Cos Sentence Examples

Sulphides of cobalt of composition C04S3, CoS, C03S4, C02S3 and CoS 2 are known.

The potential due to a small magnet of moment M, at a point whose distance from the centre of the magnet is r, is V=M cos 0/r 2, (io) where 0 is the angle between r and the axis of the magnet.

The most important inlet, the Ceramic Gulf, or Gulf of Cos, extends inland for 70 m., between the great mountain promontory terminating at Myndus on the north, and that which extends to Cnidus and the remarkable headland of Cape Krio on the south.

Of these the most celebrated are Rhodes and Cos.

Its cartesian equation, when the line joining the two fixed points is the axis of x and the middle point of this line is the origin, is (x 2 + y 2)2 = 2a 2 (x 2 - y 2) and the polar equation is r 2 = 2a 2 cos 20.

When passed with carbon dioxide through a red-hot tube it yields carbon oxysulphide, COS (C. Winkler), and when passed over sodamide it yields ammonium thiocyanate.

The polar equation is r= I -f - 2 cos 0 and the form of the curve is shown in the figure.

Its control of the Aegean was, however, contested not without success by the Antigonids, who won the two great sea-fights of Cos (c. 256) and Andros (227), and wrested the overlordship of the Cyclades from the Ptolemies.

The siege, which was finally conducted by the sultan in person, was successful after six months' duration; the forts of Cos and Budrum were also taken.

Of the quadratic axe+2bxy+cy2, he discovered the two invariants ac-b 2, a-2b cos w+c, and it may be verified that, if the transformed of the quadratic be AX2=2BXY+CY2, sin w 2 AC -B 2 =) (ac-b2), sin w A-2B cos w'+C = (sin w'1 2(a - 2bcosw+c).

If r and r' make angles 0 and 0 with the axis, it is easily shown that the equation to a line of force is cos 0 - cos B'= constant.

If F T is the force along r and F t that along t at right angles to r, F r =X cos 0+ Y sin 0=M 2 cos 0, F t = - X sin 0+ Y cos 0 = - r 3 sin 0.

For a point in the line OY bisecting the magnet perpendicularly, 0 =42 therefore cos 0 =0, and the point D is at an infinite distance.

Let 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.

The strength of the induced current is - HScosO/L, where 0 is the inclination of the axis of the circuit to the direction of the field, and L the coefficient of self-induction; the resolved part of the magnetic moment in the direction of the field is equal to - HS 2 cos 2 6/L, and if there are n molecules in a unit of volume, their axes being distributed indifferently in all directions, the magnetization of the substance will be-3nHS 2 /L, and its susceptibility - 3S 2 /L (Maxwell, Electricity and Magnetism, § 838).

The middle element alone contributes without deduction; the effect of every other must be found by introduction of a resolving factor, equal to cos 0, if 0 represent the difference of phase between this element and the resultant.

If the primary wave at 0 be cos kat, the effect of the secondary wave proceeding from the element dS at Q is dS 1 dS - p cos k(at - p+ 4 A) = - -- sin k(at - p).

The amplitude of the light at any point in the axis, when plane waves are incident perpendicularly upon an annular aperture, is, as above, cos k(at-r 1)-cos k(at-r 2) =2 sin kat sin k(r1-r2), r2, r i being the distances of the outer and inner boundaries from the point in question.

The maxima occur when u=tan u, (4), and then sin 2 u/u 2 = cos 2 u (5).

When, as in the application to rectangular or circular apertures, the form is symmetrical with respect to the axes both of x and y, S = o, and C reduces to C = ff cos px cos gy dx dy,.

Trans., 1834) in his original investigation of the diffraction of a circular object-glass, and readily obtained from (6), is z z 3 25 27 J1(z) = 2 2 2.4 + 2 2.4 2.6 2 2.4 2.6 2.8 + When z is great, we may employ the semi-convergent series Ji(s) = A/ (7, .- z)sin (z-17r) 1+3 8 1 ' 6 (z) 2 3.5.7.9.1.3.5 5 () 3 1 3.5.7.1 1 3 cos(z - ?r) 8 ' z (z) 3.5.7.9.11.1.3.5.7 1 5 + 8.16.24.32.40 (z

A 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)').

