Three-field system

“ This is wrong, as if it prove a “foul,” the umpire will announce it in time for the player to return, [58] and should the “fly ball” be missed or “muffed,” the player is well on his way to the base. Upon reaching his base, the striker is succeeded by the next batsman on the list, and when three of these are “put out,” the fielders take their turn at the bat. A run is scored by a player touching in succession the four bases, avoiding being himself touched by the ball while running. A home run is made by his hitting the ball to such a distance that he makes the four bases before it is returned. ”

“ The eleven circuit and base-line equations of condition having been duly constructed, the next step is to find values of the angular errors which will satisfy these equations, and be the most probable of any system of values that will do so, and at the same time will not disturb the existing harmony of the angles in each of the seventy- two triangles. Harmony is maintained by introducing the equation of condition x+y+z=o for every triangle. ”

“ As special cases, the system may reduce to a couple, or it may be in equilibrium.
In general, however, a three-dimensional system of forces cannot be replaced by a single resultant force. But it may be reduced to simpler elements in a variety of ways. For example, it may be reduced to two forces in perpendicular skew lines. For consider any plane, and let each force, at its intersection with the plane, be resolved into two components, one (P) normal to the plane, the other (Q) in the plane. ”

“ If a point-mass of electric unit pole moves in an electro-magnetic field, then the force acting upon it is equivalent to the electric force existing at the position of the unit pole, which we obtain by the transformation of the field to a co-ordinate system which is at rest relative to the electric unit pole [New mode of expression] . ”

“ If the charge on the small conductor were a negative unit, instead of a positive, the direction of the force would be reversed; the magnitude of the force would remain the same. To make the field-intensity quite definite, a positive unit is chosen for its specification. For a charge on the trial-conductor consisting of any number of units, the force is that number of times the field-intensity. The field-intensity is often specified by its components, X, Y, Z in three chosen directions at right angles to one another. ”

“ When each one is in his appointed place, the captain of the fielding nine calls out “ready,” to which the umpire promptly responds “play!”—and upon the first ball which leaves the pitcher’s hand the game commences.
The batsman or striker stands at the home base on a line drawn through its center, parallel to one extending from first to third base and extending three feet on each side of it. The batsman requires considerable judgment to assist him in effectually striking at balls. He must have a quick eye and ready hand to meet the deceptive pitching of an experienced player. ”

“ Many of our clubs have an iron quoit for the home base, that is in direct violation of the rule which states that the home base must be marked by “a flat circular iron plate.” Those we allude to rise in the center, and the consequence is, when a ball touches the base, it flies off at a tangent, instead of rebounding as if it had touched the ground, as it would do were it flat, as the rule prescribes. ”

“ Of the three fielding positions, right-field is by far the most important. He must be sure of ground balls as well as flies and also, in common with all the fielders, be a good judge of the batsmen and try to be where the batted ball is going. The centre-fielder must be especially quick on his feet, as he is expected to back up both shortstop and second base as well as to run in for line hits that just go over the in-fielders’ heads. The ability to start quickly when running for a ball can be greatly developed by practice and will greatly improve the player’s game. ”

“ Players must make their bases in the order of striking; and when a fair ball is struck, and not caught flying, the first base must be vacated, as also the second and third bases, if they are occupied at the same time. Players may be put out on any base, under these circumstances, in the same manner as the striker when running to the first base. ”

“ Hence any three-dimensional system can be reduced to a single force R acting in a certain line, together with a couple G in a plane perpendicular to the line. This theorem was first given by L. Poinsot, and the line of action of R was called by him the central axis of the system. The combination of a force and a couple in a perpendicular plane is termed by Sir R. S. Ball a wrench. Its type, as distinguished from its absolute magnitude, may be specified by a screw whose axis is the line of action of R, and whose pitch is the ratio G/R.
The case of two forces may be specially noticed. ”

“ They depend upon the masses, although not upon the forces of the system. In the simple case of material points, where each point is limited to a given space, the extension-in-configuration is the product of the volumes within which the several points are confined (these may be the same or different) , multiplied by the square root of the cube of the product of the masses of the several points. The extension-in-velocity for such systems is most easily defined as the extension-in-configuration of systems which have moved from the same configuration for the unit of time with the given velocities. ”

“ Should the pitcher repeatedly fail to deliver to the striker fair balls for the apparent purpose of delaying the game, or for any cause, the umpire, after warning him, shall call one ball, and if the pitcher persists in such action, two and three balls; when three balls shall have been called, the striker shall take the first base; and should any base be occupied at that time, each player occupying it or them shall take one base without being put out. ”

“ Finding that the capacities of similar conductors are proportional to their linear dimensions, he adopted a sphere of one inch diameter as the unit of capacity, and when he speaks of a capacity of so many "inches of electricity," he means a capacity so many times that of his one-inch sphere, or equal to that of a sphere whose diameter is so many inches. The modern unit of capacity in the electro-static system is that of a sphere of one centimetre radius, and the capacity of any sphere is numerically equal to its radius expressed in centimetres. ”

“ At the triple point also, three curves cut, viz. the curves representing the conditions of equilibrium of the three univariant systems formed by the combination of the three phases in pairs. The most common triple point of a one-component system is, of course, the triple point, solid, liquid, vapour (S-L-V) , but other triple points [99] are also possible when, as in the case of {56}sulphur or benzophenone, polymorphic forms occur. Whether or not all the triple points can be experimentally realized will, of course, depend on circumstances. ”

