D Sentence Examples

The value of d can be evaluated by considering the combustion of amorphous carbon to carbon monoxide and carbon dioxide.

M/H = (d 2 -1 2) tan 0/2d, where 1 is half the length of the magnet, which is placed in the " broadside-on " position as regards a small suspended magnetic needle, d the distance between the centre of the magnet and the needle, and 0 the angle through which the needle is deflected by the magnet.

Thus it has annihilators of the forms a0 db - 0 +al d 1+a2d 22+...

The its natural position; d, appendage right and left halves are conextended or unrolled.

Let the distance of each pole of the rod AB from the centre of the magnetometer needle = d.

Denoting the distance AM by d 1, BM by d2, and AB by 1, we have for the force at M due to the magnetism of the rod H P =d 12 - horizontal component (dla - d 2 3).

If the operation is again reversed, the upward course will be nearly, but not exactly, of the form shown by the line d c a, fig.

The closed figure a c d e a is variously called a hysteresis curve or diagram or loop. The area f HdB enclosed by it represents the work done in carrying a cubic centimetre of the iron through the corresponding magnetic cycle; expressed in ergs this work is I HdB.

The current passes through the rocking key K, which, when thrown over to the right, places a in contact with c and b with d, and when thrown over to the left, places a in contact with e and b with f.

In this way points can be found lying anywhere between c and d of fig.

Between the magnetizing coils is a small induction coil D, which is connected with a ballistic galvanometer.

If the field is uniform, H=O/wd, where 0 is the rotation, d the thickness of the substance arranged as a plate at right angles to the direction of the field, and w Verdet's constant for the substance.

Let each of the effects A, B, C, D and E be called positive when it is such as is exhibited by moderately magnetized iron, and negative when its sense is opposite.

A, D, E Several gaps remain to be filled, but the results so far recorded can leave no doubt that the five effects, varied as they may at first sight appear, are intimately connected with one another.

Until the mysteries of molecular constitution have been more fully explored, perhaps D may be most properly regarded as the fundamental phenomenon from which the others follow.

The tranverse electromotive force is equal to KCH/D, where C is the current, H the strength of the field, D the thickness of the metal, and K a constant which has been termed the rotatory power, or rotational coefficient.

D, Transverse section of a retinula of the lateral eye of Limulus, showing ten retinula cells (ret), each bearing a rhabdomere (rhab).

A, Youngest stage with no mesosomatic somites; B and C, stages with two mesosomatic somites between the prosomatic and telsonic carapaces; D, adult condition, still with only two free mesosomatic somites.

Thelyphonusassamensis d .Ventral surface of theanteriorregionof the opisthosoma, the first somite being pushed upwards and forwards so as to expose the subjacent structures.

The segmentation of the prosoma and the form of the appendages bear a homoplastic similarity to the head, pro-, meso-, and meta-thorax of a Hexapod with mandibles, maxillary palps and three pairs of walking legs; while the opistho io i e d c b o a S' S" 2 I VT V S IV III II I Opisthosoma Prosoma FIG.

Coxae of 3rd, 4th, 5th and 6th appendages movable 3 Prosoma 10 II d an FIG.

According to Schmidt's short account, Sitzungs- .berichte d.

See Peter Scriver, Beschryvinge der Stad Harlem (Haarlem, 1628); Scheltema, Levensschets van Laurens d.

A fund bearing this name was formed in the 18th century for the purpose The sous of converting to the Catholic faith the native Indians of fu d of Upper and Lower California, both of which then belonged to Mexico, and of maintaining a Catholic priesthood there.

The earliest temple in Paestum, the socalled Basilica, must in point of style be associated with the temples D and F at Selinus, and is therefore to be dated about 57 0 -554 B.C.'

The grammatical forms are expressed, as in Turkish, by means of affixes modulated according to the high or low vowel power of the root or chief syllables of the word to which they are appended-the former being represented by e, o, S, ii, i l l, the latter by a, d, o, 6, u, it; the sounds e, i, i are regarded as neutral.

Among authors of other historical or humorous romances and tales which have appeared from time to time are Francis Marton alias Lewis Abonyi, Joseph Gaal, Paul Gyulai, William GyOri, Lazarus Horvath, the short-lived Joseph Irinyi, translator of Uncle Tom's Cabin, Francis Ney, Albert ' D affy, Alexander Vachott and his brother Emeric (Vahot), Charles Szathmary, Desider Margittay, Victor Vajda, Joseph Bodon, Atala Kisfaludy and John Kratky.

They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.

These may be compared and contrasted with such quaternion formulae as S(VabVcd) =SadSbc-SacSbd dSabc = aSbcd - bScda+cSadb where a, b, c, d denote arbitrary vectors.

For instance, there are the symbols A, D, E used in the calculus of finite differences; Aronhold's symbolical method in the calculus of invariants; and the like.

Against Bulgaria the Yugoslav delegation claimed considerable frontier rectifications - (a) the Strumnica salient, which threatened the Vardar railway from the east, (b) the district of Kochana (Tocana) and the Bregalnitsa (Bregalnica), (c) a strip of territory running parallel with the old Serbo-Bulgarian frontier the whole way from Zajecar to Kyustendil, and (d) the town of Vidin on the Danube and the salient between it and the Timok.

Analytically expressed ff+ co x I 2 d dn=ff dxdy= A (9) We have seen that Io (the intensity at the focal point) was equal to A 2 /X 2 f2.

The greatest brightness is at the centre, where dC = 27rp d p, C = 7rR2.

If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.

The distance f i, which the actual focal length must exceed, is given by d (f1 2 R2) x; so that f1 = 2 R2/X (1) Thus, if X = p j, R= i ?, we find f1= 800 inches.

If now we suppose the aperture AB to be covered by a great number of opaque strips or bars of width d, separated by transparent intervals of width a, the condition of things in the directions just spoken of is not materially changed.

We conclude that, with a grating composed of transparent and opaque parts, the utmost light obtainable in any one spectrum is in the first, and there amounts to I/wr 2, or about 6, and that for this purpose W a and d must be equal.

Thus, if a= d, we should have 1=2+4+77(49425+...) which is true by a known theorem.

In the case of the D lines the value of Sa/X is about 1/1000; so that to resolve this double line in the first spectrum requires moo lines, in the second spectrum 500, and so on.

If we suppose that the force impressed upon the element of mass D dx dy dz is DZ dx dy dz, being everywhere parallel to the axis of Z, the only change required in our equations (I), (2) is the addition of the term Z to the second member of the third equation (2).

Since the dimensions of T are supposed to be very small in com d parison with X, the factor dy (--) is sensibly constant; so that, if Z stand for the mean value of Z over the volume T, we may write TZ y d e T ?

