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tan

Her hair sparkled in the sunlight against the dark tan of his hand.

227The prevailing colour is tan with large black spots.

147Thick dark lashes and a deep tan intensified the blue of his eyes, and his freshly shaven face had attractive angles.

65vertical, where Wh tan 0 = N = (c 2 - cl) c2 g2 tan 0, (6) (7) in which we have put k' 2 = ek 2, where E is a numerical factor depending on the shape.

53She couldn.t see the Sanctuary through her blurry eyes, just the blue of water and the tan sand beneath her hands.

54Every inch of her was firm from working outside, and the tan simply put a finishing touch to all of it.

54"I'll give you a whack at 'em," Hunter said as he pulled his tan Ford into the parking lot.

43To give a simple instance, hanging to the stereographic projection by putting tan 20=x, ill give a possible state of motion of the axis of the body; and the otion of the centre may then be inferred from (22).

43A young man in a tan jacket waited at the foot of the stairs looking ill at ease.

44As he spoke, he peeled off his shirt to reveal a whip-like, muscular upper body coated by a thin layer of tan skin.

32I was a lady for a long and lovely Sunday afternoon while a tan mare serenaded us with her tinkling bells as the runners wooshed along on the packed snow.

32Beyond where the compound ended, she saw the tan sands of the desert punctuated by short, round shrubs It's called Traveling.

32He had the same air of confidence, and the bronzed tan... but surely Alex would have said something.

21He wore light colors this day of tan, a shade that brought out the depth of honey in his skin.

21Shorty, you stay out of this or I'll tan your hide the way I should have done years ago.

21His strong profile was masculine without being rugged, and a healthy olive tan suggested an outdoor hobby.

21This light railway runs at a considerable elevation (some 700 ft.), commanding a view across the valley and lake of Tan y Bwlch.

213 tan 8, d l - I _ idlv j d23 d2/ I - 1d12H tan ©.

21Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.

21In a multiply connected space, like a ring, with a multiply valued velocity function ¢, the liquid can circulate in the circuits independently of any motion of the surface; thus, for example, 4) =mB=m tan - l y/x (5) will give motion to the liquid, circulating in any ring-shaped figure of revolution round Oz.

21If the cardboard scale upon which the beam of light is reflected by the magnetometer mirror is a flat one, the deflections as indicated by the movement of the spot of light are related to the actual deflections of the needle in the ratio of tan 20 to 0.

10If the distance of the mirror from the scale is equal to n scale divisions, and if a deflection 0 of the needle causes, the reflected spot of light to move over s scale divisions, we shall have s/n = tan 20 exactly, s/2n = tan 0 approximately.

10In the first quadrant there is no root after zero, since tan u> u, and in the second quadrant there is none because the signs of u and tan u are opposite.

10If the semi-angular aperture (w) be T 36, and tan 0' might be as great as four millions before the error of phase would reach 4X.

10The righting couple of the wedges of immersion and emersion will be ZwydA tan 8.y =w tan 0Zy 2 dA =w tan 0.Ak 2 ft.

10tan 0; but if weights inside the ship are raised to bring G above B, the righting couple is diminished by W.BG.

10tan 0, so that the resultant righting couple is W.GM.

10tan 8.

10(22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.

10If the direction of motion makes an angle 0' with Ox, tan B' = d0 !dam _ ?xy 2 = tan 20, 0 =-10', (9) dy/ y and the velocity is Ua2/r2.

10Taking two planes x = =b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U - Ua 2 r2 cos 20 +mr i sin 0) (Ua 2 r 2 sin 2 0+mr 1 cos 0) + pdy (- U+Ua 2 r 2 cos 2 0 +mr1 sin 0) (Ua 2 r 2 sin 2 0 -mr 1 cos 0) =2pdymUr '(cos 0 -a 2 r 2 cos 30), (8) and with b tan r =b sec this is 2pmUdo(i -a 2 b2 cos 30 cos 0), (9) and integrating between the limits 0 = 27r, the resultant, as before, is 27rpmU.

100= {(n +I)Ar" - where P. denotes the zonal harmonic of the nth order; also, in the exceptional case of =Ao cos 0, 4) = Ao/r; 4'= Bor, 49 = - Bo log tan 2B sh - lx/y.

100, 1, = -ZUa 3 sin e B/r; (13) and then =Ux(I+1a3/r2), 4=ZUa 3 cos 0/r2, -d r = Ua3 cos B, -d9=ZUa3 sin 0, so that, if the direction of motion makes an angle >G with Ox, tan (4y-0) =Z tan 0, tan =3 tan 0/(2-tan 2 e).

10tan 8.

100, 1, = -ZUa 3 sin e B/r; (13) and then =Ux(I+1a3/r2), 4=ZUa 3 cos 0/r2, -d r = Ua3 cos B, -d9=ZUa3 sin 0, so that, if the direction of motion makes an angle >G with Ox, tan (4y-0) =Z tan 0, tan =3 tan 0/(2-tan 2 e).

10Hotel guests may dine in the lounge decorated with dark mahogany furniture and chandeliers, accented with warm colors of brown, tan and orange.

10The off-the-shoulder style with its white lace made the most of her newly acquired tan, and the shiny black belt and full skirt made her waist look small.

11Bulldog, bulldog (miniature), mastiff, Great Dane, Newfoundland (black, white and black, or other than black), St Bernard (rough and smooth), Old English sheepdog, collie (rough and smooth), Dalmatian, poodle, bull terrier, white English terrier, black and tan terrier, toy spaniel (King Charles or black and tan, Blenheim, ruby or red and tricolour), Japanese, Pekingese, Yorkshire terrier, Maltese, Italian greyhound, chowchow, black and tan terrier (miniature), Pomeranian, pug (fawn and black), Schipperke, Griffon Bruxellois, foreign dogs (bouledogues frangais, elk-hounds, Eskimos, Lhasa terriers, Samoyedes and any other varieties not mentioned under this heading).

11On the 4th of May 1898 a sub-committee of the Kennel Club decided that the following breeds should be classified as "toy dogs": - Black and tan terriers (under 7 lb), bull terriers (under 8 lb), griffons, Italian greyhounds, Japanese, Maltese, Pekingese, poodles (under 15 in.), pugs, toy spaniels, Yorkshire terriers and Pomeranians.

11Bulldog, bulldog (miniature), mastiff, Great Dane, Newfoundland (black, white and black, or other than black), St Bernard (rough and smooth), Old English sheepdog, collie (rough and smooth), Dalmatian, poodle, bull terrier, white English terrier, black and tan terrier, toy spaniel (King Charles or black and tan, Blenheim, ruby or red and tricolour), Japanese, Pekingese, Yorkshire terrier, Maltese, Italian greyhound, chowchow, black and tan terrier (miniature), Pomeranian, pug (fawn and black), Schipperke, Griffon Bruxellois, foreign dogs (bouledogues frangais, elk-hounds, Eskimos, Lhasa terriers, Samoyedes and any other varieties not mentioned under this heading).

11the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

12His pupils were contracted by the bright sunlight and his light green eyes contrasted sharply with his bronze tan.

00One hearty soul was clothed in shorts, as if trying to wow his neighbors with an out of season, near full body tan.

00He was watching her intently and his face was pale under the tan.

00He looked elegant in a light gray suit that accentuated his dark tan.

00His eyes flashed darkly and his face went pale under the tan.

00His skin flushed under the dark tan.

00If w now relate to the edge of the grating, on which there are altogether n lines, no- = 2a sin w, and the value of the last term in (I o) becomes no- sin 3w sin O'tan 0', - 1 1 - 6 mnX sin' w tan 0'.

00The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

00(9) c 2 Ci If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan S = ird/nd = 2 d p/u, (10) '°If a denotes the density of the metal, and if the shell has a cavity homothetic with the external ellipsoidal shape, a fraction f of the linear scale; then the volume of a round shot being sird 3, and sird 3 x of a shot x calibres long W =*ird 3 x(I -f 3)v, (20) 2 Wki 2= 61rd 3 xo(I-f 5)Q, (21) Wk22=67rd3x 2 2+0 2(I - f5)Q.

00If p denotes the density of the air or medium W' = sird 3 xp, (23) W' I p __ W I -1 3 k12 I k22 x2 ±i a 2= 101-1 3 '111 2= 2 tan g S = Q (l - a) x 2+ I (26) in which a/p may be replaced by 800 times the S.G.

00of the metal, taking water as 800 times denser than air on the average, in round numbers, and formula (to) may be written n tan 6=ir, or n6=180, when 6 is a small angle, and given in degrees.

00SODERHAMN, a seaport of Sweden, in the district (tan) of Gefleborg, on an inlet of the Gulf of Bothnia, near the mouth of the Ljasne River, 183 m.

00The later poetry of the Augus tan age had ended in trifling dilettantism, for the continuance of which the atmosphere of the court was no longer favourable.

00The old state capitol, dating from 1839, is of considerable interest; in it were held the secession convention (1861), the "Black and Tan Convention" (1868), and the constitutional convention of 1890, and in it Jefferson Davis made his last speech (1884).

00Tantalum forms a sulphide, TaS 2, and two nitrides, TaN 2 and Ta3N5, have been described.

