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ao-Kutani, so called because of a green (ao) enamel of great brilliancy and beauty which was largely used in its decoration, and Kirtani with painted and enamelled pate varying from hard porcelain to pottery.

11ao-Kutani, so called because of a green (ao) enamel of great brilliancy and beauty which was largely used in its decoration, and Kirtani with painted and enamelled pate varying from hard porcelain to pottery.

11000 English Miles ao 20 30 an 5 c+ ?

00ao.

00Every plant is constrained to carry Out its functions of germination, growth, nutrition, reproduction, &c., between certain limits of temperature, and somewhere between the extremes of these limits each function finds ao optimum temperature at which the working of the living machinery is at its best, and, other things being equal, any great departure from this may induce pathological conditions; and many disasters are due to the failure to provide such suitable temperaturese.g.

00ao; Dan.

00p. 256 (19 Ao).

00We have to multiply a01; -alas+a2 by ao, -aif32+a2 and we obtain ao (3 - aoal(f31N2 +01133) +aoa2(SI+13) -i-a?31a2 - aIa2(31 + 02) + al, 131+02 = b, 131132 = b t'i +s2 = 2bob2, and clearing of fractions R 1,5 = (a o b 2 - a2 b o) 2 + (a i b o - aobi) (aib2 - a2b1).

00and by elimination we obtain the resultant ao 0 bo 0 0 al ao b1 bo 0 a 2 a i b 2 b 1 bo a numerical factor being disregarded.

001 X discriminant of f = ao X disct.

00This arises from the circumstance that the general operator Ao,a0aa1 + ialaa2 + 2a2 a 3 +...

00is transformed into the operator d 1 by the substitution (ac, al, a2, ï¿½ï¿½ï¿½as, ï¿½ï¿½ï¿½) _ (ao, Xoai, X 6 X i a 2, ï¿½ï¿½ï¿½, XcX1..%s_las,ï¿½ï¿½ï¿½), so that the theory of the general operator is coincident with that of the particular operator d1.

00For such functions remain unaltered when each root receives the same infinitesimal increment h; but writing x-h for x causes ao, a1, a 2 a3,...

00to become respectively ao, ai+hao, a2+2ha1, a 3 +3ha 2, ...

00ao -ialaan+l m !

00ao (m -2) m !

00being formed, the expansion being carried out, an operand ao or bo or co ...

00F(a ' a ' a, ...a) =r A F(ao, a1, a2,ï¿½ï¿½ï¿½an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.

00;51, 2) = r F(ao, al, a2,...; xi, x2), the function F(a 01 a 1, a 2, ...

00Instead of a single quantic we may have several f(ao, a1, a2...; x1, x2), 4 (b o, b1, b2,...; x1, x2), ...

00For the substitution rr xl =A 11 +1 2 12, 52=A21+ï¿½2E2, of modulus A1 ï¿½i = (Alï¿½.2-A2ï¿½1) = (AM), A 2 ï¿½2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A lï¿½l +ai(A1/.22+A2ï¿½1) +7,2X2/22, A2 = aoï¿½l +2a1ï¿½1/ï¿½2 +a 2ï¿½2 ï¿½ We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?

00A 1, A2 ï¿½ Ai, A 1 A 2, A2 and then Ao = al Ai+2a1a2AIA2+a2 A2 - (a1A1+a2A2) 2 = a?, A l = (a 1 A 1 +a2A2) (alï¿½l +a2ï¿½2) = aAaï¿½, A 2 = (alï¿½l +a2/-12) 2 = aM; so that A = aa l +2a A a u 152+aM5 2 = (aA6+a,e2)2; whence A1, A 2 become a A, a m, respectively and ?(S) = (a21+a,E2) 2; The practical result of the transformation is to change the umbrae a l, a 2 into the umbrae a s = a1A1 +a2A2, a ï¿½ = a1/ï¿½1 + a21=2 respectively.

00By similarly transforming the binary n ic form ay we find Ao = (aI A 1 +a2 A2) n = aAn A l = (alAi - I -a 2 A 2) n1 (a1ï¿½1 +a2m2) = aa a ï¿½ - A i n-1 A2, n-k k n-k k n-k k A = (al l+a2A2) (alï¿½1+a2ï¿½2) = a A ï¿½ =A 1 A2, so that the umbrae A1, A 2 are a A, a ï¿½ respectively.