The force operative upon the positive half is parallel to OZ, and of amount per unit of area equal to - b 2 D = b 2 kD cos nt; and to this force acting over the whole of the plane the actual motion on the positive side may be conceived to be due.

The d may come from the French fleur d'ajodilee.

The Hexaplar text of the LXX., as reduced by Origen into greater conformity with the Hebrew by the aid of subsequent Greek versions, was further the mother (d) of the Psalterium gallicanum - that is, of Jerome's second revision of the Psalter (385) by the aid of the Hexaplar text; this edition became current in Gaul and ultimately was taken into the Vulgate; (e) of the SyroHexaplar version (published by Bugati, 1820, and in facsimile from the famous Ambrosian MS. by Ceriani, Milan, 1874).

If the ray suffers one internal reflection at D, then it is readily seen that, if DB be the path of the reflected ray, the angle ADB equals 2r, i.e.

The total deviation of the ray is consequently given by D =2(i - r) +7r - 2r.

Similarly it may be shown that each internal reflection introduces a supplementary deviation of 7r - 2r; hence, if the ray be reflected n times, the total deviation will be D =2(i - r) +n (7r - 2r) .

The Platonic testimony, if it proved anything, would prove too much, namely, that the doctrine of the unity of Being originated, not with Xenophanes, but before him; and, in fact, the passage from the Sophist no more proves that Plato attributed to Xenophanes the philosophy of Parmenides than Theaetetus, 160 D, proves that Plato attributed to Homer the philosophy of Heraclitus.

On raising the piston, the valve F remains closed and a vacuum tends to be created in the cylinder, but the pressure of the atmosphere forces the liquid up the tube D and it raises the valve E and passes into the cylinder.

The pump devised by D FIG.

In this table n is the refractive index of the glass for sodium light (the D line of the solar spectrum), while the letters C, F and G' refer to lines in the hydrogen spectrum by which dispersion is now generally specified.

Ignoring temperature effect, and taking the density as a function of the pressure, surfaces of equal pressure are also of equal density, and the fluid is stratified by surfaces orthogonal to the lines of force; n ap, dy, P d z, or X, Y, Z (4) are the partial differential coefficients of some function P, =fdplp, of x, y, z; so that X, Y, Z must be the partial differential coefficients of a potential -V, such that the force in any direction is the downward gradient of V; and then dP dV (5) ax + Tr=0, or P+V =constant, in which P may be called the hydrostatic head and V the head of potential.

These equations can be made to represent the state of convective equilibrium of the atmosphere, depending on the gas-equation p = pk =RA (6) where 0 denotes the absolute temperature; and then d9 d p R dz - dz (p) n+ 1' so that the temperature-gradient deldz is constant, as in convective equilibrium in (I I).

From the gas-equation in general, in the atmosphere n d dp _ I dp 1 de _ d0 de i de (8) z p dz-edz-p-edz-k-edz' which is positive, and the density p diminishes with the ascent, provided the temperature-gradient de/dz does not exceed elk.

The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

Clebsch has shown, from purely analytical considerations (Crelle, lvi.); and then = Z d(?G, m), ?

Thus if d,/ is the increase of 4, due to a displacement from P to P', and k is the component of velocity normal to PP', the flow across PP' is d4 = k.PP'; and taking PP' parallel to Ox, d,, = vdx; and similarly d/ ' = -udy with PP' parallel to Oy; and generally d4,/ds is the velocity across ds, in a direction turned through a right angle forward, against the clock.

Uniplanar Motion of a Liquid due to the Passage of a Cylinder through it.-A stream-function 4, must be determined to satisfy the conditions v24 =o, throughout the liquid; (I) I =constant, over any fixed boundary; (2) d,t/ds = normal velocity reversed over a solid boundary, (3) so that, if the solid is moving with velocity U in the direction Ox, d4y1ds=-Udy/ds, or 0 +Uy =constant over the moving cylinder; and 4,+Uy=41' is the stream function of the relative motion of the liquid past the cylinder, and similarly 4,-Vx for the component velocity V along Oy; and generally 1,1'= +Uy -Vx (4) is the relative stream-function, constant over a solid boundary moving with components U and V of velocity.

Motion symmetrical about an Axis.-When the motion of a liquid is the same for any plane passing through Ox, and lies in the plane, a function ' can be found analogous to that employed in plane motion, such that the flux across the surface generated by the revolution of any curve AP from A to P is the same, and represented by 2s-4 -11'o); and, as before, if d is the increase in due to a displacement of P to P', then k the component of velocity normal to the surface swept out by PP' is such that 274=2.7ryk.PP'; and taking PP' parallel to Oy and Ox, u= -d/ydy, v=dl,t'/ydx, (I) and 1P is called after the inventor, " Stokes's stream or current function," as it is constant along a stream line (Trans.

Employing the equation of continuity when the liquid is homogeneous, 2 (cly - d z)?

When the motion is such that d?

Inside the sphere d I d'd rd?

Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A' n c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2 n 2 +X, 2p d = ds; (8) Thence d?

Expressed as a differential relation, with the value of c-TKL ai,G+2 (a 2 +A) a d ?

The quiescent ellipsoidal surface, over which the motion is entirely tangential, is the one for which (a2+X)d?

Thus if T is expressed as a quadratic function of U, V, W, P, Q, R, the components of momentum corresponding are dT dT dT (I) = dU + x2=dV, x3 =dW, dT dT dT Yi dp' dQ' y3=dR; but when it is expressed as a quadratic function of xi, 'x2, x3, yi, Y2, Y3, U = d, V= dx, ' w= ax dT Q_ dT dT dy 1 dy2 dy The second system of expression was chosen by Clebsch and adopted by Halphen in his Fonctions elliptiques; and thence the dynamical equations follow X = dt x2 dy +x3 d Y = ..., Z ..., (3) = dt1 -y2?y - '2dx3+x3 ' M =..

The starting point was ordinary(d)mannite (mannitol),C 6 H 14 0 61 a naturally occurring hexahydric alcohol, which only differed from a-acritol, the alcohol obtained by reducing a-acrose, with regard to optical activity.

On mixing the eslactones and reducing (d + l)-mnanitol was obtained, identical with a-acritol.

Also (d +1) mannonic acid can be split into the d and 1 acids by fractional crystallization of the strychnine or brucine salts.

Since both d-glucose and d-gulose yield the same active (d) saccharic acid on oxidation, the configuration of this and the corresponding /-acid must be sought from among those numbered 5-10 in the above table.

The uterus (X in figure C) begins in all cases at the shell gland (c, d) and may exhibit a swelling (R S) for the retention of the spermatozoa..