00(l) tan a = A .

00Now if the notch of the tan gent sight be carried to H' in order to lay on T, the fore-sight, and with it the axis, H will be moved to F', the line of fire will be HF'D', and the shot will strike T since D'T = DT.

00Then (as the difference of two triangles) area ABCD - (h cot 2 (h cot -a)2 2(cot ¢- cot 4) 2(cot +cot 0) (ii) If 0=0, this becomes tan area (h + a tan 0) 2 - a tan 0.

00cot Then volume of prismoid = length X If mini + m2n2 + 2 (m i ne + m270-3a 2 1 tan 0.

00This latter area is Obte -Datd = Abtg-Datd = 8h2 tan GTB - $h2 tan DAT.

00Hence, if the angle which the tangent at the extremity of the ordinate u 0 makes with the axis of x is denoted by fie, we have area from uo to u1= 2h(uo + ui) - -- i i h 2 (tan y l - tan t u 2 = Wu ' + u2) - 1 Tih 2 (tan 4,2 - tan um-1 t0 26 m, - 2 h(um-1 + um) i h (tan 4, m - and thence, by summation, A =C I - i i h 2 (tan - tan 1,1/o).

00It might be shown in the same way that A=Ti+ ih 2 (tan Yamtan 4) = T1 + [h2u]::.

00If we call this last resistance R, the voltage of the working dynamo V, and the current through the insulator C, then tan 0 = C/V = R.

00tan i = 2y/x.

00In the central and southern parts of the belt oak and hickory constitute valuable hard woods, and certain varieties of the former furnish quantities of tan bark.

00Me (Mother) tan (you) yu (live) ti (place) nai (where), or "Where is your mother ?"

00For some purposes it is preferable to retain the circular measure, i radians, as being undistinguishable from sin i and tan i when i is small as in direct fire.

00Now, since v sec i (54) di sec i dq C f(q sec i)' and multiplying by /dt or q, (55) dx C q sec i dq - f (q sec i)' and multiplying by dy/dx or tan i, (56) dy C q sec i tan dq - f (q sec i) ' also (57) di Cg dq g sec i .f (g sec i)' (58) d tan i C g sec i dq - q.

00f (q sec i)' from which the values of t, x, y, i, and tan i are given by integration with respect to q, when sec i is given as a function of q by means of (51).

00di g d tan i g dt - v cos i ' and now (53) dx d 2 y dy d2xdx Cif dt 2 dt dt2 _ - _ gdt' and this, in conjunction with (46) dy _ d y tan i = dx dt/dt' (47)di d 2 d d 2 x dx sec 2 idt = (ctt d t - at dt2) I (dt), reduces to (48) Integrating from any initial pseudo-velocity U, (60) du t _ C U uf(u) x= C cos n f u (u) y=C sin n ff (a); and supposing the inclination i to change from 0, to 8 radians over the arc.

00- tan B=C sec n [I(U) - I (u)], while, expressed in degrees, (73) 0°-8° =C cos n [D(U) - D(u)].

00S., 18 77): but this method requires n to be known with accuracy, as I% variation in n causes more than 1% variation in tan n.

00The difficulty is avoided by the use of Siacci's altitude-function A or A(u), by which y/x can be calculated without introducing sin n or tan n, but in which n occurs only in the form cos n or sec n, which varies very slowly for moderate values of n, so that n need not be calculated with any great regard for accuracy, the arithmetic mean 1(0+0) of ¢ and B being near enough for n over any arc 4)-8 of moderate extent.

00Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

00Now calculate the pseudo-velocity uo from =v 95 cos 4) sec n, and then, from the given values of 0 and 8, calculate u e from either of the formulae of (72) or (73): (82) I (u 9) - I (u0) tan 0 - tan 8 C sec n (83) D(ue) =D (uq5) 4)°-B° cos n' Then with the suffix notation to denote the beginning and end of the arc 0-0, mt e = C[Tum) - T (u0)], 5 ((x x9 1l 0.

00In direct fire the pseudo-velocities U and u, and the real velocities V and v, are undistinguishable, and sec n may be replaced by unity so that, putting y =o in (79), (88) tan 4) = C [I (V) - y-s] Also (89) tan 4 - tan S=C [I(V) - L(v)] so that (9 °) tan 1 3=C [1 -s.

00After 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 %.

00The logarithm is also a function of frequent occurrence in analysis, being regarded as a known and recognized function like sin x or tan x; but in mathematical investigations the base generally employed is not 10, but a certain quantity usually denoted by the letter e, of value 2.71828 18284 ...

00The general or typical coloration is, however, a rich tan upon the head, neck, body, outside of legs, and tail near the root.

00- N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in areal co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.

00If h be given, we can use c 2 +4h 2 =8ah, zh =c tan 4B to determine 0.

008 4 In modern trigonometrical notation, I +sec 0: tan 0 :: I : tan Z0.

00II) whose centre is 0, AC its chord, and HK the tangent drawn at the middle point of the arc and bounded by OA, OC produced, then, according to Archimedes, AMC AC. In modern trigonometrical notation the propositions to be compared stand as follows: 2 tan 20 >2 sin 28 (Archimedes); tan 10+2 sin 3B>0> 3 sin B (Snell).

00Even among the mere computers the series =tan -a tan' 0+1 tan' 0-..., specially known as Gregory's series, has ever since been a necessity of their calling.

00In 1699 Abraham Sharp, on the suggestion of Edmund Halley, took Gregory's series, and, putting tan 0=11/3, found the ratio equal to 1 112 (I { 5 32 - 7 33 +...), from which he calculated it correct to 71 fractional places.'

00Fautet de Lagny, still using tan 30°, advanced to the 127th place.'

00122) is as follows: - it/4 = tan 12 +tan '; +tan 1 s (Dase, 1844), 7r/4=4tan 1 - tan 11 +tan Ys (Rutherford), and Gregory's series were employed.'

00The Plant Stove differs in no respect from the greenhouse except in having a greater extent of hot-water pipes for the purpose, of securing a greater degree of heat, although, as the plants in stove houses often attain a larger size, and many of them require a bed of coco-nut fibre, tan or leaf mould to supply with bottom heat, b: !, b a somewhat greater elevation may perhaps be occasionally required in some of the houses.

00These regenerators are the essence of the Siemens or " regenerative furnace "; they are heat-traps, catching and storing by their -11, Ton Traver 7s 20 Tan Tra y.

00Tan BLACK ISLE, a district in the east of the county of Ross and Cromarty, Scotland, bounded N.

00They weave and dye several kinds of cloth, tan and dress leather and manufacture oil and soap. Without the assistance of the wheel the women produce a variety of pottery utensils, often of very graceful design, and decorated with patterns in red and black.

00This appears to be the beginning of a new anticlinal which has altered the levels of the Balkh plain, and is indicative of those elevating processes which Afghan tan, together with the minor dependencies of the provinces.

00one road crosses the mountains to Shang Chow, and on to the Tan river, an affluent of the Han-kiang, and is thus connected with the trade of the Yangtsze-kiang; and another leads to Han-chung Fu and Sze-ch'uen.

00decurrens, tan wattle, and A.

00These two forces X, Y, may be combined into a single resultant R making an angle 4> with Ox, provided X = Rcos4,, Y = Rsin4~, (2) whence R2 = X~ + Yi, tan 4) = Y I X.

00Hence the line will be a nullline provided tan 8=k/r,.

00It appears also from (II) that the null-lines whose distance from the central axis is r are tangent lines to a system of helices of slope tan 1(r/k); and it is to be noticed that these helices are left-handed if the given wrench is righthanded, and vice versa.

00Hence S=W tan OW.

00If the chain be uniform we have W = ws, where s is the arc AP: hence ws=To tan ~.

00This leads to U U0 g~ Vi V2+uof tan V=tan1V_V, x= ~-~log V2+u2 (27)

00provided R = (j,i en)1 +koi1l I, tan ~i ~ (36)

00If a be the inclination of the instantaneous axis to the axis of symmetry, (3 the inclination of the latter axis to the invariable line, we have rcosfl=Cw cos a, r sin ~3 = Aw sin a, (6) whence tan ~ =~ tan a.

00The ratio of the two components of that velocity is = p/2lrr = tan 0.

00tts value at intermediate instants is given by the following equations: let ~,, 4f be the angles respectively made by the central planes of the forks and shafts with the plane OCiC, at a given instant; then cos 0=tan 4~ tan ~,)

00af d4e tan ~,+ cot 4i~ ~ (40) aj d~i tan ~1+cot ti)

00Let A be any origin, and let Ac represent the acceleration of the b point C, Ct the radial acceleration of B about C which must be in a direction parallel to BC, and tb the tan gential acceleration of B about C, C

00R=fN==N tan q5=T sin 4, S ~5

00He then tried to win recognition as dukes of Aquitaine for the sons of his wife Agnes by William the Great, who were still minors, but Fulk Nerra promptly took up arms to defend his suzerain William the Fat, from whom he held the Loudunois and a tan g S h= - Saintonge in fief against his son.

00Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.

008, we have O'Q'/OQ = a' tan w' la tan w = 1/N, where N is the " scale " or magnification of the image.