“ The true bearing of the lines AC or BC being known, the true bearing of the base stations A and B can be deduced.
Extension of Base. — A base of any description is seldom long enough to plot from directly, and in order to diminish errors of plotting it is necessary to begin on the longest side possible so as to work inwards. A short base measured on flat ground will give a better result than a longer one measured over inequalities, provided that the triangulation is carefully extended by means of judiciously selected triangles, great care being taken to plumb the centre of each station. ”

“ In this method each sector (target) is covered by more than one fire unit. For example, in a company of four platoons the entire company sector would be divided in two parts, the right part being covered by the first and second platoons and the left part by the third and fourth platoons. When the first platoon ceases fire to advance, the second platoon would replace the lost rifles by firing faster. With three platoons the company sector would be divided into two parts, one being assigned to each flank platoon and the whole company sector to the center platoon. ”

“ The four squares, K 4 and Q 4 on each side respectively, are the centre squares, and control of these squares is called control of the centre. The control of the centre is of great importance. No violent attack can succeed without controlling at least two of these squares, and possibly three. Many a manœuvre in the opening has for its sole object the control of the centre, which invariably ensures the initiative. It is well always to bear this in mind, since it will often be the reason of a series of moves which could not otherwise be properly understood. ”

“ Could the Army reduce the size of the square division to increase mobility? Recommendations to achieve this included a reduction in the number of platoons in the infantry company from four to three and a cut in the number of companies in the battalion by a like amount, a realignment of the ratio between rifles and machine guns, elimination of the 155-mm. howitzers, and the removal of unnecessary support troops. The division could obtain additional troops from pools of combat support and service units located at the army corps or army level. ”

“ Our force-fields are globular, because the generator's inside. If you want a force-field to have a definite shape, you have to generate it differently. Their cities and their machines weren't substance, though they were solid enough. ”

“ The electrostatic system of measurement is founded on the mechanical action between electrified bodies, and is independent of, and incompatible with, the electromagnetic system; so that the units of the different kinds of quantity have different values according to the system we adopt, and to pass from the one system to the other, a reduction of all the quantities is required.
According to the electrostatic system, the repulsion between two small bodies charged with quantities of electricity is
where is the distance between them. ”

“ With the help of the Phase Rule we can group together into classes the large number of different isolated cases of systems in equilibrium; with its aid we are able to state, in a general manner at least, the conditions under which a system can be in equilibrium, and by its means we can gain some insight into the relations existing between different kinds of systems. ”

“ I have pointed out that, under certain conditions, the sudden disturbances of the machine do not act through the differential system on the governor, or vice versa. When these conditions are fulfilled, the equations of motion are not only simple, but the motion itself is not liable to disturbances depending on the mutual action of the machine and the governor.
Distinction between Moderators and Governors.
In regulators of the first kind, let be the driving-power and the resistance, both estimated as if applied to a given axis of the machine. ”

“ There is one solid basis for all base ball organizations, and that is the reserve rule. The proposed organization ignores this fundamental and necessary principle, and consequently can only be compared to that foolish man who built a house on sand. ”

“ The third law is the expression of a property of all attractions which may be conceived of as depending on the inverse square of the distance from a fixed system of points; and the fourth shews that the electro-magnetic forces may always be reduced to the attractions and repulsions of imaginary matter properly distributed. ”

“ We have so far been drilling in close order formation, so called because we always maintain our front and rear ranks together as such. This order has two purposes, one for parade and review, the other for quickest marching to any given place. But for fighting, which after all is our real purpose, the close order must be discarded in favor of extended order, which you will understand better if I call it skirmish line formation. Here front and rear rank form in one long line, in order not to do damage to each other in firing.
Our drill field at the camp distinctly has its drawbacks. ”

“ The treatment of the problems that are now coming into play is most simple, when instead of the co-ordinate system used above, we introduce another one which is rigidly connected with ponderable matter and therefore shares its displacement.
While the coordinates of a point with respect to the fixed system were called x, y, z, let those, which refer to the moving system and which I call the relative coordinates, denoted by (x) , (y) , (z) for the time being. ”

“ The difficulty in framing a proper rule for the purpose is, to properly define the difference between a palpable fielding error, which enables a base to be run on the error, and an error plainly induced by the very effort made to steal a base. ”

“ Confining our attention for a short time to the homogeneous division of a plane, remark that the division into parallelograms by two sets of crossing parallels is singular in this respect—each cell is contiguous with three neighbours at every corner. Any shifting, large or small, of the parallelograms by relative sliding in one direction or another violates this condition, brings us to a configuration like that of the faces of regularly hewn stones in ordinary bonded masonry, and gives a partitioning which fulfils the condition that at each corner each cell has only two neighbours. ”

“ These units of different orders have different properties of space; the platoon occupies more space in the field than the individual soldier; the company occupies more space than the platoon; the battalion more space than the company; and the same is true of the other units in the hierarchy. If we have two armies exactly alike in a hierarchy of units and spaces, then any two corresponding units and spaces in the hierarchy would be similar. In speaking of the bodies of the universe it is necessary sometimes to speak of the corresponding unit in the different bodies, and we call them substances. ”