Its northern part forms the basin of the Wadi Rumma, which, rising in the Nej d.

Apart from this his chief merits lie in his studies on the subject of the traditional authorities, the results of which are given by Ibn Sa`d, and in his chronology, which is often excellent.

Gottwaldt, St Petersburg, 1844); Ibn al-Qutiya wrote a History of Spain; Ibn Zulaq (d.

This evidence is confirmed by (a) the canon of Theodore of Edessa (800) allowing metropolitans of China, India and other distant lands to send their reports to the catholikos every six years; (b) the edict of Wu Tsung destroying Buddhist monasteries and ordering 300 foreign priests to return to the secular life that the customs of the empire might be uniform; (c) two 9th-century Arab travellers, one of whom, Ibn Wahhab, discussed the contents of the Bible with the emperor; (d) the discovery in 1725 of a Syrian MS. containing hymns and a portion of the Old Testament.

At the junction of 2 D the Cauches with that river, that Ecuadorean line descends the Chinchipe to the Maranon, and the Peruvian ascends to a point where it is intersected by a line following the eastern Cordillera northward to the head-waters of the Caqueta, or Japura, which forms the northern boundary down to the Brazilian frontier.

A, Fasciola hepatica, from the ventral surface (X 2); the alimentary and nervous systems only shown on the left side of the figure, the excretory only on the right; a, right main branch of the intestine; c, a diverticulum; g, lateral ganglion; n, lateral nerve; o, mouth; p, pharynx; s, ventral sucker; cs, cirrus sac; d, left anterior dorsal excretory vessel; m, main vessel; v, left anterior ventral trunk; x, excretory pore.

D, a flame-cell from the excretory apparatus, highly magnified (from Fraipont).

A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut; f, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.

D, An adult redia, containing a daughter-redia, two almost mature cercariae, and germs. E, A free cercaria.

It contains numerous illustrations; maps of the routes of the ancient aqueducts and the city of Rome in the time of Frontinus; a photographic reproduction of the only MS. (the Monte Cassino); several explanatory chapters, and a concise bibliography, in which special reference is made to P. d Tissot, E tude sur la condition des agrimensores (1879).

About 885 IEthelfla d, lady of the Mercians, with the consent of Æthelred her husband, gave Hadleigh to Christ Church, Canterbury.

This unit is called a "dioptric" (usually written "D").

A lens of twice its strength has a refractive power of 2 D, and a focal length of half a metre, and so on.

Three towns are known to d ave been destroyedHerculaneum at the western base of the y olcano, Pompeii on the south-east side, and Stabiae, still farther sl outh, on the site of the modern Castellamare.

Though the inhabitants bad been arned by the earlier convulsions of the mountain, so swiftly d destruction come upon them that 18,ooo are said to have St their lives.

There was some talk of inducing d J Y Th f i $ g Glad stone to join the Tory government, and on the 29th of November Lord Malmesbury dubiously remarked, " I cannot make out Gladstone, who seems to me a dark horse."

The constant wars of the time left their impress Th D k upon everything.

Tradition ascribes the origin of the drama to a religious dance of a panto- Th D mimic character, called Kagura and associated with C raffia.

Louis Auguste de Bourbon, sovereign prince of Dombes, having transferred his parliament to Trevoux, set up a printing press, and was persuaded by two Jesuits, Michel le Tellier and Philippe Lalleman, to establish the Me-moires pour servir d l'histoire des sciences et des arts (1701-1767), more familiarly known as the Journal des Trevoux, long the best-informed and best-written journal in France.

The sound was that of the unvoiced dental stop. The English t, however, is not dental but alveolar, being pronounced, as d also, not by putting the tongue against the teeth but against their sockets.

In modern Greek the ancient b (d) has become the voiced spirant (8), though it is still written b.

Hence to represent D, Greek has now to resort to the clumsy device of writing NT instead.

The hinder portion of the body being drawn of ter, some part of it (c) finds another support on the rough ground or a projection; and, the anterior bends being stretched in a straight line, the front part of the body is propelled (from a to d) in consequence.

Moreover, the three solids S,D and W will differ in minute structure and therefore, probably, in mechanical properties.

There are thus two eutectic alloys B and D, and the alloys with compositions between B and D have higher melting-points.

It is probable that all the alloys of compositions between B and D, when they begin to solidify, deposit crystals of the compound; the lower eutectic B probably corresponds to a solid complex of mercury and the compound.

The higher eutectic D may correspond to a complex of solid thallium and the compound; but the possible existence of solid solutions makes further investigation necessary here.

An important event must be referred probably to the year 451, - the law of Pericles, by which citizenship (including the right to vote in the Ecclesia and to sit on paid juries) was restricted to those who could prove themselves the children of an Athenian father and mother (E d,u001v avroiv).

If the two small conducting spheres are placed with centres at a distance d centimetres, and immersed in an insulator of dielectric constant K, and carry charges of Q and Q' electrostatic units respectively, measured as above described, then the mechanical force between them is equal to QQ'/Kd 2 dynes.

If S is the surface of each plate, and d their distance, then the electric force E in the space between them is E = es.

One of the best methods for doing this is to charge the Ab l condenser by the known voltage of a battery, and then d e t erdischarge it through a galvanometer and repeat this minations.

Let V be the potential at the centre of the prism, then the normal forces on the two faces of area dy.dx are respectively RI dx2 d xl and (dx 2 d x), dV d2 and similar expressions for the normal forces to the other pairs of faces dx.dy, dz.dx.

Hence, multiplying these normal forces by the areas of the corresponding faces, we have the total flux parallel to the x-axis given by - (d 2 V/dx 2)dxdydz, and similar expressions for the other sides.

Hence the total flux is - (+ d2V d 2 V d2V dye + dz2) dy dz, dx2 and by the previous theorem this must be equal to 4'rrp dxdydz.

Suppose that the dielectric has a constant K, then we must multiply both sides by K and the expression for the energy per unit of volume of the field is equivalent to z DE where D is the displacement or polarization in the dielectric.

If we make a distribution of negative electricity over it, which has a density a varying according to the law a = -(d 2 -r 2) q /42rr AP3.

The area BCDdb under the path represents the external work done by the substance in expanding from B to D, which is analytically represented by the integral of pdv taken along the given path.

Since the two expressions (9) are the partial differential-coefficients of a single function E of the independent variables v and 0, we shall obtain the same result, namely d 2 E/d0dv, if we differentiate the first with respect to v and the second with respect to 0.

The energy E and the total heat F are functions of the temperature only, by equations (9) and (I I), and their variations take the form dE = sdO, d F = Sd0.