00For N to be constant for all values of w, a' tan w'/ a tan w must also be constant.

00tan w'/ tan w=a constant.

00Trans., 1830, 3, p. 1) is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named " symmetrical or holosymmetrical objectives "), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w'/ tan w= 1.

00von Rohr showed that for systems fulfilling neither the Airy nor the Bow-Sutton condition, the ratio a' tan w' la tan w will be constant for one distance of the object.

00By putting =x 2 /4 for x in F(o,x) and F(i,x), and putting at the same time y =1/2, we obtain x 2 x 2 x2 x 2 x2 tan x x x tanh x x x x I - 3 - 5-7-...

00After speaking of Dositheus the Samari tan, who persuaded some of his countrymen that he was the Christ prophesied by Moses, he goes on to say: " Also Simon the Samaritan, a magician, wished to filch away some by his magic. And at the time indeed he succeeded in his deception, but now I suppose it is not possible to find 30 Simonians altogether in the world; and perhaps I have put the number higher than it really is.

00Finally, if a is made extremely small, so that practically tan (A = Zl/Gs, the sensitiveness is independent of the amount weighed by the balance.

00For the weighing of very small quantities with balances of great delicacy, the following method is adopted: - If the balance be in perfect adjustment, and 1 be the length of each arm, and w a very minute difference of the weights in the two scale-pans, by which the beam is deflected from the horizontal by a very small angle (/), it can easily be shown that tan 0, or 4), varies as w XI.

00If W be the weight in each pan when the goods-pan commenced to sink, / the length of each arm, m the distance of the fulcrum below the line joining the end knife-edges, and 13 the angle at the fulcrum which defines the range of sway of the beam, it can easily be shown that w, the ad - ditional weight required in the weights-pan to enable the goods-pan to rise from its stop, is given by the equation w =W 2m tan, 3/L m tan S.

00which is needed in the weights-pan to enable the goods-pan to rise off its stop, is given by the equation w= W 2m tan 6(3-0)/L - m tan 6(3-0).

00The condition that must exist in order that the balance may weigh correctly for all positions of the weight W is w = o, or tan 0 = that is, the stay KG must be adjusted parallel to the line joining the points A and C. From the equation for w, it is seen that the larger h is the smaller w will be.

00The double tan larities - gent or inflection; gent; arising as follows: 1.

00The cartesian equation, when A is the origin and AB = 2a, is y 2 (2a - x) =x 8; the polar equation is r= 2a sin 0 tan 0.

00such as ad-ib where i=1/ - i, the "argument" (or "amplitude") is the angle 0 given by tan 0 = b/a.

00V = 3rA = 2 1 4 / 3 n F tan -II cot e a = 2 I 1 3 n F cot e a cos a/ (sin' a -cos t 13) 2 R =1-/ tan IT tan 0=1/ sin 13/(sin e a-cost r =Zl tan 21 cot a= Il cot a cos 13/(sin" a -cos' (3)L 1 In the language of Proclus, the commentator: " The equilateral triangle is the proximate cause of the three elements, ` fire,' ` air ' and ` water '; but the square is annexed to the ` earth.'

00This was supplied by Fresnel, who, starting from a mechanical hypothesis, showed by ingenious but not strictly dynamical reasoning that if the incident stream have unit amplitude, that of the reflected stream will be - sin (i - r) /sin (i -{- r) or tan (i - r) /tan (i -{- r), according as the incident light is polarized in or perpendicularly to the plane of incidence i, r, being the angles of incidence and refraction connected by the formula sin i =,u sin r.

00At normal incidence the intensity of the reflected light, measured by the square of the amplitude, is { (µ -1) /(µ+ I) } 2 in both cases; but whereas in the former the intensity increases uniformly with i to the value unity for i =90°, in the latter the intensity at first decreases as i increases, until it attains the value zero when i -Fr = 90°, or tan i =,u - the polarizing angle of Brewster - and then increases until it becomes unity at grazing incidence.

00Hence if 1 3 be the angle between the plane of incidence and that in which the reflected light is polarized tan (3= - tan a cos (i+r)/cos (i - r).

00Applying this interpretation to the formulae given above, it follows that when the incident light is polarized at an azimuth a to the plane of incidence and the second medium is the less refracting, the reflected light at angles of incidence exceeding the critical angle is elliptically polarized with a difference of phase A between the components polarized in the principal azimuths that is given by tan (A/2) =cot i l l (1 - µ 2 cosec 2 i).

00Solving for cot e i we obtain 2 cot 2 i= (p 2 -1) 2 {(p2 - tan2 (7r - A)/4) {p - cot2 - A)/411, and since tan { (ir - A)/4-} is less than unity, p must exceed cot {Or - A)/41 if cot 2 i is to be real.

00ConsonantsFinal I readily disappears after nor 1 (tan, t a n t U In; aman, venin, pantin, for amant, venint, &c.; mai, rn u I t u in; ocul, o.c u 1 t u m); the reappears in composition before a vowel (Jon, assimilation to past participles in it.

00Old Portuguese the nasal vowel or diphthon~ was not as now marked by the lii (__), but was expressed indifferently and without regard to the etymology by m or n: bern (b e n e), tan (t a n t u m), disserom (dixerunt), sermom (sermonem).

00Since H' P = F 0, = y, from the focal length of the simple microscope, the visual angle w' is given by tan w'/y=I/f'=V, (I) in which f', = H' F', is the image-side focal length (see Lens).

00I) tan w = y/l, where l = i o in., whilst the apparent size of the object viewed through the magnifying glass would result from the formula (I) tan w' = y/f.

00Consequently the number of diameters will be N = tan w'/tan w = y/f.

00distance, it follows (to him) the apparent size is tan w =y14; and to secure convenient vision through the lens the short-sighted person would bring the object to such a distance that a virtual, magnified image would be projected in his punctum remotum.

00The apparent size of the object seen through the lens is then tan w' = y/f.

00focus, is here N = tan w'/tan w = y/f.4/y=4/f=4 Thus, while a lens of i in.

00The image viewed through the eyepiece appears then to the observer under the angle w", and as with the single microscope tan w" = I /f 2 ' (4) where f' 2 is the image-side focal length of the eyepiece.

00If we replace y' in equation (4) by the value given by (3), we obtain tan w"/ y i/f2"=V, (5) the magnification of the complete microscope.

00i that the apparent size is tan w =3/11.

00If this value of y be inserted in equation (5), we obtain the magnification number of the compound microscope N =tan w"/ tan w =Ol/f i 'f 2 ' =Vl.

00By substituting y, the size of the object, for d, the smallest value which a single object can have in order to be analysed, and the angle w' by 2', we obtain the magnifying power and the magnification number: V2 = tan w'Id= 2A tan 2'/X; N2 = 2Al tan 2'/A; where 1 equals the sight range of io in.

00The magnification and magnifying number which are most necessary for a microscope with an objective of a given aperture can then be calculated from the formulae: V4 = 2A tan 4'/X; N4 = 2Al tan 4'/A.

00The sine-condition is in contrast to the tangent-condition, which must be regarded as the point-by-point representation of the whole object-space in the image-space (see Lens), and according therefore the equation n tan u/tan u' = C must exist.

00Large tanneries were attracted to the state, soon after the Civil War, by the abundance of tan bark in the forests, and the cheapness of labour.

00Thick dark lashes and a deep tan intensified the blue of his eyes, and his freshly shaven face had attractive angles.

00Her hair sparkled in the sunlight against the dark tan of his hand.

00Even though her skin now had a healthy tan, the sun was doing its best to burn it.

00His pupils were contracted by the bright sunlight and his light green eyes contrasted sharply with his bronze tan.

00As he spoke, he peeled off his shirt to reveal a whip-like, muscular upper body coated by a thin layer of tan skin.

00He had the same air of confidence, and the bronzed tan... but surely Alex would have said something.

00The off-the-shoulder style with its white lace made the most of her newly acquired tan, and the shiny black belt and full skirt made her waist look small.

00She couldn.t see the Sanctuary through her blurry eyes, just the blue of water and the tan sand beneath her hands.

00He wore light colors this day of tan, a shade that brought out the depth of honey in his skin.

00I was a lady for a long and lovely Sunday afternoon while a tan mare serenaded us with her tinkling bells as the runners wooshed along on the packed snow.

00One hearty soul was clothed in shorts, as if trying to wow his neighbors with an out of season, near full body tan.

00He was watching her intently and his face was pale under the tan.

00"I'll give you a whack at 'em," Hunter said as he pulled his tan Ford into the parking lot.

00A young man in a tan jacket waited at the foot of the stairs looking ill at ease.

00He looked elegant in a light gray suit that accentuated his dark tan.

00His eyes flashed darkly and his face went pale under the tan.

00His skin flushed under the dark tan.

00Shorty, you stay out of this or I'll tan your hide the way I should have done years ago.

00Every inch of her was firm from working outside, and the tan simply put a finishing touch to all of it.

00His strong profile was masculine without being rugged, and a healthy olive tan suggested an outdoor hobby.

00Beyond where the compound ended, she saw the tan sands of the desert punctuated by short, round shrubs It's called Traveling.

00A spray tanning room with a fantasy tan spray booth.