00For, if c(ao i ...x l, x 2) be a covariant of order e appertaining to a quantic of order n, t (T.

001 2) = (A /-?) ' (ao,...

00The Binary Quartic.-The fundamental system consists of five forms ax=f; (f,f')2=(ab) 2axbx=Ax; (f,f')4=(ab) 4= 2; (f, 0)1= (ao) azsi = (ab) 2 (cb) a:b x c5 =1; (f 4) 4 = (as) 4 = (6) 2 00 2 (ca) 2 = j, viz.

00l aa k -x 2 d d- = 0; Z(nk)ak+l adk - x ldd2=0; or in the form d d 52-x 2(7 =0, O - x1ax2 = 0; where 0 = ao d a l + 2a 1 -?...+na,,_id an, 0 = nal dao -?

00One advantage we have obtained is that, if we now write ao =o, and substitute a 8 _ 1 for a,, when s>o, we obtain d d aO da l +al da 2 +a2 da ï¿½....+an_2dan_1 which is the form of SZ for a binary (n- Henceby merely diminishing each suffix in a seminvariant by unity, we obtain another seminvariant of the same degree, and of weight w-8, appertaining to the (n-I) ic. Also, if we increase each suffix in a seminvariant, we obtain terms, free from a 0, of some seminvariant of degree 8 and weight w+8.

00Hence, excluding ao, we may, in partition notation, write down the fundamental solutions of the equation, viz.

00(2), (3), (4),...(n), and say that with ao, we have an algebraically complete system.

00Observe that, if we subject any symmetric function the diminishing process, it becomes ao 1 - P2 (p2p3...)ï¿½ Next consider the solutions of 0=o o which are of degree 0 and weight w.

00When the proper degree 0 is < w a factor ao -e must be of course understood.

001 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second Binary Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2.

001 Z2' The First Perpetuant Is The Last Seminvariant Written, Viz.: A O (B O B 2 3B O B 3) A L (Bi 2B0B2), Or, In Partition Notation, Ao(21) B (1)A(2)B; And, In This Form, It Is At Once Seen To Satisfy The Partial Differential Equation.

00(0')B Denotes A Seminvariant, If 0, 0', Be Neither Of Them Unity, For, After Operation, The Terms Destroy One Another In Pairs: When 0, Must Be Taken To Denote Ao And So For 0'.

00For The Case In Hand, From The Simplest Perpetuant Of Degrees I, 2, We Derive The Perpetuants Of Weight W, Ao(21W 2)B A1(21"R 3) I A2(21" 4)B ..ï¿½ Man 2(2)B, Ao(221W 4(B Al(221W 5)B A2 (221 " S)B ...

00Maw 4(22)B, Ao(231W 9B A, (221" 7)B A2(231W 8)B ...

00For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.

00(14) a (4322) b - (13) a (432 2 1) b + (12)a (432212) b - (1) a (432213)b +ao(432214)b, and thence the general form (1 A i + 4) a (4ï¿½4 + 1.3 ï¿½ 3 + 121 1, 2 + 2) b - ... ?ao(4ï¿½4+13ï¿½a+l2ï¿½2+21 Al+4)b, due to the generating function 2 15 1 -z.

00This is the fundamental system; we may, if we choose, replace (ab) 2 by ab =a, 2, +2a1+a2 since the identity a a b b - a, = (ab) 2 shows the syzygetic relation (74+a 2) 2 - (ao +2a +ï¿½2) = 2(aoa2 - ai).

00Another example of a sequence is afforded by the successive convergents to a continued fraction of the form ao+ I I, al+ a2+ï¿½ where ao,a 1, a 2, ...

00Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the integration being along the original path Ao.

00A similar expression can be found for Q'P - Q"A; and thus, if Q' A =v, Q' AO = where v =a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').

00The grating at A and the eye-piece at 0 are rigidly attached to a bar AO, whose ends rest on carriages, moving on rails OQ, AQ at right angles to each other.