It is found by experiment that the change of pv with pressure at moderate pressures is nearly proportional to the change of p, in other words that the coefficient d(pv)/dp is to a first approximation a function of the temperature only.

In this case the condition of flow is simply that of constant total heat, or in symbols, d(E+pv) =0.

We have therefore, by equation, (11), Sd0 = (Odv/d0 - v) d p,.

The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..

In the limiting case of a long fine tube, the bore of which varies in such a manner that U is constant, the state of the substance along a line of flow may be represented by the line of constant total heat, d(E+pv) = o; but in the case of a porous plug or small throttling aperture, the steps of the process cannot be followed, though the final state is the same.

The value of Od4 is then the same as d(64), which is a perfect differential, so that the condition may be written d(46-E) =dW.

The product 94, may be represented at any point such as D in Fig.

I by the whole area B"DZ'VO under the isothermal 9"D and the adiabatic DZ', bounded by the axes of pressure and volume.

The difference 90-E is represented by the area 9"DdO to the left of the isometric Dd under the isothermal B"D.

The function G is represented by the negative area D"DM under the isothermal, bounded by the isopiestic DM and the axis of pressure.

The king retired to Naples, abdicated once The more (1802), and entered the Society of Jesus; he d i ed in Rome in 1819.

Rose the third day, A, B, D, E (F omits " the third day " being a theological creed; the translation of C is uncertain).

Thus if d be the relative density, then Iod represents the weight of a gallon in lb.

The substance whose volume is to be determined is placed in the cup PE, and the tube PC is immersed in the vessel of mercury D, until the mercury reaches the mark P. The plate E is then placed on the cup, and the tube PC raised until the surface of the mercury in the tube stands at M, that in the vessel D being at C, and the height MC is measured.

If this be not so, a graduated tube (d) is filled with water, and inverted over the delivery tube.

This may be accomplished by using a vessel with a somewhat wide bottom, and inserting the substance so that it may be volatilized very rapidly, as, for example, in tubes of Wood's alloy, D and by filling the tube with hydrogen.

The substance is now placed on the support already mentioned, and the apparatus closed to the air by inserting the cork at D and turning the cock C. By turning or withdrawing the support the substance enters the bulb; and during its vaporization the free limb of the manometer is raised so as to maintain the mercury at a.

By successive trials two beads, of known density, say di, d 2, are obtained, one of which floats above, and the other below, the test crystal; the distances separating the beads from the crystal are determined by means of a scale placed behind the tube.

If the bead of density dl be at the distance l l above the crystal, and that of d 2 at l 2 below, it is obvious that if the density of the column varies uniformly, then the density of the test crystal is (d1l2-+d211)/(ll+l2).

See further Smend, Listen d.

Geissler, Die litterarischen Beziehungen d.

This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under D to Dar.

The block A carries the disk D, B carries the roller R and counting gear.

The change in the distance d is proportional to the change in the torque transmitted from the shaft to the pulley.

A torque applied to the shaft A can be transmitted to D, neglecting friction, without change only if the central pulley K is held from turning; the torque required to do this is twice the torque transmitted.

A general introduction to the system is given in the tractate Ober den Begriff der Wissenschaftslehre (On the Notion of the Theory of Science), 1794, and the theoretical portion is worked out in the Grundlage der gesammten Wissenschaftslehre (Foundation of the whole Theory of Science, 1794) and Grundriss des Eigenthiimlichen d.

If we divide throughout by T, we obtain d 2 (n+3)RN T +RNd v, showing that dQ/T is a perfect differential.

In Kantian terminology Dialektik is the name of that portion of the Kritik d.

The group has numerous other lofty peaks, of which the chief are the Pizzo d Intermesole (8680 ft.), the Corno Piccolo (8650 ft.), the Pizzo Cefalone (8307 ft.) and the Monte della Portella (7835 ft.).

In spite of the defects of Kant's statement - to which it is necessary to return - the place of the concepts and ideals of the mind and the synthetic organizing 1 Kritik d.

D is the dispart sight, S the tangent sight, A'DS the clearance angle.

D is the dispart, M the muzzle sight, ights.

The rocking-bar consists of a carrier a fixed to the cradle, a rockingbar d pivoted to the carrier at e, a sight bar f carrying the sights and sighting telescope.

If a .JP solid circle be fixed in any one position and a tube be pivoted on its centre so as to move; and if the line C D be drawn upon the circle pointing towards any object Q in the heavens which lies in the plane of the circle, by turn ing the tube A B towards any other object P in the plane of the circle, the angle B 0 D will be the angle subtended by the two objects P and Q at the eye.

Then, if we take ordinates Kb, Lg, Mc, Nd, Pf, equal to B'B, GG', C'C, D'D, FF', the figure abgcdfe will be the equivalent trapezoid, and any ordinate drawn from the base to the a LM N P e X top of this trapezoid will be equal to the portion of this ordinate (produced) which falls within the original figure.

This value of 0 is the same for all parabolas which pass through D and E and have their axes at right angles to KL.

By drawing Ac and Ad parallel to BC and BD, so as to meet the plane through CD in c and d, and producing QP and RS to meet Ac and Ad in q and r, we see that the area of Pqrs is (x/h - x 2 /h 2) X area of cCDd; this also is a quadratic function of x.

The formulae may be used for extending the accuracy of tables, in cases where, if v represents the quantity tabulated, hdv/dx or h 2 d 2 v /dx 2 can be conveniently expressed in terms of v and x to a greater degree of accuracy than it could be found from the table.

Among the incidental operations are (a) the valuation of the bullion by weighing and assaying it; (b) " rating" the bullion, or calculating the amount of copper to be added to make up the standard alloy; (c) recovering the values from ground-up crucibles, ashes and floor sweepings (the Mint " sweep "); (d) assaying the melted bars; (e) " pyxing " the finished coin or selecting specimens to be weighed and assayed; (f) " telling " or counting the coin.

This is done by the little crank B on the axle of the fly-wheel, acting through the rod C, and the bent lever D, which forms a toggle-joint at E with the vertical piece of metal below it.

The reverse movement of D lifts up the upper die and the collar drops simultaneously so that its upper surface is level with the face of the lower die on which the finished coin lies.

While the coin is being moved the hanger D is held firmly by the forceps E to prevent the pan from being pushed sideways.

For this purpose the ohmmeter is provided with a small dynamo D, contained in a box, which produces a continuous electromotive force of from 200 to 500 volts when the handle of the instrument is steadily turned.

John Goodricke established in 1782 the periodicity of its change in about 2 d 21 h, and suggested their cause in recurring eclipses by a large dark satellite.