00brindle coats and black and tan coats are not allowed in show dogs.

00The oak carvings were executed by Mary Oakley of Plas Tan y Bwlch.

00Top up the tan on deck and sip cocktails by the pool.

00Wang Kiu applied the Tan sau hit from the wooden dummy to finish the fight fast.

00To maintain your color, moisturize every day and use a tan extender.

00While swimming and catching a tan [okay, sunburn ], I met some fellow travelers from London.

00Body shop cocoa butter as it makes your tan shine and you don't get flaky.

00The colors desired are self-colours in all shades of red, wheaten, tan, grizzle or black, white is not desired.

00The coat should be black and tan, blue and tan, red, wheaten, red grizzle, liver, blue or black.

00growgrew particularly fond of the automatic mirror lights, which I swear made me look as if I had a healthy tan.

00Up the sail goes, colorless in the early half-light, a tan gunter lug, on a honey-coloured wooden spar.

00He was wearing a black boiler suit and he had a tan colored leather holster around his waist on the left side.

00hourglass pattern of tan and gray on the flanks.

00Tan Lei (Warwick) Orbits correspondence in parabolic implosion.

00Starship Troopers isn't going to tell you how to tan leather with urine, now is it?

00Comes in a tan leather carry case with internal speaker.

00lengthen the duration of your tan.

00lily-white skin with a light Mediterranean tan whilst leaving all the other colors in the shot true.

00For those who yearn for a tan, a safer method is to use tanning lotions.

00You should always wear a good sun tan lotion.

00Their coats are white with black or tan markings or can be a combination of these.

00And this is the reason why some people tan faster than others - we form melanin at differing rates.

00The ratio of loss and storage modulus, tan d, is also reported.

00Increased pigmentation of the skin (like a sun tan) is common in Addison's disease.

00applying a tan remover such as San Tropez Self Tan Remover within four hours of applying the solution removed it instantly.

00Top up your tan while sipping free sangria and watching our belly flop competition.

00The private solarium will ensure you go home with a tan.

00Abu'l-Wafa and Abu Nasr Mansur both applied spherical geometry to astronomy and also used formulas involving sin and tan.

00A spray tanning room with a fantasy tan spray booth.

00Watch out for the fire corals in shallow water these creamy tan or mustard colored corals can give a nasty sting.

00sun tan cream before I could relax and enjoy myself.

00There are many salons where you can get fake tan applied professionally.

00For those seeking an all-over tan there is the beach at Costa Natura.

00For a totally natural-looking tan in just one hour!

00Pot of 100 tablets said to give you a ' golden tan all over ' without the damaging effects of the sun!

00tan lotion a December year end would make more sense than a June year end.

00tan leather carry case with internal speaker.

00tan markings or can be a combination of these.

00tan interior, with the covered roll hoops.

00It being April you'll probably even get a sun tan too!

00Here there is jam tan, we are all fine.

00It can be used anywhere where you want to remove any excess self tan.

00For those who yearn for a tan, a safer method is to use tanning lotions.

00The leftmost column is column 0. TAN A function returning the tangent of its radian argument.

00unemployed for a while, don't feel sorry for me cos I had a great tan last summer.

00Girls and guys alike look rather out of place with their rather unnatural dark tan on faces and hands.

00There's nothing wrong this summer with carrying a tan leather valise with mustard patent sandals.

00wheaten, tan, grizzle or black, white is not desired.

00"Napier's analogies" are the four formulae - tan (A +B) cos = cos l(a - b) cotzC, tan2(A - B) - sin(a - b)cot2C; a (a+b) sine (a+b) tan a(a +b) = cos(A - B) tan1c, tan2(a - b) = s in(A - B) tan2c.

00This light railway runs at a considerable elevation (some 700 ft.), commanding a view across the valley and lake of Tan y Bwlch.

00Given the area A of the plane between the two horizontal contours, the height h of the upper above the lower contour, the length of the upper contour 1, and the area of the face presented by the edge of the upper stratum l.h = A 1, the slope a is found to be tan a = h.l I (A - A i); hence its superficies, A = A2 sec a.

00- Bloodhound, otterhound, foxhound, harrier, beagle, basset hound (smooth and rough), dachshund, greyhound, deerhound, Borzoi, Irish wolfhound, whippet, pointer, setter (English, Irish and black and tan), retriever (flat-coated, curlycoated and Labrador), spaniel (Irish water, water other than Irish, Clumber, Sussex, field, English springer, other than Clumber, Sussex and field: Welsh springer, red and white and Cocker); fox terriers (smoothand wire-coated); Irish terrier, Scotch terrier, Welsh terrier, Dandie Dinmont terrier, Skye terrier (prick-eared and drop-eared), Airedale terrier and Bedlington terrier.

00On the 4th of May 1898 a sub-committee of the Kennel Club decided that the following breeds should be classified as "toy dogs": - Black and tan terriers (under 7 lb), bull terriers (under 8 lb), griffons, Italian greyhounds, Japanese, Maltese, Pekingese, poodles (under 15 in.), pugs, toy spaniels, Yorkshire terriers and Pomeranians.

00The abolition of the cropping of the ears of Great Danes, bull terriers, black and tan terriers, white English terriers, Irish terriers and toy terriers, in 1889 gained the approval of all humane lovers of dogs, and although attempts have been made to induce the club to modify the rule which prohibits the exhibition of cropped dogs, the practice has not been revived; it is declared, however, that the toy terriers and white English terriers have lost such smartness by the retention of the ears that they are becoming.

00The colour is black or tan, and the hair of the face, body and tail is close and curly, although wavy-coated strains exist.

00The prevailing colour is tan with large black spots.

00kesKK uu tlo tan o / ?

00M/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.

00We get therefore M 2 = MH X M/H = 27r 2 A(d 2 - l 2) 2 tan 0/t 2 d (42) s H 2 =Mhxh/M = 87r 2 Ad/tt 2 (d 2 -1 2) 2 tan B} (43) When a high degree of accuracy is required, the experiments and calculations are less simple, and various corrections are applied.

00Let 0 be the angle which the standard magnet M makes with the meridian, then M'/R = sin 0, and M/R = cos 0, whence M' = M tan 0.

00The direction of the resultant field of force will then make, with that of H E, an angle 0, such that Hp/H E tan 0, and the suspended needle will be deflected through the same angle.

00We have therefore HP=HE tan 0.

00We then have approximately for the field at M due to the rod 4 HP= (dm1)2 (d + 1) = m (d 2 _ M Therefore 2m1= = (d2 - 12)2Ht, - (d2-12)2HEtan 0 2d 2d (44) M (d2-12)2HE (45) And I = v - 2dv tan 0, whence we can find the values of I which correspond to different angles of deflection.

00d3H P = d3H And I = v tan B.

003 tan 8, d l - I _ idlv j d23 d2/ I - 1d12H tan ©.

00If the cardboard scale upon which the beam of light is reflected by the magnetometer mirror is a flat one, the deflections as indicated by the movement of the spot of light are related to the actual deflections of the needle in the ratio of tan 20 to 0.

00that tan 20 =2 tan 0.

00If the distance of the mirror from the scale is equal to n scale divisions, and if a deflection 0 of the needle causes, the reflected spot of light to move over s scale divisions, we shall have s/n = tan 20 exactly, s/2n = tan 0 approximately.

00We may therefore generally substitute s/2n for tan 0 in the various expressions which have been given for I.

00In the first quadrant there is no root after zero, since tan u> u, and in the second quadrant there is none because the signs of u and tan u are opposite.

00If w now relate to the edge of the grating, on which there are altogether n lines, no- = 2a sin w, and the value of the last term in (I o) becomes no- sin 3w sin O'tan 0', - 1 1 - 6 mnX sin' w tan 0'.

00If the semi-angular aperture (w) be T 36, and tan 0' might be as great as four millions before the error of phase would reach 4X.

00The cartesian equation referred to the axis and directrix is y=c cosh (x/c) or y = Zc(e x / c +e x / c); other forms are s = c sinh (x/c) and y 2 =c 2 -1-s 2, being the arc measured from the vertex; the intrinsic equation is s = c tan The radius of curvature and normal are each equal to c sec t '.

00Suppose the ship turns about an axis through F in the water-line area, perpendicular to the plane of the paper; denoting by y the distance of an element dA if the water-line area from the axis of rotation, the change of displacement is EydA tan 8, so that there is no change of displacement if EydA = o, that is, if the axis passes through the C.G.

00The righting couple of the wedges of immersion and emersion will be ZwydA tan 8.y =w tan 0Zy 2 dA =w tan 0.Ak 2 ft.

00tons, (4) w denoting the density of water in tons/ft.', and W =wV, for a displacement of V ft.3 This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BB 1 =wAk 2 tan 8, (5) BM =BB 1 cot B=Ak e /V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak e the moment of inertia of the water-line area about an axis through F, perpendicular to the plane of displacement.

00tan 0; but if weights inside the ship are raised to bring G above B, the righting couple is diminished by W.BG.

00tan 0, so that the resultant righting couple is W.GM.