00= constant, _ ff 00 NdA N BA-AA X - JA (a' +X) (b 2 +A)P - abc' a2 -b2 ' and at the surface A = o, I I N Bo-A 0 N I R - (a2+b2) abc a 2 -b 2 abc a2b2 I /b 2 N = R I /b2 - I /a2 abc I 1 I Bo - AO' a 2 b 2 - a2 b2 a 2 b2 = R (a 2 - b 2) /(a 22 + /b2) 2 - r (B o - Ao) U Bo+Co - B I - CI' Since - Ux is the velocity function for the liquid W' filling the ellipsoid A = o, and moving bodily with it, the effective inertia of the liquid in the interspace is Ao+B1+C1 Bo+Co - B1 - C, If the ellipsoid is of revolution, with b=c, - 2 XBo - - C BI' and the Stokes' current function 4, can be written down (I) is (5) (7) (6) The velocity function of the liquid inside the ellipsoid A=o due to the same angular velocity will be = Rxy (a2 - b2)/(a2 + b2), (7) and on the surface outside _ N Bo -Ao c1)0xy abc 2 62' so that the ratio of the exterior and interior value of at the surface is ?o= Bo-Ao (9) 4)1 (a 2 -6 2)/(a2 + b) - (Bo - Ao)' and this is the ratio of the effective angular inertia of the liquid, outside and inside the ellipsoid X = o.

00This was the tribe of Kinda under the sway of the family of AO ul Murar, who came from the south.

00This can be done by placing at B an equal negative point-charge -q in the place which would be occupied by the optical image of A if PO were a mirror, that is, let -q be placed at B, so that the distance BO is equal to the distance AO, whilst AOB is at right angles to PO.

00The areas of the sides for which 0 and x=xo+2h, and of the section by the plane x=xo+h, may be found by Simpson's second formula; call these Ao and A2, and Al.

00x 2,2 - k 2 a2,o - h 2 a6,2 +ia4h2k2ao,0 5 2x - 1100-1,1 5 2x h2x k2x3,o+41-gh2k°0-1,o where ao,o is the total volume of the briquette.

00Also since dx has been stretched to +dy p&,(dx +dy) =po&odx or p&'(I +dy/dx) = (29) Substituting from (28) in (27) Y&a + P(2)U 2 (I + dy (3) 2 = p oc?oU 2, 0) and substituting from (29) in (30) Y&ao dx + pocZoU 2 + dx) = p owoU 2, (31) whence Yc = powoU2, or U2 = Y/ p, (32) where now p is the normal density of the rod.

00M?[aughfin .. ?Mor ° D Ao,;?:,K Frederick.

00Some of the political leaders escaped over the frontier - among them Prof. Thomas Garrigue Masaryk and Dr. Eduard Benes, who were subsequently to lead a success :3,500,000 English Miles 1, 0 ao Kilometres Czechoslovakia Frontier 1921 poilow stria-Hungary 191C411.

00Thus, if a ray of white light AO (fig.

00The last verse, with its two-fold greeting (6 14:nos, uera Tou 7rveuµar6s co y, 7) x6.pcs AO' upL ' v), shows unconsciously but plainly that, while the epistle professes to be a private letter to Timothy, it is in reality addressed to a wider circle, like 1 Tim.

00?P ?Op aMo ?a, n ao ?

00b, buccal mass; m, retractor muscles of the buccal mass; ov, ovary; od, oviduct; i, coils of intestines; ao, aorta; c', left auricle; c, ventricle.

00The English Miles ro ao 30 Albae -tbae Capitals of Counties County Boundaries Railways --i--- Canals Marshes ?_ - ' 1s3nge ?

00or negative according as they lie to the right or left of AO.

00of the vectors AB and AC (or BD), and of their sum AD, on a line perpendicular to AO, this is obvious.

00Thus a, negative rotation about OA may be regarded as a positive rotation about OA, the prolongation of AO.

00If)~, u, 1 be the components of momentum, we have X = AO, aT

00131 AO represents an upright axis or spindle; B a weightcalled a bob, suspended by rod OB from a horizontal axis at 0, carried by the vertical axis.

00Then, the crank standing at any angle with the line of stroke, draw LP at right angles to the connecting rod, PN at right angles to the line of stroke OB and NA at right angles to the connecting rod; then AO is the acceleration of the point B to the scale on which KO represents the acceleration of the point K.

00ao `v„ irehar s.

00Gomez Herrero, Diccionario-gwta legislativo espanol (5 vols., Madrid, 1901-1903); Estadistica de la administracidn de justicia en to criminal durante; Boleiin mensual de estadistica demo grdfica-sanitaria de la peninsula y islas adjacenies (Madrid, monthly); Estado general de la armada para el ao; C. Fernandez Duro, Armada espanola desde la union de los reinos de Castilla y de Leon (9 vols., Madrid, 1895I 903); Boletin oficial del minisierio de marina.