If we put for shortness 7 for the quantity under the last circular function in (I), the expressions (i), (2) may be put under the forms u sin T, v sin (T - a) respectively; and, if I be the intensity, I will be measured by the sum of the squares of the coefficients of sin T and cos T in the expression u sin T +v sin (T - a), so that I =u 2 +v 2 +2uv cos a, which becomes on putting for u, v, and a their values, and putting f =Q .

Only in this case can cos {p' +(m- -27th/Af) f } retain the constant value - I throughout the integration, and then only when and a = 27Th/A f (8) cos p'=- 1 ..

The integrated intensity, I', or 21-14 +2 cos pw, is thus I' =27rh,.

By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 1.3.5.7 1.3.5.7.9.11 These series are convergent for all values of v, but are practically useful only when v is small .

Comparing the expressions for C, S in terms of M, N, and in terms of G, H, we find that G = z (cos u+sin u)-M, H = z (cos u-sin u) +N.

Retaining only the real part of (16), we find, as the result of a local application of force equal to DTZ cos nt (17), the disturbance expressed by TZ sin 4, cos(nt - kr) ?

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

According to (18), the effect of the force acting at dS parallel to OZ, and of amount equal to 2b2kD dS cos nt, will be a disturbance - dS sin cos (nt - kr) (20), regard being had to (12).

By applying the method of the differential calculus, we obtain cos i= { (µ 2 - 1)/(n24-2n)} as the required value; it may be readily shown either geometrically or analytically that this is a minimum.

Of these certainly many are falsely ascribed to the historical Hippocrates of Cos; others are almost as certainly rightly so ascribed; others again are clearly works of his school, whether from his hand or not.

There are clearly two schools represented in the collection - that of Cnidus in a small proportion, and that of Cos in far the larger number of the works.

The school of Cnidus, as distinguished from that of Cos, of which Hippocrates is the representative, appears to have differed in attaching more importance to the differences of special diseases, and to have made more use of drugs.

Herophilus (335-280 B.C.) was a Greek of Chalcedon, a pupil of the schools both of Cos and of Cnidus.

The Erasistrateans paved the way for what was in some respects the most important school which Alexandria produced, that known as the empiric, which, though it recognized no master by name, may be considered to have been founded by Philinus of Cos (280 B.C.), a pupil of Herophilus; but Serapion, a great name in antiquity, and Glaucias of Tarentum, who traced the empirical doctrine back to the writings of Hippocrates, are also named among its founders.

I n a straight uniform current of fluid of density p, flowing with velocity q, the flow in units of mass per second across a plane area A, placed in the current with the normal of the plane making an angle 0 with the velocity, is oAq cos 0, the product of the density p, the area A, and q cos 0 the component velocity normal to the plane.

Generally if S denotes any closed surface, fixed in the fluid, M the mass of the fluid inside it at any time t, and 0 the angle which the outward-drawn normal makes with the velocity q at that point, dM/dt = rate of increase of fluid inside the surface, (I) =flux across the surface into the interior _ - f f pq cos OdS, the integral equation of continuity.

Consider the motion given by w=U(z+a2/z), (I) 4,=U(r+- r) cos 0= U + a1x, so that (2) = U (r-)sin 0= U(i -¢) y.

If the liquid is reduced to rest at infinity by the superposition of an opposite stream given by w = - Uz, we are left with w = Ua2/z, (6) =U(a 2 /r) cos 0= Ua2x/(x2+y2), (7) 4, = -U(a 2 /r) sin 0= -Ua2y/( x2+y2), (8) giving the motion due to the passage of the cylinder r=a with velocity U through the origin 0 in the direction Ox.

When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?

Taking 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.

Consider the streaming motion given by w =m =a+si, (5) 4=m ch (n -a)cos(-0), p=m sh(n-a)sin(-13).

Example 3.-Analysing in this way the rotation of a rectangle filled with liquid into the two components of shear, the stream function 1//1 is to be made to satisfy the conditions v 2 /1 =0, 111+IRx 2 = IRa 2, or /11 =o when x= = a, +b1+IRx 2 = I Ra2, y ' 1 = IR(a 2 -x 2), when y = b Expanded in a Fourier series, 2 232 2 cos(2n+ I)Z?rx/a a -x 7r3 a Lim (2n+I) 3 ' (1) so that '?"

