# AF Sentence Examples

- For any particular root, the equations (5) determine the ratios of the quantities
**Af**, A1,. **Af**N Bourg AISNE Laon ALLIER Moulins .- See Martin Veibull, Sveriges Storhedstid (Stockholm, 1881); Frederick Ferdinand Carlson, Sveriges Historia under Konungarne
**af**Pfalziska Huset (Stockholm, 1883-1885); Robert Nisbet Bain, Scandinavia (Cambridge, 1905); O. - The factors
**Af**(u-v cos i) and Bf (v sin i) give the frictional resistance to sinking, per unit length of the cable, in the direction of the length and transverse to the length respectively. - Expenditure of Energy by Plants.The energy of the plant is,
**af**we have seen, derived originally from the kinetic radiant energy 01 the sun. **Af**ter the discovery of the north-west by the French in 1 731 and succeeding years the prairies of the west were occupied by them, and Fort La Jonquiere was established near the present city of Calgary (1752).**Af**Expression in Terms of Roots.-Since x+y y =mf, if we take cx any root x 3, y1, ofand substitute in mf we must obtain, y 1 C) zaZ1 ï¿½; hence the resultant of and f is, disregarding numerical factors, y,y2...y,,.- % -k Y k = (
**af**) k a n x. - Uo; 4, 1=0=f.; where u 0 =1, u1=o, assume that tfik = (
**af**) k ay -k = f. - Ukx(n-2) ï¿½ Taking the first polar with regard to y (n - k) (a f) xa x -k-l ay+ k (
**af**) k-l ay -k (ab) (n -1) b12by n kn-2k-1 n-1 k(n-2) =k(n- 2)a u x u5+nax ayux and, writing f 2 and -f l for y1 and 3,21 (n-k)(a f) k+ta i k-1 + k (n - 1)(ab)(a f) k-1 (b f)4 1 k by-2 = (uf)u xn-2k-1? - Moreover the second term on the left contains (a f)' c -2b z 2 = 2 (a f) k-2b x 2 - (b) /0-2a 2 ï¿½ if k be uneven, and (
**af**)?'bx (i f) of) '-la if k be even; in either case the factor (**af**) bx - (bf) ax = (ab) f, and therefore (n-k),bk+1 +Mï¿½f = k(n-2)f.(uf)uxn-2k-1; and 4 ' +1 is seen to be of the form f .14+1. - Take and Uk = (
**af**) k ai k the linear factor which occurs to the second power in f. - If ai, bx, cx be different forms we obtain,
**after**development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -**af**t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines. - Only in this case can cos {p' +(m- -27th/
**Af**) f } retain the constant value - I throughout the integration, and then only when and a = 27Th/A f (8) cos p'=- 1 .. - In the second term if we observe that cos {p'+ 27rh/
**Af**)E} =cos{p' - g,E} = cos p cos g, +sin p sin giE, we see that the second part vanishes when integrated, and that the remaining integral is of the form w = f +.0 sin z h, cos where h,=7rh/**Af**, g,=a-27Th/**Af**. - 2s = 277-h/A f (14) e =
**Af**/h (15) The bands are thus of the same width as those due to two infinitely narrow apertures coincident with the central lines of the retarded and unretarded streams, the subject of examination being itself a fine luminous line. - He was on friendly terms with the prince's mistress,Henrietta Howard,
**af**terwards countess of Suffolk. **Af**ter the death of her husband, by whom she had no children, she married Henry of Albret, king of Navarre; and thus the count 563 ship of Armagnac came back to the French crown along with the other dominions of Henry IV.- The chilling stereotypes the structure existing in the ingot at the moment it was withdrawn from the furnace, and we can
**af**terwards study this structure by means of the microscope. - SWEDEN] See Martin Veibull, Sveriges Storhedstid (Stockholm, 1881); Frederick Ferdinand Carlson, Sveriges Historia under Konungarne
**af**Pfalziska Huset (Stockholm, 1883-1885); E. - 19) represent a gun at height BD above water-level DC, elevated to such an angle that a shot would strike the water at C. Draw EB parallel to DC. It is clear that under these conditions, if a tangent sight
**AF**be raised to a height F representing the elevation due to the range BC, the object C will be on the line of sight. - 67 a) in a fitting position to represent part of the polygon of forces at Xefa; beginning with the upward thrust EX, continuing down XA, and drawing
**AF**parallel to**AF**in the frame we complete the polygon by drawing EF parallel to EF in the frame. **Af**ter losing the commander in the Philippines and discovering Borneo, the two surviving ships reached the Moluccas late in 1520.