00(22) Conjugate functions can be employed also for the motion of liquid in a thin sheet between two concentric spherical surfaces; the components of velocity along the meridian and parallel in colatitude 0 and longitude A can be written d¢_ i _ d4, I dip _ dy (13) d8 sin - 0 dX' sin 0 dX de' and then = F (tan O.

00If the direction of motion makes an angle 0' with Ox, tan B' = d0 !dam _ ?xy 2 = tan 20, 0 =-10', (9) dy/ y and the velocity is Ua2/r2.

00Taking two planes x = =b, and considering the increase of momentum in the liquid between them, due to the entry and exit of liquid momentum, the increase across dy in the direction Oy, due to elements at P and P' at opposite ends of the diameter PP', is pdy (U - Ua 2 r2 cos 20 +mr i sin 0) (Ua 2 r 2 sin 2 0+mr 1 cos 0) + pdy (- U+Ua 2 r 2 cos 2 0 +mr1 sin 0) (Ua 2 r 2 sin 2 0 -mr 1 cos 0) =2pdymUr '(cos 0 -a 2 r 2 cos 30), (8) and with b tan r =b sec this is 2pmUdo(i -a 2 b2 cos 30 cos 0), (9) and integrating between the limits 0 = 27r, the resultant, as before, is 27rpmU.

000= {(n +I)Ar" - where P. denotes the zonal harmonic of the nth order; also, in the exceptional case of =Ao cos 0, 4) = Ao/r; 4'= Bor, 49 = - Bo log tan 2B sh - lx/y.

00In a multiply connected space, like a ring, with a multiply valued velocity function ¢, the liquid can circulate in the circuits independently of any motion of the surface; thus, for example, 4) =mB=m tan - l y/x (5) will give motion to the liquid, circulating in any ring-shaped figure of revolution round Oz.

006, n ei„s /c =tan 0, ch (z7rs/c) sin 20 = I, (4) sh 27rx/c = cot 0, sh 27ry /c = tan B, sh 27rx/c sh irry/c = I, ei r (x+Y)l ei rxlc +ei.Y/c +I.

00To give a simple instance, hanging to the stereographic projection by putting tan 20=x, ill give a possible state of motion of the axis of the body; and the otion of the centre may then be inferred from (22).

00vertical, where Wh tan 0 = N = (c 2 - cl) c2 g2 tan 0, (6) (7) in which we have put k' 2 = ek 2, where E is a numerical factor depending on the shape.

00the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.

00(9) c 2 Ci If the shot is moving as if fired from a gun of calibre d inches, in which the rifling makes one turn in a pitch of n calibres or nd inches, so that the angle S of the rifling is given by tan S = ird/nd = 2 d p/u, (10) 'Ã‚°If a denotes the density of the metal, and if the shell has a cavity homothetic with the external ellipsoidal shape, a fraction f of the linear scale; then the volume of a round shot being sird 3, and sird 3 x of a shot x calibres long W =*ird 3 x(I -f 3)v, (20) 2 Wki 2= 61rd 3 xo(I-f 5)Q, (21) Wk22=67rd3x 2 2+0 2(I - f5)Q.

00If p denotes the density of the air or medium W' = sird 3 xp, (23) W' I p __ W I -1 3 k12 I k22 x2 ±i a 2= 101-1 3 '111 2= 2 tan g S = Q (l - a) x 2+ I (26) in which a/p may be replaced by 800 times the S.G.

00of the metal, taking water as 800 times denser than air on the average, in round numbers, and formula (to) may be written n tan 6=ir, or n6=180, when 6 is a small angle, and given in degrees.

00SODERHAMN, a seaport of Sweden, in the district (tan) of Gefleborg, on an inlet of the Gulf of Bothnia, near the mouth of the Ljasne River, 183 m.

00The later poetry of the Augus tan age had ended in trifling dilettantism, for the continuance of which the atmosphere of the court was no longer favourable.

00The old state capitol, dating from 1839, is of considerable interest; in it were held the secession convention (1861), the "Black and Tan Convention" (1868), and the constitutional convention of 1890, and in it Jefferson Davis made his last speech (1884).

00Tantalum forms a sulphide, TaS 2, and two nitrides, TaN 2 and Ta3N5, have been described.

00(l) tan a = A .

00Now if the notch of the tan gent sight be carried to H' in order to lay on T, the fore-sight, and with it the axis, H will be moved to F', the line of fire will be HF'D', and the shot will strike T since D'T = DT.

00Then (as the difference of two triangles) area ABCD - (h cot 2 (h cot -a)2 2(cot ¢- cot 4) 2(cot +cot 0) (ii) If 0=0, this becomes tan area (h + a tan 0) 2 - a tan 0.

00cot Then volume of prismoid = length X If mini + m2n2 + 2 (m i ne + m270-3a 2 1 tan 0.

00This latter area is Obte -Datd = Abtg-Datd = 8h2 tan GTB - $h2 tan DAT.

00Hence, if the angle which the tangent at the extremity of the ordinate u 0 makes with the axis of x is denoted by fie, we have area from uo to u1= 2h(uo + ui) - -- i i h 2 (tan y l - tan t u 2 = Wu ' + u2) - 1 Tih 2 (tan 4,2 - tan um-1 t0 26 m, - 2 h(um-1 + um) i h (tan 4, m - and thence, by summation, A =C I - i i h 2 (tan - tan 1,1/o).

00It might be shown in the same way that A=Ti+ ih 2 (tan Yamtan 4) = T1 + [h2u]::.

00If we call this last resistance R, the voltage of the working dynamo V, and the current through the insulator C, then tan 0 = C/V = R.

00tan i = 2y/x.

00In the central and southern parts of the belt oak and hickory constitute valuable hard woods, and certain varieties of the former furnish quantities of tan bark.

00Me (Mother) tan (you) yu (live) ti (place) nai (where), or "Where is your mother ?"

00For some purposes it is preferable to retain the circular measure, i radians, as being undistinguishable from sin i and tan i when i is small as in direct fire.

00Now, since v sec i (54) di sec i dq C f(q sec i)' and multiplying by /dt or q, (55) dx C q sec i dq - f (q sec i)' and multiplying by dy/dx or tan i, (56) dy C q sec i tan dq - f (q sec i) ' also (57) di Cg dq g sec i .f (g sec i)' (58) d tan i C g sec i dq - q.

00f (q sec i)' from which the values of t, x, y, i, and tan i are given by integration with respect to q, when sec i is given as a function of q by means of (51).

00di g d tan i g dt - v cos i ' and now (53) dx d 2 y dy d2xdx Cif dt 2 dt dt2 _ - _ gdt' and this, in conjunction with (46) dy _ d y tan i = dx dt/dt' (47)di d 2 d d 2 x dx sec 2 idt = (ctt d t - at dt2) I (dt), reduces to (48) Integrating from any initial pseudo-velocity U, (60) du t _ C U uf(u) x= C cos n f u (u) y=C sin n ff (a); and supposing the inclination i to change from 0, to 8 radians over the arc.

00(63) 0-0 =Cg cos n f u Au), 6 (4) tan 4 - tan g =Cg sec ?if u f(u)' But according to the definition of the functions T, S, I and D of the ballistic table, employed for direct fire, with u written for v, (65) ('u du _ du T(U) - T(u), J uf(??) - f g (66) ru du J f(u) (67) g du f uf(u) and therefore (68) t=C [T(U) - T(u)], (69) x = C cos n [S(U) - S(u)1, (70) y =C sin n [S(U) - S(u)], 0-8= C cos n [I (U) - I (u)], (72) tan 0.

00- tan B=C sec n [I(U) - I (u)], while, expressed in degrees, (73) 0Ã‚°-8Ã‚° =C cos n [D(U) - D(u)].

00It will be noticed that n cannot be exactly the same in all these equations; but if n is the same in (69) and (74) y/x = tan n, so that n is the inclination of the chord of the arc of the trajectory, as in Niven's method of calculating trajectories (Proc. R.

00S., 18 77): but this method requires n to be known with accuracy, as I% variation in n causes more than 1% variation in tan n.

00The difficulty is avoided by the use of Siacci's altitude-function A or A(u), by which y/x can be calculated without introducing sin n or tan n, but in which n occurs only in the form cos n or sec n, which varies very slowly for moderate values of n, so that n need not be calculated with any great regard for accuracy, the arithmetic mean 1(0+0) of ¢ and B being near enough for n over any arc 4)-8 of moderate extent.

00Now taking equation (72), and replacing tan B, as a variable final tangent of an angle, by tan i or dyldx, (75) tan 4) - dam= C sec n [I(U) - I(u)], and integrating with respect to x over the arc considered, (76) x tan 4, - y = C sec n (U) - f :I(u)dx] 0 But f (u)dx= f 1(u) du = C cos n f x I (u) u du g f() =C cos n [A(U) - A(u)] in Siacci's notation; so that the altitude-function A must be calculated by summation from the finite difference AA, where (78) AA = I (u) 9 = I (u) or else by an integration when it is legitimate to assume that f(v) =v m lk in an interval of velocity in which m may be supposed constant.