00nn, mn, nj, and sometimes to initial n: ao (a nn u m), dano (d a m n u m), nudo (n 0 d u m).

00dontinae and Desmognathinae), on the vomers, Ao, Left aortic Pterygoids and parasphenoid (some Pelobates), arch.

00aviation brigade elements deploy to the AO.

00The ROE will be prepared and issued by a higher headquarters before any of the aviation brigade elements deploy to the AO.

00Tu Mu's somewhat spiteful charge against Ts`ao Kung has already been considered elsewhere.

00Rev. (1889); Meliarakes, IvTopta Tou f ao X Iov NLeaLas Kal SeaIIor6Tov T1] S 'Hiretpov, pp. 539-627 (Athens, 1898).

00000 English Miles ao 20 30 an 5 c+ ?

00The wire being paid out without slack measures the actual distance and speed over the ground, and the engineer in charge is relieved of all anxiety in estimating the depth from the scattered soundings of the preliminary survey, or in calculating the retarding strain required to produce the specified slack, since the brakesman merely has to follow the indications of the instrument and regulate the strain so as to keep the pointer at the figure required - an easy task, seeing that the ratio of speed of wire and cable is not affected by the motion of the ship, whatever be the state of the sea, whereas the will I',/ OW= o a ' 30 30 ao.

00Every plant is constrained to carry Out its functions of germination, growth, nutrition, reproduction, &c., between certain limits of temperature, and somewhere between the extremes of these limits each function finds ao optimum temperature at which the working of the living machinery is at its best, and, other things being equal, any great departure from this may induce pathological conditions; and many disasters are due to the failure to provide such suitable temperaturese.g.

00ao; Dan.

00p. 256 (19 Ao).

00We have to multiply a01; -alas+a2 by ao, -aif32+a2 and we obtain ao (3 - aoal(f31N2 +01133) +aoa2(SI+13) -i-a?31a2 - aIa2(31 + 02) + al, 131+02 = b, 131132 = b t'i +s2 = 2bob2, and clearing of fractions R 1,5 = (a o b 2 - a2 b o) 2 + (a i b o - aobi) (aib2 - a2b1).

00Thus to obtain the resultant of aox 3 +a i x 2 +a 2 x+a 3, 4, =box2+bix+b2 we assume the identity (Box+Bi)(aox 3 +aix 2 +a2x+a3) = (Aox 2 +Aix+ A 2) (box2+bix+b2), and derive the linear equations Boa Ã‚° - Ac b o = 0, Boa t +B i ao - A 0 b 1 - A 1 bo =0, Boa t +B 1 a 1 - A0b2 - A1b1-A2bÃ‚° = 0, Boa3+Bla2 - A l b 2 -A 2 b 1 =0, B 1 a 3 - A 2 b 2 =0, = = (y l, y2,...ynl `x1, x2,...xnl for brevity.

00and by elimination we obtain the resultant ao 0 bo 0 0 al ao b1 bo 0 a 2 a i b 2 b 1 bo a numerical factor being disregarded.

00Put (aox 3 -}-a l x 2 +a 2 x +a 3) (box' +b1x'+b2) - (aox'3+aix'2+a2x'+a3) (box' + bix + b2) = 0; after division by x-x the three equations are formed aobcx 2 = aobix+aob2 =0, aobix 2 + (aob2+a1b1-a2bo) x +alb2 -a3bo = 0, aob2x 2 +(a02-a3bo)x+a2b2-a3b1 =0 and thence the resultant aobo ao aob2 aob 1 aob2+a1b1-a2bo alb2-a3b0 aob 2 a1b2 - a 3 bo a2b2 - a3b1 which is a symmetrical determinant.

001 X discriminant of f = ao X disct.

00This arises from the circumstance that the general operator Ao,a0aa1 + ialaa2 + 2a2 a 3 +...

00is transformed into the operator d 1 by the substitution (ac, al, a2, Ã¯¿½Ã¯¿½Ã¯¿½as, Ã¯¿½Ã¯¿½Ã¯¿½) _ (ao, Xoai, X 6 X i a 2, Ã¯¿½Ã¯¿½Ã¯¿½, XcX1..%s_las,Ã¯¿½Ã¯¿½Ã¯¿½), so that the theory of the general operator is coincident with that of the particular operator d1.