It shortened fitfully by eight seconds between 1790 and 1879; soon afterwards, restoration set in, and its exact length in 1903 was 2 d 20h 48' n 568, being only two seconds short of its original value.

Thus he accepts the shallow dictum of Condillac that toute science se reduit d une langue bien faite.

On his return to Vienna in 1756 he became famous as teacher and composer, in 1759 he was appointed conductor to the private band of Count Morzin, for whom he wrote several orchestral works (including a symphony in D major erroneously called his first), and in 1760 he was promoted to the sub-directorship of Prince Paul Esterhazy's Kapelle, at that time the best in Austria.

Haydn, thus released from his official duties, forthwith accepted a commission from Salomon, the London concertdirector, to write and conduct six symphonies for the concerts in the Hanover Square Rooms. He arrived in England at the beginning of 1791 and was welcomed with the greatest enthusiasm, receiving among other honours the degree of D Mus.

His most important works were the Missa hispanica, which he exchanged for his diploma at Stockholm, a Mass in D minor, a Lauda Sion, a set of graduals, forty-two of which are reprinted in Diabelli's Ecclesiasticon, three symphonies (1785), and a string quintet in C major which has been erroneously attributed to Joseph Haydn.

As AB returns from EF towards CD the layer of air next to it follows it as if it D E F were pulled back by AB.

That is to say, instead of using Boyle's law, which supposes that the pressure changes so exceedingly slowly that conduction keeps the temperature constant, we must use the adiabatic relation p = kpy, whence d p /d p = y k p Y 1= yp/p, and U = (yp/p) [Laplace's formula].

On the whole the air S within ABCD neither gains nor g D loses momentum, so that on the whole it receives as much through AB as it gives up to CD.

The wave from D has travelled to a circle of radius nearly equal to DF, that from C to a circle of radius nearly CF, and so on.

Taking the successive key-notes D, A, E, B, it is found that besides small and negligible differences, each introduces a new sharp, and so we get the five sharps, C, D, F, G, A, represented nearly by the black keys.

In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e f g a b c'.

The octave above is c' d'e' f' g' a' b' c".

The points A, B, C, D are termed " nodes," and the points half-way between them " loops."

At the nodes A, B, C, D, E there is no displacement, but there are maximum volume and pressure changes.

If d is measured for two gases in succession for the same frequency N, we have 72 p 2P1 d22 71 p i p s d12' where the suffixes denote the gases to which the quantities relate.

When a known temperature was attained the sounder was excited, and d 2 and d 1 could be measured.

In the third mode A and D represent the ends and AD = P. 3 =1 and n 3 = U/A3 = 3U/2l = (3/21)¦(Tim) and so on.

A string is fixed at C on the top of a hollow box, and C" A D B um FIG.

If D is removed and the string is bowed in the middle, the fundamental is brought out.

Substituting in (33) we get U 2 = n/p. (34) If we now keep the wire at rest the disturbance travels along it with velocity U= d (nip), and it depends on the rigidity and density of the wire and not upon its radius.

The port has assumed first-class importance, mail steamers calling vL23 d regularly as well as men-of-war and the mercantile marine of all nations; and it is now one of the finest artificial harbours in the world.

If r, r i be the radii of two spheres, d the distance between the centres, and 0 the angle at which they intersect, then d2=r2+ r12 2rr l cos ¢ hence 2rr 1 cos =d2r2 - r22.

Two spheres intersect in a plane, and the equation to a system of spheres which intersect in a common circle is x 2 + y 2 + z 2 +2Ax -fD = o, in which A varies from sphere to sphere, and D is constant for all the spheres, the plane yz being the plane of intersection, and the axis of x the line of centres.

The pressure on the rollers is limited to about p= 600 d in lb per in.

If it revolves about a vertical axis d its centre of gravity must always lie in that axis; if it rolls the centre of gravity must always lie over the e abutment.

Next let the loads advance a distance a so that W2 comes to C. Then the shear at C is R(n+a)/l - WI, plus any reaction d at B, due to any additional load which has come on the girder during the movement.

As the loads move over the girder, the points C, D, E describe the parabolas M1, M2, M3 i the middle ordinates of which are 4W 1 1, 4W 2 1, and 4W3l.

To use this line to investigate the maximum moment at C due to a series A D ' C'i iE..

If the load is in the bay D'E' and is carried by a rail girder which distributes it to cross girders at D'E', the part of the influence line under this bay is altered.

The loads at D', E, due to unit weight on the rail girder are (p-n)/p and n/p. The reaction at B' is {(p- n)xi+n(xi+p)}' /pi.

Let the load move to D, so that its distance from the left abutment is x+a.

Draw a vertical at D, intersecting fh, kg, in s and q.

Any error of this kind will merely affect the form of the frame; if, however, another member be introduced between A and D, then if BC be shortened AD will be strained so as to extend it, and the four other members will be compressed; if G CB is lengthened AD will thereby be compressed, and the four other members extended; if the workman does not make CB and AD of exactly the right length they and all the members will be permanently strained.

The sides of the polygon may be arranged in any order, provided care is taken so to draw them that in passing round the polygon in C D _E FIG.

Then the deviation y= DE of the neutral axis of the bent beam at any point D from the axis OX is given by the relation d 2 y Ml dx 2 = EI' where M is the bending moment and I the amount of inertia of the beam at D, and E is the coefficient of elasticity.

Then the deflection at the centre is the value of y for x = a, and is _ 5 wa4 S - 14 EI' The radius of curvature of the beam at D is given by the relation R=EI/M.

In 1840 he ', as thus enabled to give a quantitative statement of the law acc s rding to which heat is produced in a conductor by the pas ageof an electric current, and in succeeding years he publish d a series of valuable researches on the agency of electricity in ansformations of energy.

The large loans raised in Europe, the first instalment of which Byron had himself brought over, while providing the Greeks with the sinews of war, provided seco n d civil w them also with fresh material for strife.

The Greeks, advancing prematurely over broken ground and in no sort of order, were fallen upon in flank by d feat at Reshid's horsemen, and fled in panic terror.

Trains of waves nearly but not quite homogeneous as regards wave-length will as usual be propagated as wave-groups travelling with the slightly different velocity d(VX-1)/dX-', the value of K occurring in V being a function of X determined by the law of optical dispersion of the medium.

In this stage the body is composed of two layers, ectoderm (d) externally, and endoderm (c) internally, surrounding a central cavity, the archenteron (b), which communicates with the exterior by a pore (a), the blastopore.