00Now calculate the pseudo-velocity uo from =v 95 cos 4) sec n, and then, from the given values of 0 and 8, calculate u e from either of the formulae of (72) or (73): (82) I (u 9) - I (u0) tan 0 - tan 8 C sec n (83) D(ue) =D (uq5) 4)Ã‚°-BÃ‚° cos n' Then with the suffix notation to denote the beginning and end of the arc 0-0, mt e = C[Tum) - T (u0)], 5 ((x x9 1l 0.

00In direct fire the pseudo-velocities U and u, and the real velocities V and v, are undistinguishable, and sec n may be replaced by unity so that, putting y =o in (79), (88) tan 4) = C [I (V) - y-s] Also (89) tan 4 - tan S=C [I(V) - L(v)] so that (9 Ã‚°) tan 1 3=C [1 -s.

00The effect is as if there was a mean sidelong thrust w tan S on the shot from left to right in order to deflect the plane of the trajectory at angle 6 to the vertical.

00After 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 %.

00The logarithm is also a function of frequent occurrence in analysis, being regarded as a known and recognized function like sin x or tan x; but in mathematical investigations the base generally employed is not 10, but a certain quantity usually denoted by the letter e, of value 2.71828 18284 ...

00Ai-yet '1770"013S OUK l(rrl y Sektos 7rp0017T77S iv Tj7 7rarpLSL abr[o]U, obSi iarpOs 7roiEl Oepa7rdiaS EIS Tan ytvavyKOVTas abrbv.

00The general or typical coloration is, however, a rich tan upon the head, neck, body, outside of legs, and tail near the root.

00- N / (z cot IC) =o, with centre sin A, sin B, sin C; the escribed circle opposite the angle A is - N I (- x cot ZA)+ -1 (y tan 2B) + -V (z tan 2C) =o, with centre - sin A, sin B, sin C; and the selfconjugate circle is x 2 cot A+y 2 cot B+z 2 cot C =o, with centre tan A, tan B, tan C. Since in areal co-ordinates the line infinity is represented by the equation x+y+z=o it is seen that every circle is of the form a 2 yz+b 2 zx+c 2 xy+(lx+my+nz)(x+y+z) = o.

00If h be given, we can use c 2 +4h 2 =8ah, zh =c tan 4B to determine 0.

008 4 In modern trigonometrical notation, I +sec 0: tan 0 :: I : tan Z0.

00II) whose centre is 0, AC its chord, and HK the tangent drawn at the middle point of the arc and bounded by OA, OC produced, then, according to Archimedes, AMC AC. In modern trigonometrical notation the propositions to be compared stand as follows: 2 tan 20 >2 sin 28 (Archimedes); tan 10+2 sin 3B>0> 3 sin B (Snell).

00Even among the mere computers the series =tan -a tan' 0+1 tan' 0-..., specially known as Gregory's series, has ever since been a necessity of their calling.

00In 1699 Abraham Sharp, on the suggestion of Edmund Halley, took Gregory's series, and, putting tan 0=11/3, found the ratio equal to 1 112 (I { 5 32 - 7 33 +...), from which he calculated it correct to 71 fractional places.'

00Fautet de Lagny, still using tan 30Ã‚°, advanced to the 127th place.'

00122) is as follows: - it/4 = tan 12 +tan '; +tan 1 s (Dase, 1844), 7r/4=4tan 1 - tan 11 +tan Ys (Rutherford), and Gregory's series were employed.'

00The Plant Stove differs in no respect from the greenhouse except in having a greater extent of hot-water pipes for the purpose, of securing a greater degree of heat, although, as the plants in stove houses often attain a larger size, and many of them require a bed of coco-nut fibre, tan or leaf mould to supply with bottom heat, b: !, b a somewhat greater elevation may perhaps be occasionally required in some of the houses.

00These regenerators are the essence of the Siemens or " regenerative furnace "; they are heat-traps, catching and storing by their -11, Ton Traver 7s 20 Tan Tra y.

00Tan BLACK ISLE, a district in the east of the county of Ross and Cromarty, Scotland, bounded N.

00They weave and dye several kinds of cloth, tan and dress leather and manufacture oil and soap. Without the assistance of the wheel the women produce a variety of pottery utensils, often of very graceful design, and decorated with patterns in red and black.

00This appears to be the beginning of a new anticlinal which has altered the levels of the Balkh plain, and is indicative of those elevating processes which Afghan tan, together with the minor dependencies of the provinces.

00one road crosses the mountains to Shang Chow, and on to the Tan river, an affluent of the Han-kiang, and is thus connected with the trade of the Yangtsze-kiang; and another leads to Han-chung Fu and Sze-ch'uen.

00decurrens, tan wattle, and A.

00These two forces X, Y, may be combined into a single resultant R making an angle 4> with Ox, provided X = Rcos4,, Y = Rsin4~, (2) whence R2 = X~ + Yi, tan 4) = Y I X.

00Hence the line will be a nullline provided tan 8=k/r,.

00It appears also from (II) that the null-lines whose distance from the central axis is r are tangent lines to a system of helices of slope tan 1(r/k); and it is to be noticed that these helices are left-handed if the given wrench is righthanded, and vice versa.

00Hence S=W tan OW.

00If the chain be uniform we have W = ws, where s is the arc AP: hence ws=To tan ~.

00This leads to U U0 g~ Vi V2+uof tan V=tan1V_V, x= ~-~log V2+u2 (27)

00provided R = (j,i en)1 +koi1l I, tan ~i ~ (36)

00If a be the inclination of the instantaneous axis to the axis of symmetry, (3 the inclination of the latter axis to the invariable line, we have rcosfl=Cw cos a, r sin ~3 = Aw sin a, (6) whence tan ~ =~ tan a.

00The ratio of the two components of that velocity is = p/2lrr = tan 0.

00tts value at intermediate instants is given by the following equations: let ~,, 4f be the angles respectively made by the central planes of the forks and shafts with the plane OCiC, at a given instant; then cos 0=tan 4~ tan ~,)

00af d4e tan ~,+ cot 4i~ ~ (40) aj d~i tan ~1+cot ti)

00Let A be any origin, and let Ac represent the acceleration of the b point C, Ct the radial acceleration of B about C which must be in a direction parallel to BC, and tb the tan gential acceleration of B about C, C

00R=fN==N tan q5=T sin 4, S ~5

00He then tried to win recognition as dukes of Aquitaine for the sons of his wife Agnes by William the Great, who were still minors, but Fulk Nerra promptly took up arms to defend his suzerain William the Fat, from whom he held the Loudunois and a tan g S h= - Saintonge in fief against his son.

00Since the electrical repulsion of the balls is equal to C 2V2 4 12 sin 2 0 dynes, where C = r is the capacity of either ball, and this force is balanced by the restoring force due to their weight, Wg dynes, where g is the acceleration of gravity, it is easy to show that we have _ 21sin 0 r " tan V 8 r as an expression for their common potential V, provided that the balls are small and their distance sufficiently great not sensibly to disturb the uniformity of electric charge upon them.

008, we have O'Q'/OQ = a' tan w' la tan w = 1/N, where N is the " scale " or magnification of the image.

00For N to be constant for all values of w, a' tan w'/ a tan w must also be constant.

00tan w'/ tan w=a constant.

00Trans., 1830, 3, p. 1) is fulfilled in all systems which are symmetrical with respect to their diaphragm (briefly named " symmetrical or holosymmetrical objectives "), or which consist of two like, but different-sized, components, placed from the diaphragm in the ratio of their size, and presenting the same curvature to it (hemisymmetrical objectives); in these systems tan w'/ tan w= 1.

00von Rohr showed that for systems fulfilling neither the Airy nor the Bow-Sutton condition, the ratio a' tan w' la tan w will be constant for one distance of the object.

00By putting =x 2 /4 for x in F(o,x) and F(i,x), and putting at the same time y =1/2, we obtain x 2 x 2 x2 x 2 x2 tan x x x tanh x x x x I - 3 - 5-7-...

00After speaking of Dositheus the Samari tan, who persuaded some of his countrymen that he was the Christ prophesied by Moses, he goes on to say: " Also Simon the Samaritan, a magician, wished to filch away some by his magic. And at the time indeed he succeeded in his deception, but now I suppose it is not possible to find 30 Simonians altogether in the world; and perhaps I have put the number higher than it really is.

00Finally, if a is made extremely small, so that practically tan (A = Zl/Gs, the sensitiveness is independent of the amount weighed by the balance.

00For the weighing of very small quantities with balances of great delicacy, the following method is adopted: - If the balance be in perfect adjustment, and 1 be the length of each arm, and w a very minute difference of the weights in the two scale-pans, by which the beam is deflected from the horizontal by a very small angle (/), it can easily be shown that tan 0, or 4), varies as w XI.

00If W be the weight in each pan when the goods-pan commenced to sink, / the length of each arm, m the distance of the fulcrum below the line joining the end knife-edges, and 13 the angle at the fulcrum which defines the range of sway of the beam, it can easily be shown that w, the ad - ditional weight required in the weights-pan to enable the goods-pan to rise from its stop, is given by the equation w =W 2m tan, 3/L m tan S.

00which is needed in the weights-pan to enable the goods-pan to rise off its stop, is given by the equation w= W 2m tan 6(3-0)/L - m tan 6(3-0).