00For such functions remain unaltered when each root receives the same infinitesimal increment h; but writing x-h for x causes ao, a1, a 2 a3,...

00to become respectively ao, ai+hao, a2+2ha1, a 3 +3ha 2, ...

00ao -ialaan+l m !

00ao (m -2) m !

00being formed, the expansion being carried out, an operand ao or bo or co ...

00F(a ' a ' a, ...a) =r A F(ao, a1, a2,Ã¯¿½Ã¯¿½Ã¯¿½an), 0 1 2 n the function F(ao, al, a2,...an) is then said to be an invariant of the quantic gud linear transformation.

00;51, 2) = r F(ao, al, a2,...; xi, x2), the function F(a 01 a 1, a 2, ...

00Instead of a single quantic we may have several f(ao, a1, a2...; x1, x2), 4 (b o, b1, b2,...; x1, x2), ...

00For the substitution rr xl =A 11 +1 2 12, 52=A21+Ã¯¿½2E2, of modulus A1 Ã¯¿½i = (AlÃ¯¿½.2-A2Ã¯¿½1) = (AM), A 2 Ã¯¿½2 the quadratic form a k xi -1-2a 1 x i x 2 +a 2 4 = x =f (x), becomes A41 +2A1E16 =At = OW, where Ao = aoA i +2a1AiA2 +a2Az, _ _ A 1 = ao A lÃ¯¿½l +ai(A1/.22+A2Ã¯¿½1) +7,2X2/22, A2 = aoÃ¯¿½l +2a1Ã¯¿½1/Ã¯¿½2 +a 2Ã¯¿½2 Ã¯¿½ We pass to the symbolic forms a:= (aixi+a2x2) 2, A 2 = (A 151+ A 26) 2/ by writing for ao, al, a2 the symbols ai, a 1 a 2, a?

00A 1, A2 Ã¯¿½ Ai, A 1 A 2, A2 and then Ao = al Ai+2a1a2AIA2+a2 A2 - (a1A1+a2A2) 2 = a?, A l = (a 1 A 1 +a2A2) (alÃ¯¿½l +a2Ã¯¿½2) = aAaÃ¯¿½, A 2 = (alÃ¯¿½l +a2/-12) 2 = aM; so that A = aa l +2a A a u 152+aM5 2 = (aA6+a,e2)2; whence A1, A 2 become a A, a m, respectively and ?(S) = (a21+a,E2) 2; The practical result of the transformation is to change the umbrae a l, a 2 into the umbrae a s = a1A1 +a2A2, a Ã¯¿½ = a1/Ã¯¿½1 + a21=2 respectively.

00By similarly transforming the binary n ic form ay we find Ao = (aI A 1 +a2 A2) n = aAn A l = (alAi - I -a 2 A 2) n1 (a1Ã¯¿½1 +a2m2) = aa a Ã¯¿½ - A i n-1 A2, n-k k n-k k n-k k A = (al l+a2A2) (alÃ¯¿½1+a2Ã¯¿½2) = a A Ã¯¿½ =A 1 A2, so that the umbrae A1, A 2 are a A, a Ã¯¿½ respectively.

00For, if c(ao i ...x l, x 2) be a covariant of order e appertaining to a quantic of order n, t (T.

001 2) = (A /-?) ' (ao,...

00The Binary Quartic.-The fundamental system consists of five forms ax=f; (f,f')2=(ab) 2axbx=Ax; (f,f')4=(ab) 4= 2; (f, 0)1= (ao) azsi = (ab) 2 (cb) a:b x c5 =1; (f 4) 4 = (as) 4 = (6) 2 00 2 (ca) 2 = j, viz.

00l aa k -x 2 d d- = 0; Z(nk)ak+l adk - x ldd2=0; or in the form d d 52-x 2(7 =0, O - x1ax2 = 0; where 0 = ao d a l + 2a 1 -?...+na,,_id an, 0 = nal dao -?

00One advantage we have obtained is that, if we now write ao =o, and substitute a 8 _ 1 for a,, when s>o, we obtain d d aO da l +al da 2 +a2 da Ã¯¿½....+an_2dan_1 which is the form of SZ for a binary (n- Henceby merely diminishing each suffix in a seminvariant by unity, we obtain another seminvariant of the same degree, and of weight w-8, appertaining to the (n-I) ic. Also, if we increase each suffix in a seminvariant, we obtain terms, free from a 0, of some seminvariant of degree 8 and weight w+8.