The polar equation of the cross-section being rI cos 19 =al, or r + x = 2a, (3) the conditions are satisfied by = Ur sin g -2Uairi sin IB = 2Uri sin 10(14 cos 18a'), (4) 1J/ =2Uairi sin IO = -U1/ [2a(r-x)], (5) w =-2Uaiz1, (6) and the resistance of the liquid is 2lrpaV2/2g.

Similarly, with the function (19) (2n+ I) 3 ch (2n+ I) ITrb/a' (2) Changing to polar coordinates, x =r cos 0, y = r sin 0, the equation (2) becomes, with cos 0 =µ, r'd + (I -µ 2)-d µ = 2 ?-r3 sin 0, (8) of which a solution, when = o, is = (Ar'+) _(Ari_1+) y2,, ?

In the absolute path in space cos Ili = (2 - 3 sin 2 6)/1/ (4-sin 2 6), and sin 3 B = (y 3 -c 2 y)/a 3, (19) which leads to no simple relation.

Denoting the cross-section a of a filament by dS and its mass by dm, the quantity wdS/dm is called the vorticity; this is the same at all points of a filament, and it does not change during the motion; and the vorticity is given by w cos edS/dm, if dS is the oblique section of which the normal makes an angle e with the filament, while the aggregate vorticity of a mass M inside a surface S is M - l fw cos edS.

If there are more B corners than one, either on xA or x'A', the expression for i is the product of corresponding factors, such as in (5) Restricting the attention to a single corner B, a = n(cos no +i sin 110) _ (b-a'.0-a) +1!

Taking Ox along OS, the Stokes' function at P for the source S is p cos PSx, and of the source H and line sink OH is p(a/f) cos PHx and - (p/a) (PO - PH); so that = p (cos PSx+f cos PHx PO a PH), (q) and Ili = -p, a constant, over the surface of the sphere, so that there is no flow across.

It contains a borough of the same name and the villages of Cos Cob, Riverside and Sound Beach, all served by the New York, New Haven & Hartford Railway; the township has steamboat and electric railway connexions with New York City.

The cartesian equation is y=a cos /2a.

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

In course of time admission to the rank of a hero became far more common, and was even accorded to the living, such as Lysimachus in Samothrace and the tyrant Nicias of Cos.

After having withstood an attempt under Epaminondas to restore it to the Lacedaemonians, Byzantium joined with Rhodes, Chios, Cos, and Mausolus, king of Caria, in throwing off the yoke of Athens, but soon after sought Athenian assistance when Philip of Macedon, having overrun Thrace, advanced against it.

His earlier studies were prosecuted in the famous Asclepion of Cos, and probably also at Cnidos.

Gradually individual cities which had formed part of the Athenian empire returned to their alliance with Athens, until the Spartans had lost Rhodes, Cos, Nisyrus, Teos, Chios, Mytilene, Ephesus, Erythrae, Lemnos, Imbros, Scyros, Eretria, Melos, Cythera, Carpathus and Delos.

Chios, Rhodes, Cos, Byzantium, Erythrae and probably other cities were in revolt by the spring of 356, and their attacks on loyal members of the confederacy compelled Athens to take the offensive.

The Doric Sporades - Melos, Pholegandros, Sikinos, Thera, Anaphe, Astropalia and Cos - were by some considered a southern cluster of the Cyclades.

The earliest of the elegiac poets was Philetas, the sweet singer of Cos.

Let ON(= OP cos 0) be the perpendicular on PQ.

Hence all rays between =0 will be confined in the space between the outer dome and a circle of radius OP cos 0, and the weakening of intensity will be chiefly due to vertical spreading.

If then y=a sin (x - Ut),, t=2,ro-ra cos (x - Ut).

If we measure the time from an instant at which the two are in the same phase the resultant disturbance is y=a sin i t+a sin 27rn2t =2a cos ir(n i - n 2)t sin ir(nl-t-n2)t, which may be regarded as a harmonic disturbance of frequency (ni+n2)/2 but with amplitude 2a cos 7r(n i - n 2)t slowly varying with the time.

Taking the squares of the amplitude to represent the intensity or loudness of the sound which would be heard by an ear at the point, this is 4a 2 cos t ir(ni - n2)t =2a 2 {1 -cos 27r(n l - n2)t}, a value which ranges between o and 4a 2 with frequency .n1 - n2.