00The condition that must exist in order that the balance may weigh correctly for all positions of the weight W is w = o, or tan 0 = that is, the stay KG must be adjusted parallel to the line joining the points A and C. From the equation for w, it is seen that the larger h is the smaller w will be.

00The double tan larities - gent or inflection; gent; arising as follows: 1.

00The cartesian equation, when A is the origin and AB = 2a, is y 2 (2a - x) =x 8; the polar equation is r= 2a sin 0 tan 0.

00such as ad-ib where i=1/ - i, the "argument" (or "amplitude") is the angle 0 given by tan 0 = b/a.

00If F be the number of faces, n the number of edges per face, m the number of faces per vertex, and l the length of an edge, and if we denote the angle between two adjacent faces by I, the area by A, the volume by V, the radius of the circum-sphere by R, and of the in-sphere by r, the following general formulae hold, a being written for 21r/n, and a for 27r/m:- Sin z I =cos 1 3/sin a; tan II =cos l3/ (sin'- a -cos t R) 2.

00V = 3rA = 2 1 4 / 3 n F tan -II cot e a = 2 I 1 3 n F cot e a cos a/ (sin' a -cos t 13) 2 R =1-/ tan IT tan 0=1/ sin 13/(sin e a-cost r =Zl tan 21 cot a= Il cot a cos 13/(sin" a -cos' (3)L 1 In the language of Proclus, the commentator: " The equilateral triangle is the proximate cause of the three elements, ` fire,' ` air ' and ` water '; but the square is annexed to the ` earth.'

00This was supplied by Fresnel, who, starting from a mechanical hypothesis, showed by ingenious but not strictly dynamical reasoning that if the incident stream have unit amplitude, that of the reflected stream will be - sin (i - r) /sin (i -{- r) or tan (i - r) /tan (i -{- r), according as the incident light is polarized in or perpendicularly to the plane of incidence i, r, being the angles of incidence and refraction connected by the formula sin i =,u sin r.

00At normal incidence the intensity of the reflected light, measured by the square of the amplitude, is { (µ -1) /(µ+ I) } 2 in both cases; but whereas in the former the intensity increases uniformly with i to the value unity for i =90Ã‚°, in the latter the intensity at first decreases as i increases, until it attains the value zero when i -Fr = 90Ã‚°, or tan i =,u - the polarizing angle of Brewster - and then increases until it becomes unity at grazing incidence.

00Hence if 1 3 be the angle between the plane of incidence and that in which the reflected light is polarized tan (3= - tan a cos (i+r)/cos (i - r).

00Applying this interpretation to the formulae given above, it follows that when the incident light is polarized at an azimuth a to the plane of incidence and the second medium is the less refracting, the reflected light at angles of incidence exceeding the critical angle is elliptically polarized with a difference of phase A between the components polarized in the principal azimuths that is given by tan (A/2) =cot i l l (1 - µ 2 cosec 2 i).

00Solving for cot e i we obtain 2 cot 2 i= (p 2 -1) 2 {(p2 - tan2 (7r - A)/4) {p - cot2 - A)/411, and since tan { (ir - A)/4-} is less than unity, p must exceed cot {Or - A)/41 if cot 2 i is to be real.

00ConsonantsFinal I readily disappears after nor 1 (tan, t a n t U In; aman, venin, pantin, for amant, venint, &c.; mai, rn u I t u in; ocul, o.c u 1 t u m); the reappears in composition before a vowel (Jon, assimilation to past participles in it.

00Old Portuguese the nasal vowel or diphthon~ was not as now marked by the lii (__), but was expressed indifferently and without regard to the etymology by m or n: bern (b e n e), tan (t a n t u m), disserom (dixerunt), sermom (sermonem).

00Since H' P = F 0, = y, from the focal length of the simple microscope, the visual angle w' is given by tan w'/y=I/f'=V, (I) in which f', = H' F', is the image-side focal length (see Lens).

00I) tan w = y/l, where l = i o in., whilst the apparent size of the object viewed through the magnifying glass would result from the formula (I) tan w' = y/f.

00Consequently the number of diameters will be N = tan w'/tan w = y/f.

00distance, it follows (to him) the apparent size is tan w =y14; and to secure convenient vision through the lens the short-sighted person would bring the object to such a distance that a virtual, magnified image would be projected in his punctum remotum.

00The apparent size of the object seen through the lens is then tan w' = y/f.

00focus, is here N = tan w'/tan w = y/f.4/y=4/f=4 Thus, while a lens of i in.

00The image viewed through the eyepiece appears then to the observer under the angle w", and as with the single microscope tan w" = I /f 2 ' (4) where f' 2 is the image-side focal length of the eyepiece.

00If we replace y' in equation (4) by the value given by (3), we obtain tan w"/ y i/f2"=V, (5) the magnification of the complete microscope.

00i that the apparent size is tan w =3/11.

00If this value of y be inserted in equation (5), we obtain the magnification number of the compound microscope N =tan w"/ tan w =Ol/f i 'f 2 ' =Vl.

00By substituting y, the size of the object, for d, the smallest value which a single object can have in order to be analysed, and the angle w' by 2', we obtain the magnifying power and the magnification number: V2 = tan w'Id= 2A tan 2'/X; N2 = 2Al tan 2'/A; where 1 equals the sight range of io in.

00The magnification and magnifying number which are most necessary for a microscope with an objective of a given aperture can then be calculated from the formulae: V4 = 2A tan 4'/X; N4 = 2Al tan 4'/A.

00The sine-condition is in contrast to the tangent-condition, which must be regarded as the point-by-point representation of the whole object-space in the image-space (see Lens), and according therefore the equation n tan u/tan u' = C must exist.

00Large tanneries were attracted to the state, soon after the Civil War, by the abundance of tan bark in the forests, and the cheapness of labour.

00Applying a tan remover such as San Tropez Self Tan Remover within four hours of applying the solution removed it instantly.

00For a richer tan use daily to replenish lost moisture.

00It comes on the original signed tan leather strap with sandblasted steel signed buckle.

00Top up your tan while sipping free sangria and watching our belly flop competition.

00The private solarium will ensure you go home with a tan.

00Abu'l-Wafa and Abu Nasr Mansur both applied spherical geometry to astronomy and also used formulas involving sin and tan.

00I needed to make sure she was fed, watered and lathered with sun tan cream before I could relax and enjoy myself.

00More Biotech tan jab could put the heat on suntan salons.

00There are many salons where you can get fake tan applied professionally.

00For those seeking an all-over tan there is the beach at Costa Natura.

00For a totally natural-looking tan in just one hour !

00Pot of 100 tablets said to give you a ' golden tan all over ' without the damaging effects of the sun !

00For example, if your business is selling sun tan lotion a December year end would make more sense than a June year end.

00This example was rosso with the tan interior, with the covered roll hoops.

00It being April you'll probably even get a sun tan too !

00Here there is jam tan, we are all fine.

00It can be used anywhere where you want to remove any excess self tan.

00The leftmost column is column 0. TAN A function returning the tangent of its radian argument.

00We also note that Lea 's tan has not run during her teary moments.

00After being unemployed for a while, do n't feel sorry for me cos I had a great tan last summer.

00Girls and guys alike look rather out of place with their rather unnatural dark tan on faces and hands.

00There 's nothing wrong this summer with carrying a tan leather valise with mustard patent sandals.

00Very little history is documented although it is believed the breed is probably descended from old black and tan and wheaten terriers.

00They may feature sports themes, or they may simply be made out of sturdy canvas, vinyl, or cotton material in tan, navy, hunter green, and other guy colors.

00Mientras que la selección para la fraseología española de la invitación puede no ser tan simple encontrar como selecciones inglesas, están hacia fuera allí.

00Nuestro bebé es una bendición que es tan hermosa como puede ser. . . ¡venido ayúdenos agradables ella en la familia del ? s del dios!

00For the walls, use a pale blue or tan paint, and choose wall art with a lodge feel.

00Complete the fishing cabin look with the Gone Fishing Crib Bedding from Cabin Place in brown, tan, and green.

00Gender colors can include yellow, green, brown, red, black, beige, tan, white, orange, and taupe.

00While blue is often considered a boy's color, soft blues combined with tan or brown can create a lovely girl's nursery as well.

00For example, paint two walls yellow and the two opposite walls tan or green.

00When designing unisex themes for baby and toddler rooms, neutral colors work well, such as yellow, green, cream, tan, taupe and white.

00Common background colors are red, blue, dark brown and camel tan.

00Choose a tan "embossed" style, for example, and then pair it with jacquard pillows or rich satin throw blankets.

00Some of the obvious color schemes include blue, white, tan, and green.

00Spanish Roja- has a strong, spicy flavor and a brown to tan color.

00Pale tan sand, soft blue skies with a few bright white clouds floating by, and aquamarine water as far as the eye can see.

00You will notice all the different colors of light and dark tan as well as flecks of white and black.

00White walls - Paint your trim in either a pale blue or sandy colored tan.

00Sandy tan walls - Stick with white again here.

00Paint a focal wall - For example, if you have decided to paint your master bedroom in a warm aqua color, paint the wall your bed rests against in a rich tan or beige color.

00Most of the wallpaper used red, blue or green with tan accents.