00Hence, excluding ao, we may, in partition notation, write down the fundamental solutions of the equation, viz.

00(2), (3), (4),...(n), and say that with ao, we have an algebraically complete system.

00Observe that, if we subject any symmetric function the diminishing process, it becomes ao 1 - P2 (p2p3...)Ã¯¿½ Next consider the solutions of 0=o o which are of degree 0 and weight w.

00When the proper degree 0 is < w a factor ao -e must be of course understood.

00For Two Forms The Seminvariants Of Degrees I, I Are Enumerated By 1 Z, And The Only One Which Is Reducible Is Ao 0 Of Weight Zero; 1 Hence The Perpetuants Of Degrees I, I Are Enumerated By 11 1 Ã¯¿½ Z 1Zz' And The Series Is Evidently A O B 1 Aibo, A 0 B 2 A B A2Bo, A O B 3 A L B 2 A 2 B 1 A3Bo, One For Each Of The Weights I, 2, 3,..Ad Infin.

001 And The Actual Forms For The First Three Weights Are 1 Aobzo, (Ao B 1 A 1 B O) Bo, (A O B 2 A 1 2 0 Bo, Ao(B2, 3 A1B2 A2B1 A O (B L B 2 3B O B 3) A I (B 2 1 2B 0 B 2); Amongst These Forms Are Included All The Asyzygetic Forms Of Degrees 1, 1, Multiplied By Bo, And Also All The Perpetuants Of The Second Binary Form Multiplied By Ao; Hence We Have To Subtract From The 2 Generating Function 1Z And 1 Z Z2, And Obtain The Generating Function Of Perpetuants Of Degrees I, 2.

001 Z2' The First Perpetuant Is The Last Seminvariant Written, Viz.: A O (B O B 2 3B O B 3) A L (Bi 2B0B2), Or, In Partition Notation, Ao(21) B (1)A(2)B; And, In This Form, It Is At Once Seen To Satisfy The Partial Differential Equation.

00(0')B Denotes A Seminvariant, If 0, 0', Be Neither Of Them Unity, For, After Operation, The Terms Destroy One Another In Pairs: When 0, Must Be Taken To Denote Ao And So For 0'.

00For The Case In Hand, From The Simplest Perpetuant Of Degrees I, 2, We Derive The Perpetuants Of Weight W, Ao(21W 2)B A1(21"R 3) I A2(21" 4)B ..Ã¯¿½ Man 2(2)B, Ao(221W 4(B Al(221W 5)B A2 (221 " S)B ...

00Maw 4(22)B, Ao(231W 9B A, (221" 7)B A2(231W 8)B ...

00For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.

00(14) a (4322) b - (13) a (432 2 1) b + (12)a (432212) b - (1) a (432213)b +ao(432214)b, and thence the general form (1 A i + 4) a (4Ã¯¿½4 + 1.3 Ã¯¿½ 3 + 121 1, 2 + 2) b - ... ?ao(4Ã¯¿½4+13Ã¯¿½a+l2Ã¯¿½2+21 Al+4)b, due to the generating function 2 15 1 -z.

00For the quadratic aoxi +2a i x i x 2 +a 2 x, we have (i.) ax = 7/1x1+2aixix2-I-7/24, (ii.) xx=xi+xzi (ab) 2 =2(aoa2 - ai), a a = a o+712, _ (v.) (xa)ax= i'?- (a2 - ao)xix2 - aix2.

00This is the fundamental system; we may, if we choose, replace (ab) 2 by ab =a, 2, +2a1+a2 since the identity a a b b - a, = (ab) 2 shows the syzygetic relation (74+a 2) 2 - (ao +2a +Ã¯¿½2) = 2(aoa2 - ai).

00oe 000000 0 o co e io??,a _e ` ao O o' 3 4;Ã‚° :o o moo-:„..„:0-„,-----0 ?O 1/ // /O i Q n.

00Another example of a sequence is afforded by the successive convergents to a continued fraction of the form ao+ I I, al+ a2+Ã¯¿½ where ao,a 1, a 2, ...

00Accordingly, the optical distance from AoBo to A is represented by f (A +S/c)ds, the integration being along the original path Ao.