C,C', D,D', two types of medusa organization; C and D are composite sections, showing a radius (R) on one side, an interradius (IR) on the other; C' and D' are plans; the mouth and manubrium are indicated at the centre, leading into the gastral cavity subdivided by the four areas of concrescence in each interradius (IR).

He demanded the equalization of wages, and the merging of personal interests in the common good - "d chacun selon ses besoins, de chacun selon ses facultes."

Among other works may be mentioned Staudlin, Geschichte and Geist d.

This interesting people, whose origin is to this day the most baffling of ethnographical puzzles, originally d welt amidst the forests and marshes of the Upper Niemen.

Sodium is most distinctly recognized by the yellow coloration which volatile salts impart to a Bunsen flame, or, better, by its emission spectrum which has a line (double), the Fraunhofer D, line, in the yellow (the wave-lengths are 5896 and 5890).

After his surrender in 1847 he devoted himself anew to theology and philosophy, and composed a philosophical treatise, of which a French translation was published in 1858 under the title of Rappel d l'intelligent.

The resistance R can thus be divided into two factors, one of which is d 2, where d denotes the diameter of the shot in inches, and the other factor is denoted by p, where p is the resistance in pounds at the same velocity to a similar I-in.

We first determine the time t in seconds required for the velocity of a shot, d inches in diameter and weighing w lb, to fall from any initial velocity V(f/s) to any final velocity v(f/s).

The differences OD and DI are thus calculated, while the values of D(v) and I (v) are obtained by summation with the arithmometer, and entered in their respective columns.

These functions, T, S, D, 1, A, are shown numerically in the following extract from an abridged ballistic table, in which the velocity is taken as the argument and proceeds by an increment of 10 f/s; the column for p is the one determined by experiment, and the remaining columns follow by calculation in the manner explained above.

The initial values of T, S, D, I, A must be accepted as belonging to the anterior portion of the table.

After a certain discount for friction and the recoil of the gun, the net work realized by the powder-gas as the shot advances AM is represented by the area Acpm, and this is equated to the kinetic energy e of the shot, in foot-tons, (I) e d2 I + p, a in which the factor 4(k 2 /d 2)tan 2 S represents the fraction due to the rotation of the shot, of diameter d and axial radius of gyration k, and S represents the angle of the rifling; this factor may be ignored in the subsequent calculations as small, less than I %.

The aim of that association is " to promote the development, and maintain the well-being, of classical studies, and in particular (a) to impress upon public opinion the claim of such studies to an eminent place in the national scheme of education; (b) to improve the practice of classical teaching by free discussion of its scope and methods; (c) to encourage investigation and call attention to new discoveries; (d) to create opportunities of friendly intercourse and co-operation between all lovers of classical learning in this country."

Arbogast's rule of the last and the last but one; in fact, taking the value of a to be unity, and, understanding this letter in each term, the rule gives b; c, b2; d, bc, b; e, bd, c, b c, b, &c., which, if b, c, d, e, &c., denote I, 2, 3, 4, &c., respectively, are the partitions of 1, 2, 3, 4, &c., respectively.

Gulf of Gabes I o g Lemg.W.of Greenwicir 0 Longitude East of Greenwich B 4 D very complete sequence of formations from the Lias to those of recent date.

A, B, C, D, E, F, Terminals to which standard cell or voltages to be tested are attached.

If a= logg = - log (1-10)' 81 (1) c = 10g 80 = log 1 +sr, 126 (8) e =10g1 o = log 1 +1000 then log 2=7a-2b+3c, log 3=IIa-3b+5c, log 5=16a-4b +7c, and log 7 =2(39a - IOb+17c - d) or=19a-4b+8c +e, and we have the equation of condition, a-2b+c=d+2e.

As has been stated, Abraham Sharp's table contains 61-decimal 10 b= log 24 = - log (1-160) d =10g 49 = - log (1-160) 17253 8 35 62 21868 Briggian logarithms of primes up to I ioo, so that the logarithms of all composite numbers whose greatest prime factor does not exceed this number may be found by simple addition; and Wolfram's table gives 48-decimal hyperbolic logarithms of primes up to 10,009.

The logarithm is then obtained by use of the formula d l d2 l d3 2 log e (x+d) = log e x-f- - x2+3 x3 - &c., in which of course the object is to render dlx as small as possible.

Rao D 0 UEU i-an;, w ma.

Even when seen in minute features only he recognized them as constant progressive characters or " chronologic varieties " in 3b --i C D E F G H I -14-21 -I-31 1 - I - 41 contrast with contemporaneous or " geographic varieties," which he considered inconstant and of slight systematic value.

The extraing to foot of rotifers; at, median blastoporic opening of antenna, united by a nerve to br, brain the cloaca leads us to a (letter omitted in B); bl, bladder, re ver y different view, which ceiving ramified kidney in B, C, D; finds negative support f, foot, and f.g, its cement-gland;.

The exact position of the selected ray does not matter much, but the yellow D line of sodium Air FIG.

But the light of slightly greater wave-length than the D lines, being refracted strongly downward by the sodium vapour, illuminates the.

The light corresponding to the D lines and the space between them is absorbed, as evidenced by the dark interval.

Here the light corresponding to the space between the D lines is transmitted, being strongly refracted upward near D I, and downward near D 2.

The equations finally arrived at are DX2(A2_ 2) (x2_ A2m)2+g2A2 ' DgA3 (A A l m) 2 +g 2 A2 ' where is the wave-length in free ether of light whose refractive index is n, and A m the wave-length of light of the same period as the electron, is a coefficient of absorption, and D and g are constants.

A - D shows the formation of the two nuclear elements (trophonucleus and kinetonucleus) from the definitive nucleus (synkaryon) of the ookinete.

There I d is also a coalfield in Nova Scotia and New Brunswick, bryan.

Finally, of true lignite beds, or of lignite mix d with sub-bituminous qualities, the states of North Dakota, Montana, Texas and South Dakota are credited with deposits of 500,000; 279,500; 23,000; and 10,000 millions of tons respectively.

The latter have the management of county buildings, such as courthouses ar,d prisons, have power to lay out new main highways, to grant licences, and to apportion among the towns and cities the taxation necessary to meet county expenses.

See Honore Mirabeau, Les Lettres de cachet et des prisons d'etat (Hamburg, 1782), written in the dungeon at Vincennes into which his father had thrown him by a lettre de cachet, one of the ablest and most eloquent of his works, which had an immense circulation and was translated into English with a dedication to the duke of Norfolk in 1788; Frantz Funck-Brentano, Les Lettres de cachet d Paris (Paris, 1904); and Andre Chassaigne, Les Lettres de cachet sous l'ancien regime (Paris, 1903).

The church (D) is cruciform, with a nave of nine bays, and a semicircular apse at either extremity.