00Paint a focal wall - For example, if you have decided to paint your master bedroom in a warm aqua color, paint the wall your bed rests against in a rich tan or beige color.

00This style is no longer only black and white, but it has incorporated monochromatic decors of brown, tan, gray, and blue.

00For resell value, walls painting in a Tuscan tan color will appeal to almost any potential buyer.

00Green, brown, blue, tan, and soft pastels offer great choices that can help make your family room a place to rest and recharge.

00Sophisticated colors can range from reserved deep tan to high-powered magenta.

00Neutral tones of tan, brown and oyster pearl are accented with a splash of Roasted Squash orange.

00The browns in the Pottery Barn collection range from sandy khakis and tan to deep, rich, dark brown.

00Natural shells come in a variety of colors; many are solid while most colors are a combination of the prominent color and white or tan shell.

00While the natural colors for giraffe print are warm tones of dark brown, tan and beige, the giraffe print pattern can also be done in fun neon colors such as lime green, hot pink and purple.

00You can warm up your skin tone or give yourself a faux tan with the all-over face colors available.

00QVC: In addition to the makeup, you can get the sunless tanner, Faux Tan, here.

00Another option, if you desire a sun kissed glow, is to discover a fake tan kit with tinted body glow, blusher, sparkle lipstick and brushes.

00A fresh tan typically symbolizes heath and beauty, but in the past required the risk of sun exposure.

00While we all need sunshine to survive, in order to receive the healthy glow of a tan you essentially need to stay in the sun far past our vitamin D requirement.

00With the advancement of a more natural looking tan from sunless tanning products, the potential exists for that realistic tan without going outside.

00Too much DHA creates a rusty unnatural look and too little generates only a light tan that fades quickly.

00The effects of a spray tan session with DHA last about five to seven days as the chemical reaction takes place within the most outer layer of the skin surface.

00Therefore, as the dead skin cells slosh off, so does the tan.

00About six to twelve hours before your session, gently exfoliate the skin you plan to tan, particularly the more exposed areas.

00Keep in mind that sunless tans are not a true tan and will not offer any natural sun protection like an authentic tan would.

00Keep your DHA tan well moisturized for maximum performance and always apply sunscreen when outside.

00Sunless tanning booths have cropped up all over offering a quick effective way to apply a spray tan.

00Lotion is applied to the areas that you do not want to tan, like the palms of hands and fingernails, and a cap over your head to protect your hair.

00Sunless tanning booths are the fastest method of acquiring a fake tan, but make sure the place you choose uses standard cautions.

00If you want to avoid the cost or hassle of a professional session, you can purchase your own spray tanning product for a homemade tan.

00An example is the product Spray Tan in a Can which advertises the same 8% DHA concentration found at the sunless tanning booths.

00Have you been considering a spray tan at home product?

00Thanks to celebrities like Jennifer Lopez, a spray tan has become truly fashionable.

00Once again, a tan can be described as a healthy glow.

00Visiting a salon will ensure that your tan is applied by a professional, but it also comes with the professional price.

00The following information will help you to evaluate whether you would like to try a home-done version of a spray tan.

00Whether you chose a home tan kit or a salon spray booth, both employ the same tanning process.

00DHA causes a reaction at the surface of your skin temporarily turning the skin a tan color.

00When you compare the DHA chemical reaction to the possibility of skin cancer from the sun, a spray tan sounds like a much safer tanning option.

00Spray tan products actually provide two services.

00Pigments added to the spray impart an instant tan color to your skin, while the DHA reaction takes about ten hours to achieve a change in your skin's color.

00So, at about the time the pigments wash off, the longer-lasting chemical tan has set in.

00With a variety of products available at as little as $7 a tan, many people are trying an imitation tan at home.

00The following is a step-by-step program to ensure the most naturally even tan.

00Exfoliate your entire body between three to twelve hours before applying the tan product - ideally with a moisturizing body scrub.

00Within 30 minutes before your spray tan, take a shower to remove all the body and product oils from your skin.

00As the name describes, this product provides a tan in a can by ModelCo available for purchase at Sephora.

00Applied with a fine mist, it provides both a golden pigment for an instant glow and the self-tanner chemicals for the longer lasting tan.

00Tan AirBrush offers a specially designed spray nozzle that provides 360 degree coverage for easier application.

00A particularly quick drying spray tan product, designed for both the face and body.

00While pale skin once signified your wealth, now tan skin signified you were wealthy enough to go outside and play!

00My hair is blondish-brown and I'm slightly tan.

00They call it, "The Healthiest Tan on Earth."

00It claims to leave you soft, silky, and tan.

00This allows for a smoother, more even tan.

00Vita Tanz Blending Puffs allow you to smooth and blend your tan over all the surfaces of your skin.

00Not only do they spare your good underwear from unsightly stains, but they offer great tan lines, too.

00Orange Palms Preventer counteracts the leftover DHA on your palms after you're done tanning and prevents the muddy-palm look that most often gives away a sunless tan.

00They all claim to last a full week and fade like a "normal tan" but not all follow through on the promise.

00Sunless tanners are the hip way to get some color for summer, and Jimmy Coco Spray Tan is no exception.

00The line offers sunless tanners, tan enhancers, and sunscreen to take care of all your glowing skin needs.

00Jimmy Coco's tanning method of choice is the spray tan, and for your convenience, it can be done by a pro at your home or office.

00Jimmy Jimmy Coco Buff will exfoliate your body, making you a prime candidate for a smooth, deep tan.

00Jimmy Jimmy Coco Boom is a moisturizer meant to be used daily to help maintain your spray tan.

00Dry skin doesn't hold onto the color as well as moisturized skin does, so for best spray tan results, always make sure your body's well hydrated from the inside and out.

00Jimmy Jimmy Coco Blast is a sunless tanner for those who can't get to a Jimmy Coco spray tan salon.

00Even if you can get sprayed, you may find that you prefer to maintain your tan between sessions with sunless tanners from cans.

00Jimmy Jimmy Coco Bam is another way to extend your tan.

00If you start fading in some spots, just spray this on and blend to refresh your tan.

00Jimmy Jimmy Coco Bronze is ideal for those days when someone calls and wants you to do something that will require you to look tan and cute.

00This is also good for deepening or evening out an existing, but fading, sunless tan.

00Underneath the instant bronze color, the spray works to give you a longer lasting tan.

00That'll keep the tanner from grabbing on too much, which in turn will make your tan more even from head to toe.

00Spray your tan on over that and rub in quickly.

00Leave the tan on overnight if you'd like, or just follow the directions that accompany your spray tan solution.

00Use a barrier cream or lotion on your knuckles, knees, ankles, etc. so the tan doesn't turn out too dark there.

00Do a test run before a major event so you'll know in advance how the tan reacts with your skin.

00This product is a moisturizer that also creates a light tan.

00Jergens Natural Glow is a daily moisturizer for your body that not only softens your skin, but also gradually develops a light, natural-looking tan without exposing yourself to the dangers of the sun.

00There are formulations for fair, medium and medium tan skin tones.

00Both of these products will create a natural tan on your skin.

00When you stop using this product, your tan will gradually fade away to your original skin tone.

00However, I was hoping to even out my color since I have a tendency to wear t-shirts and really am not impressed with my "farmer's tan".

00Obviously, that isn't going to help with an all over tan, so I needed to make adjustments.Remembering to use this self tanning product every day was probably my biggest challenge.

00It does produce a subtle tan and I liked the slight sparkle of the light diffusers.

00If you are looking for a deep, exotic tan, this product may not be right for you.

00For example, most people who have blue eyes think that brown or tan will work, which it can.

00You only have to do it once (unless you tan or your tan fades) and it is worth the hassle.

00Flaunting pale skin is considered trendy much in the same way a deep tan in America is.

00Bronzer Brush: A natural tan is easily achieved with one of these four sun-kissed shades.

00Southern Magnolia Minerals' foundation is available in fair to light, medium to dark and deep to tan formulas.

00In addition to a tube of coffee lip balm, the set also includes four jars of mineral eye shadow and blush (including barely-peach Apricot, soft violet-rose Berry Essence, vivid rose Raisin Red and dusky tan Mocha).

00Praline offers some semblance of a healthy tan (without the obvious dangers of the natural method).

00If you want a faux tan but have trouble applying self-tanner without embarrassing telltale lines, a spray on tanning booth is a wonderful alternative.

00Whether it's desired for a healthy dose of pre-wedding color or as a base for an upcoming vacation, a faux tan can be a convincing alternative to the sun's damaging rays when applied correctly.

00When applied in interval doses, a deep color can be achieved, mimicking a natural sun-kissed tan.

00For those seeking a very gradual glow, products like Glow Fusion are developed to apply regularly, creating a gorgeous faux tan over a lengthened period of time.

00One application of a spray booth tan will generally last anywhere between 5-10 days.

00Moisturizer is key in order to prolong your tan, and should be applied several times daily.

00Popular spray booth chains include Mystic Tan and Fantasy Tan.

00Good mid tone colors are tan, lavender, raspberry and forest green.

00Good highlighter colors would be sand, light pink, light tan or white.

00To make green flecks sparkle, choose fawn, tan, and mocha shadows.

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.