**Af**ter the 4th century other names or expressions come into use, such as mensa tremenda, sedes corporis et sanguinis Christi.- Clausen,
**Af**0. - 1898); Calendar of Letters and State Papers relating to English
**Af**f airs, principally in the Archives at Simancas (vols. **Af**, Anus.- The Nile crocodile makes a hole in white sand, which is then filled up and smoothed over; the mother sleeps upon the nest, and keeps watch over her eggs, and when these are near hatching -
**af**ter about twelve weeks - she removes the 18 in. - Nominally the beginning Df the rise of the Nile, was the beginning of the year, and as the ~ile commences to rise very regularly at about the date of the annual heliacal rising of the conspicuous dog-star Sothis (Sirius~ (which itself follows extremely closely the slow retrogression
**af**the Julian year), the primitive astronomers found in the heliacal rising of Sothis as observed at Memphis (on July 9 Julian) a very correct and useful, starting-point for the seasonal year. - Fortaellinger
**af**Nordens Historic (Copenhagen, 1892). - Mikkel, priest of St Alban's Church in Odense, wrote three sacred poems, The Rose-Garland of Maiden Mary, The Creation and 1 Collected as Samling
**af**gamle danske Love (5 vols., Copenhagen, 1821-1827). **Af**ter the death of Holberg, the**affectation**of Gallicism had reappeared in Denmark; and the tragedies of Voltaire, with their stilted rhetoric, were the most popular dramas of the day.**Af**ter the death of Cretheus, Pelias made himself master of the kingdom of Iolous, having previously quarrelled with Neleus, who removed to Messenia, where he founded Pylos.- Although this charge was demonstrably false, Randolph when confronted with it immediately resigned, and subsequently secured a retractation from Fauchet; he published A Vindication of Mr Randolph's Resignation (1795) and Political Truth, or Animadversions on the Past and Present State of Public
**Af**f airs (1796). - Rasmussen and others, Gronland Tangs polhavet, udforskningen
**af**Gronland fra Melvillebugten til Kap Morris Jesup: Skildring**af**den II. - 52, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of
**AF**and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF. - Again, the half-period of x i irf-~ lf(a) +3a_if(a) ~, and since the angular velocity in the orbit i h/
**af**, approximately, the apsidal angle is, ultimately, IS f(a) ? - IrN (
**af**(a)-f-3f(a)~ (3 - M~=Mg sin
**aF**, o=Mg cos aR, MsiU=Fa (10) **Af**d4e tan ~,+ cot 4i~ ~ (40) aj d~i tan ~1+cot ti)- Let ai, a2,
**af**be the angular velocities of the first, intermediate, and last shaft in this train of two Hookes couplings. - Required the relation between the velocity of translation 02 of W and the angular velocity
**af**of the differential barrel. - The seventh link
**AF**is equal in length to hair the distance EA when the mechanism is in its central position. - It will be seen that the piece
**Af**can ~ only slide relatively to the piece B1, and *1 these two pieces e Bi C therefore form the A sliding pair. - Du and the work performed in a unit cf time in overcoming friction, when the angular velocity is a, is
**af**f pr. - U=c (ai+ef), where u is that velocity, c the distance TI at any instant from the point of contact of the teeth to the pitch-point, and
**af**, ai the respective angular velocities of the wheels. - Let I/S =(
**af**ai)/A - (B) Asia And
**Af**Ric A. - Carlson, Sveriges historie under konungarne
**af**Pfalziska Huset (Stockholm, 1883-1885); A. - Mankell, Ofversigt
**af**svenska krigens historia (ibid., 1890); A. - Dalin's style, 1 The works of the chief writers between Sternhjelm and Dalin were edited by P. Hanselli (Upsala, 1856, &c.) as Samlade vitterhetsarbeten-
**af**svenska fOrfattare. - Lars Johan Hierta (1801-1872) was the leading journalist, Johan Henrik Thomander, bishop of Lund (1798-1865), the greatest orator, Matthias Alexander Castren (1813-1852) a prominent man of science, and Karl Gustaf
**af**Forsell (1783-1848), the principal statistician of this not very brilliant period. - From which, dividing both sides by
**Af**, we obtain the following equations: etAf = RfW/gS ~ **Af**Leopold (1756-1829), T.