00A similar expression can be found for Q'P - Q"A; and thus, if Q' A =v, Q' AO = where v =a cos (0", we get - - -AQ' = a sin w (sin 4 -sink") - - 8a sin 4 w(sin cktan 4 + sin 'tan cl)').

00The grating at A and the eye-piece at 0 are rigidly attached to a bar AO, whose ends rest on carriages, moving on rails OQ, AQ at right angles to each other.

00Similarly, the inertia parallel to Oy and Oz is NW' - 1 B W', B C (b2 +-X, c 2 ab and A +C abc/ZP, Ao For a sphere a=b=c, Ao= Bo=Co =, 'a' = Q = = z, (9) U from (II), (16) so that the effective inertia of a sphere is increased by half the weight of liquid displaced; and in frictionless air or liquid the sphere, of weight W, will describe a parabola with vertical acceleration W - W', g (30) W+ aW Thus a spherical air bubble, in which W/W' is insensible, will begin to rise in water with acceleration 2g.

00= constant, _ ff 00 NdA N BA-AA X - JA (a' +X) (b 2 +A)P - abc' a2 -b2 ' and at the surface A = o, I I N Bo-A 0 N I R - (a2+b2) abc a 2 -b 2 abc a2b2 I /b 2 N = R I /b2 - I /a2 abc I 1 I Bo - AO' a 2 b 2 - a2 b2 a 2 b2 = R (a 2 - b 2) /(a 22 + /b2) 2 - r (B o - Ao) U Bo+Co - B I - CI' Since - Ux is the velocity function for the liquid W' filling the ellipsoid A = o, and moving bodily with it, the effective inertia of the liquid in the interspace is Ao+B1+C1 Bo+Co - B1 - C, If the ellipsoid is of revolution, with b=c, - 2 XBo - - C BI' and the Stokes' current function 4, can be written down (I) is (5) (7) (6) The velocity function of the liquid inside the ellipsoid A=o due to the same angular velocity will be = Rxy (a2 - b2)/(a2 + b2), (7) and on the surface outside _ N Bo -Ao c1)0xy abc 2 62' so that the ratio of the exterior and interior value of at the surface is ?o= Bo-Ao (9) 4)1 (a 2 -6 2)/(a2 + b) - (Bo - Ao)' and this is the ratio of the effective angular inertia of the liquid, outside and inside the ellipsoid X = o.

00This was the tribe of Kinda under the sway of the family of AO ul Murar, who came from the south.

00This can be done by placing at B an equal negative point-charge -q in the place which would be occupied by the optical image of A if PO were a mirror, that is, let -q be placed at B, so that the distance BO is equal to the distance AO, whilst AOB is at right angles to PO.

00The areas of the sides for which 0 and x=xo+2h, and of the section by the plane x=xo+h, may be found by Simpson's second formula; call these Ao and A2, and Al.

00x 2,2 - k 2 a2,o - h 2 a6,2 +ia4h2k2ao,0 5 2x - 1100-1,1 5 2x h2x k2x3,o+41-gh2kÃ‚°0-1,o where ao,o is the total volume of the briquette.

00Also since dx has been stretched to +dy p&,(dx +dy) =po&odx or p&'(I +dy/dx) = (29) Substituting from (28) in (27) Y&a + P(2)U 2 (I + dy (3) 2 = p oc?oU 2, 0) and substituting from (29) in (30) Y&ao dx + pocZoU 2 + dx) = p owoU 2, (31) whence Yc = powoU2, or U2 = Y/ p, (32) where now p is the normal density of the rod.

00M?[aughfin .. ?Mor Ã‚° D Ao,;?:,K Frederick.

00Some of the political leaders escaped over the frontier - among them Prof. Thomas Garrigue Masaryk and Dr. Eduard Benes, who were subsequently to lead a success :3,500,000 English Miles 1, 0 ao Kilometres Czechoslovakia Frontier 1921 poilow stria-Hungary 191C411.

00Thus, if a ray of white light AO (fig.

00The last verse, with its two-fold greeting (6 14:nos, uera Tou 7rveuµar6s co y, 7) x6.pcs AO' upL ' v), shows unconsciously but plainly that, while the epistle professes to be a private letter to Timothy, it is in reality addressed to a wider circle, like 1 Tim.