On this side we also find the farmbuildings, the large granary and threshing-floor (a), mills (c), malthouse (d).

On the other side of the chapter-house, to the south, is a passage (D) communicating with the courts and buildings beyond.

On the other side is a chapel (D).

He also threw himself at his guest's feet, and conducted him to the chapel (D) purposely built close to the gate.

We may also call attention to the greatly lengthened choir, commenced by Abbot John of York, 1203-1211, and carried on by his successor, terminating, like Durham Cathedral, in an eastern transept, the work of Abbot John of Kent, 1220-1247, and to the tower (D), added not long before the dissolution by Abbot Huby, 1494-1526, in a very unusual position at the northern end of the north transept.

His achievement was a closely approximate D geometrical solution of the FIG.

Take AB equal to one-fourth of the given line; on AB describe a square ABCD; join AC; in AC produced find, by a known process, a point C 1 such that, when C 1 B 1 is drawn perpendicular to AB produced and C 1 D 1 perpendicular to BC produced, the rectangle BC,.

Slaughtering notably free from epizootic diseases, with a fertile D soil or the growth of fodder crops and pasture, with abundance of pure air and water, and with a plentiful supply of ice, the conditions in Canada are ideal for the dairying industry.

In this way the notches d, e of the hinder part of the mantle-skirt of Anodonta are in the siphonate forms converted into two separate holes, the edges of the mantle being elsewhere fused together along this hinder margin.

I (5), takes an outward course and leaves the sub-pallial space by the upper notch d.

The gill axis d is seen lying in the sub-pallial chamber between the foot b and the mantle c. From it depend the gillfilaments or lamellae - formed by united filaments - drawn as black lines f.

The mechanical result of the concrescence of the outer lamellae to the mantle-flap, and of the inner lamellae to one another as shown' in section D, fig.

The readings of X which can be deduced from considering the agreements in B, C, D will be of higher antiquity and of greater external aut l ority than any of the readings in B, C, D taken singly.

In the following stemma M and N are "mixed" or "conflated" MSS., being formed by the blending of readings from the "pure" or "unmixed" codices A, B and D, E respectively.

For the bettering of the transmitted text we can call in aids of a C D partial or subsidiary character which are known in general as testimonia.

For The Sake Of Greater Generality, The Days Of The Week Are Denoted By The First Seven Letters Of The Alphabet, A, B, C, D, E, F, G, Which Are Placed In The Calendar Beside The Days Of The Year, So That A Stands Opposite The First Day Of January, B Opposite The Second, And So On To G, Which Stands Opposite The Seventh; After Which A Returns To The Eighth, And So On Through The 365 Days Of The Year.

The Fourth Year Was Bissextile, And The Dominical Letters Were F, E; The Following Year D, And So On.

On Dividing By 28, The Remainder Is O, Or 28; And Opposite 28, In The First Column Of Letters, We Find D, C, The Dominical Letters Of The Year 1148.

After the 17th of April D first occurs in the calendar (Table IV.) at the 19th.

In Like Manner, When P =I, 1=D =4; For D Is The Dominical Letter Of The Calendar Belonging To The 22Nd Of March.

D, E, F, Trochosphere stage, D fp, Pore in the foot (belonging mf, The mantle-flap or limbus to the pedal gland?).

D, Further advanced Trochosphere (optical section).

D, Each of the four segment-cells gives rise by division to a small pellucid cell.

America has been the pioneer of the view that peace is the normal condition of mankind, and that, when the causes of war are eliminated, war ceases to have a raison d'être.

When now a small bead of a salt of sodium or lithium is placed in the flame the spectrum of the white hot platinum is traversed by the dark absorption of the D lines.

According to independent experiments by Paschen the radiation of the D line sent out by the sodium flame of sufficient density is nearly equal to that of a black body at 'the same temperature.

If we compare Balmer's formula with the general equation of Ritz, we find that the two can be made to agree if the ordinary hydrogen spectrum is that of the side branch series and the constants a', b, c and d are all put equal to zero.'

If a is the distance shown by the normal triplets the type of separation observed in the line D2 shows distances from the central line equal to a /3, 3a/3, 5a/3, while the type of D 1 gives 2a/3, 4a/3.

Under different conditions we obtain (a) a continuous spectrum most intense in the yellow and green, (b) the spectrum dividing itself into two families of series, (c) a spectrum of lines which appears when a strong spark passes through oxygen at atmospheric pressure, (d) a spectrum of bands seen in the kathode glow.

Kettlewell, Thomas d Kempis and the Brothers of Common Life (1882), i.

It appears to his imagination that the affinity of two atoms of hydrogen to one of oxygen, the attraction of the spermatozoon to the ovum, and the elective affinity of d pair of lovers are all alike due to sensation and will.

Further, Wundt declares that the psychical compound of sensations, with which, according to him, we actually start, is not a complex sensation, but a compound idea; so that I am expected to believe that, when I hear the chord of D, I am not conscious of single sensations of D, F, A, and have only a compound idea of the chord - as if the hearing of music were merely a series of ideas!

In order to eliminate any error due to the zero of the scale D not being exactly below the mirror magnet, the support L is then removed to the west side of the instrument, and the settings are repeated.

His first play, Marius d Minturnes (1791), immediately established his reputation.

The rejection of this budget in December by the House of Lords led to d desperate struggle at the polls in January 1910, but the confident hopes of the Unionists were doomed to disappointment.

D, Gallery, with roof formed of projecting courses of stone in large blocks.

D is due to transient induction in horizontal soft iron, the direction of which passes continuously under or over the compass.

C is compensated by permanent magnets athwartships and horizontal; D by masses of soft iron on both sides of the compass, and generally in the form of cast-iron spheres, with their centres in the same horizontal plane as the needles; E is usually too small to require correction; A is fortunately rarely of any value, as it cannot be corrected.

Not only was its very existence an obstacle to .the T he Parcy a n d the spread of their temporal power in the peninsula, Norman but it frequently acted in concert with the pope 's Kingdom enemies and thwarted the papal policy.

The next change took place in the central provinces; the ra-tags were altered into cerebral dentals, and the ya-tags became c. Later on the superscribed letters and finals d and s disappeared, except in the east and west.

It was at this stage that the language spread in Lahul and Spiti, where the superscribed letters were silent, the d and g finals were hardly heard, and as, os, us were ai, oi, ui.

The vowel sounds ai, oi, ui have become e, o, u; and a, o, u before the finals d and n are now et, o, ii.

