereal grains, much more being retained in the straw, whilst the other products of the rotation - the root and leguminous crops - which are also supposed to be retained on the farm, contain very much more potash than the cereals, and comparatively little of it is exported in meat and milk.
Of lime, very little is taken up by the cereal crops, and by the root-crops much less than of potash; more by the leguminous than by the other crops, and, by the clover especially, sometimes much more than by all the other crops of the rotation put together.
Very little of the lime of the crops, however, goes off in the saleable products of the farm in the case of the self-supporting rotation under consideration.
The still more highly nitrogenous leguminous crops, although not characteristically benefited by nitrogenous manures, nevertheless contribute much more nitrogen to the total produce of the rotation than any of the other crops comprised in it.
It is the leguminous fodder crops-especially clover, which has a much more extended period of growth, and much wider range of collection within the soil and subsoil, than any of the other crops of the rotation-that yield in their produce the largest amount of nitrogen per acre.
Cereal pests can only be treated by general cleanliness and good farming, and of course they are largely kept down by the rotation of crops.