00It distinguishes prudence (4poinacs) and wisdom (ao,ia) as the respective virtues of deliberative and scientific reason; and on the whole its account of prudence (cf.

00?P ?Op aMo ?a, n ao ?

00b, buccal mass; m, retractor muscles of the buccal mass; ov, ovary; od, oviduct; i, coils of intestines; ao, aorta; c', left auricle; c, ventricle.

00The English Miles ro ao 30 Albae -tbae Capitals of Counties County Boundaries Railways --i--- Canals Marshes ?_ - ' 1s3nge ?

00or negative according as they lie to the right or left of AO.

00of the vectors AB and AC (or BD), and of their sum AD, on a line perpendicular to AO, this is obvious.

00Thus a, negative rotation about OA may be regarded as a positive rotation about OA, the prolongation of AO.

00If)~, u, 1 be the components of momentum, we have X = AO, aT

00131 AO represents an upright axis or spindle; B a weightcalled a bob, suspended by rod OB from a horizontal axis at 0, carried by the vertical axis.

00Then, the crank standing at any angle with the line of stroke, draw LP at right angles to the connecting rod, PN at right angles to the line of stroke OB and NA at right angles to the connecting rod; then AO is the acceleration of the point B to the scale on which KO represents the acceleration of the point K.

00ao `v„ irehar s.

00Gomez Herrero, Diccionario-gwta legislativo espanol (5 vols., Madrid, 1901-1903); Estadistica de la administracidn de justicia en to criminal durante; Boleiin mensual de estadistica demo grdfica-sanitaria de la peninsula y islas adjacenies (Madrid, monthly); Estado general de la armada para el ao; C. Fernandez Duro, Armada espanola desde la union de los reinos de Castilla y de Leon (9 vols., Madrid, 1895I 903); Boletin oficial del minisierio de marina.

00nn, mn, nj, and sometimes to initial n: ao (a nn u m), dano (d a m n u m), nudo (n 0 d u m).

00dontinae and Desmognathinae), on the vomers, Ao, Left aortic Pterygoids and parasphenoid (some Pelobates), arch.

00Tu Mu 's somewhat spiteful charge against Ts`ao Kung has already been considered elsewhere.

00Science Drivers for ASMs Currently implemented astronomical AO systems operate like auxiliary instruments separate from the main telescope optics.

00The AO acts as a fair and unbiased referee when people feel they have been badly treated.

00While the publisher was instructed by ESRB to request that retailers stop selling the Mature-labeled game until an AO sticker was available, the game has been spotted on retail shelves at stores including Fry's Electronics.

00Since many major retailers will not carry games with an AO rating, this can adversely affect a game's sales.

00After the disclosure that a hack could expose an explicit consensual sex scene in Grand Theft Auto: San Andreas, the game's rating was changed to AO for Adults Only from its previous Mature rating status.

00Instead, the ESRB gave the game an AO (Adults Only) rating because after a lengthy investigation, the game was found to have some hidden content that involved nudity and prostitution.

00Retailers immediately pulled the AO version from the shelves and replaced it with the toned down Mature version.

00Developers are apprehensive about putting video game nudity into their creations because it is proven that games with the Adults Only (AO) rating are poor performers.

00The current list of AO games is at 30 and you can view this list at Moby Games.

00A quick perusal of the titles and descriptions might make you realize that they probably didn't sell very well not because of the AO rating, but because they simply stunk.

00If you notice, the last AO game that was released was in 2005.

00There is no shortage of nudity and because the character models are so realistic, it's no surprise this game received its AO rating.

00Sure there were polygon babes riding BMX bikes, but the clips are what caused the controversy and the eventual AO rating.

00AO - Adults Only - Aimed at adults over the age of 17 only, these games may include prolonged scenes of violence, graphic sexual content and nudity.

00AO for Adults Only: No explanation needed.

00AO - Adults Only: These adult video games may be pornographic in nature and may contain excessive blood and gore.

00Very few games receive this rating, because Sony, Nintendo, and Microsoft all prohibit the sale of AO games on their respective consoles.

00If you loved Switched-on-Schoolhouse, (AO's computer-based learning curriculum) you may well love Monarch even more.

00Similar to motion picture ratings, the ESRB ratings range from EC (Early Childhood - appropriate for ages three and up) to AO (Adults Only - a rating that is rarely seen and not carried by most retailers).

00

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