The Jesuit Antonio Andrada, a native of Portugal (1580-1634), travelling from India, appears to have entered Tibet on the west, in the Manasarowar Lake region, and made his way across to Tangut and north-western China; in 1661 the Jesuit fathers Johann Grueber (an Austrian) and Albert D 'Orville (a Belgian) travelled from Peking via Tangut to Lhasa, and thence through Nepal to India.

By comparison with the first equation we see that RT/F is equal to D, the diffusion constant.

This result gives a value of D for dilute hydrochloric acid equal to 2.49 to compare with the observed value of 2.30.

Gewandung, p. 250) thinks that it was probably in use by the popes themselves so early as the 3rd century, since St Cyprian (d.

A selection is published by Lidzbarski, Handbuch d.

The two achromatic lenses, C and D, bring the rays to a focus on the plane surface of the large lens, E, forming an image there.

D Company was still in the "Iris II.," but the marines were forming up on the mole to make an assault.

There are no upright front sashes, but to facilitate ventilation there are ventilators d in the front wall, and the upper roof sashes are made to move up to FIG.

Fig 36, b and c, are examples of the former, and d, e, f of the latter.

The axis N 0 passes through the brass piece M, which stands on an insulating pillar of glass, and supports the plates A and C. At one extremity of this axis is the ball D, and the other is connected with a rod of glass, N P, upon which is fixed the handle L, and also the piece G H, which is separately insulated.

In all other positions A, B, C and D are completely disconnected from each other.

On the other side of the rotating disk were placed two metal combs C, C, which consisted of sharp points set in metal rods and were each connected to one of a pair of discharge balls E, D, the distance between which could be varied.

I t r1 D Uoeree e?s/, 'c pn.

In 1659 a treaty of peace was with concluded between France, England and the United education of theer under was e ounce prince of Orange d Y e P g taken by the States of Holland under the super intendence of de Witt.

D, The same, beginning to be as, Ascogonium.

Suddenly cooled carbon steel, Steep Cast Iron no; d ` r t1?at J ustenite+ Cementite.

From A and B the materials are drawn as they are needed into large buckets D standing on cars, which carry them to the foot of the hoist track EE, up which they are hoisted to the top of the furnace.

C, D, Sheaves carrying the endless chain of moulds.

Here BB is a large fixed iron cylinder, corrugated within, and C an excentric cylinder, also corrugated, which, in turning to the right, by the friction of its corrugated surface rotates the puddled ball D which has just entered at A, so that, turning around its own axis, it travels to the right and is gradually changed from a ball into a bloom, a rough cylindrical mass of white hot iron, still dripping with cinder.

A current of great electromotive force (intensity or voltage) passed through the coil D, induces, by means of the core and frame, a current of enormous quantity (volume or amperage), but very small electromotive force, in the metal in the trough.

As soon as a hot billet A is withdrawn by pushing it endwise out of the exit door B, the whole row is pushed forward by a set of mechanical pushers C, the billets sliding on the raised water-cooled pipes D, and, in the hotter part of the furnace, on the magnesite bricks E, on which iron slides easily when red-hot.

The skin of the object, D, which is undergoing rolling, technically called " the piece," is drawn forward powerfully by the friction of the revolving.

Much as in the smith's forge the object forged rests on a massive anvil and anvil block, B and C, and is struck by the tup D of the hammer.

Increase in Production.-In 1810 the Unit d States made about 7%, and in 1830, 1850 and 1860 not far fr m io% of the world's production of pig iron, though, indeed, in 1820 their production was only about one-third as great as in 1810.

A collar is provided, which when tightened on the vertical axis, otherwise free to move, holds it rigidly in position with respect to the plate PP. To this collar is attached a slow-motion screw, working against a reaction spring, by which the plate rr can be rotated through a small arc. The upper plate carrying two, three .or four verniers vv is attached to a vertical coned pillar passing through the centre of the larger pillar and rotating in it; this plate can be clamped to the lower plate by means of the screw C, and can be rotated with respect to it by the slow-motion screw d.

On account of their resemblance to the twins of the mineral spinel (which crystallizes in octahedra) these are ?i D known as " spinel twins."

Angstrom's Method consists in observing the propagation of heat waves in a bar, and is probably the most accurate method for 4 4 thehi 's ' 'so ' d 60 measuring the diffusivity of a metal, since the conditions may be widely varied and the correction for external loss of heat can be made comparatively small.

The heat per second gained by conduction by an element dx of the bar, of conductivity k and cross section q, at a point where the gradient is dB/dx, may be written gk(d 2 6/dx 2)dx.

We thus obtain the differential equation gk(d 2 0/dx 2) =cgdo/dt+hpo, which is satisfied by terms of the type =c" sin where a 2 -b 2 = hp/qk, and ab = urnc/k.

The difference of the temperature gradients D/l at the ends of the section was simultaneously obtained from the difference D of the readings of a pair of couples at either end connected in opposition.

See Pythagoras, Neoplatonism, Essenes; and Zeller's Philosophie d.

The great battle against D f these foes was fought on the 10th of August 955 on the Lechfeld near Augsburg.

This sufficed to provoke the defiance of the Danes, and on the 1st of February 1864 the Austrian and D h Prussian troops crossed the Eider.

Now imagine this system to be suddenly displaced so that a moves to a' and d moves to d'.

Darroro,, o d

B, as far as it goes (to 977), is identical with C, both having been copied from a common original, but A, C, D, E have every right to be treated as independent chronicles.

The main points of difference are that in D, E (1) a series of northern annals have been incorporated; (2) the Bede entries are taken, not from the brief epitome, but from the main body of the Eccl.

The impulse given by Alfred was continued under Edward, and we have what may be called an official continuation of the history of the Danish wars, which, in B, C, D extends to 915, and in A to 924.

After 915 B, C insert as a separate document a short register of Mercian affairs during the same period (902-924), which might be called the acts of Æthelflaed, the famous "Lady of the Mercians," while D has incorporated it, not very skilfully, with the official continuation.

From 983 to 1018 C, D and E are practically identical, and give a connected history of the Danish struggles under Æthelred II.

From 1018 the relations of C, D, E become too complicated to be expressed by any formula; sometimes all three agree together, sometimes all three are independent; in other places each pair in turn agree against the third.

It may be noted that C is strongly anti-Godwinist, while E is equallypro-Godwinist, D occupying an intermediate position.

D ends at 1079 and is certainly mutilated.

In its later history D is associated with some place in the diocese of Worcester, probably Evesham.

In its present form D is a comparatively late MS., none of it probably much earlier, and some of it later, than 1100.

In the case of entries in the earlier part of the chronicles, which are peculiar to D, we cannot exclude the possibility that they may be late interpolations.

Besides A, B, E, F, Ingram used C and D for the first time.