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

Let E be the effective elasticity of the aether; then E = pc t, where p is its density, and c the velocity of light which is 3 X 10 10 cm./sec. If = A cos" (t - x/c) is the linear vibration, the stress is E dE/dx; and the total energy, which is twice the kinetic energy Zp(d/dt) 2 dx, is 2pn2A2 per cm., which is thus equal to 1.8 ergs as above.

The definition of the coefficients is that if (I-2h cos cp+h 2)-i be expanded in ascending powers of h, and if the general term be denoted by P„h', then P is of the Legendrian coefficient of the nth order.

Also the velocity v at the end of the arc is given by (87) ve = u e sec 0 cos n.

It is also formed by the action of sulphuretted hydrogen on the isocyanic esters, 2CONC 2 H 5 +H 2 S=COS+CO(NHC 2 H 5) 2, by the action of concentrated sulphuric acid on the isothiocyanic esters, Rncs H 2 O = Cos Rnh 2, Or Of Dilute Sulphuric Acid On The Thiocyanates.

It Is Easily Soluble In Solutions Of The Caustic Alkalis, Provided They Are Not Too Concentrated, Forming Solutions Of Alkaline Carbonates And Sulphides, Cos 4Kho = K2C03 K 2 S 2H20.

The mathematical function log x or log x is one of the small group of transcendental functions, consisting only of the circular functions (direct and inverse) sin x, cos x, &c., arc sin x or sin-' x,&c., log x and e x which are universally treated in analysis as known functions.

It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.

The polar equation is r=a+b cos 0, where 2a= length of the rod, and b= diameter of the circle.

At an early period Halicarnassus was a member of the Doric Hexapolis, which included Cos, Cnidus, Lindus, Camirus and Ialysus; but one of the citizens, Agasicles, having taken home the prize tripod which he had won in the Triopian games instead of dedicating it according to custom to the Triopian Apollo, the city was cut off from the league.

The theorem for angle-bisection which Vieta used was not that of Archimedes, but that which would now appear in the form I - cos 0 = 2 sin e 20.

It is said that this was first spun in the island of Cos by Pamphile, daughter of Plates."

Aristotle's vague knowledge of the worm may have been derived from information acquired by the Greeks with Alexander the Great; but long before this time raw silk must have begun to be imported at Cos, where it was woven into a gauzy tissue, the famous Coa vestis, which revealed rather than clothed the form.

Along with Halicarnassus and Cos, and the Rhodian cities of Lindus, Camirus and Ialysus it formed the Dorian Hexapolis, which held its confederate assemblies on the Triopian headland, and there celebrated games in honour of Apollo, Poseidon and the nymphs.

The chief crops grown for early supplies, or " primeurs " as they are called, are special varieties of cos and cabbage lettuces, short carrots, radishes, turnips, cauliflowers, endives, spinach, onions, corn salad and celery.

He travelled past Naples to Syracuse, then on shipboard by Cos and Samos to Ephesus, and thence through Asia Minor to Damascus and Jerusalem.

The directed line whose length is a, and which makes an angle 0 with the real (positive) unit line, is expressed by a (cos 0+i sin e), where i is regarded as +1,/ - 1.

From the new point of view we see at once, as it were, why it is true that (cos 0+ i sin 0) m =cos me+ i sin me.

We may state, in passing, that every quaternion can be represented as a (cos 0+ 7 sin 9), - where a is a real number, 6 a real angle, and it a directed unit line whose square is - 1.

If, as is usually most convenient, the two assigned directions are at right angles, the two components of a force P will be P cos 0, P sin 0, where 0 is the inclination of P to the direction of the p former component.

If the origin of rectangular axes fixed in the lamina be shifted through a space whose projections on the original directions of the axes are X, u, and if the axes are simultaneously turned through an angle e, the coordinates of a point of the lamina, relative to the original axes, are changed from x, y to X+x cos ey sin e, u+x sin e+y cos e, or X + x ye, u + Xe + y, ultimately.

If the forces are all parallel, making say an angle 0 with Ox, we may write Xi = Pi cos 0, Vi = P1 sin 0, Xi = P2 cos 0, VI = Pi sin 0,.

The displacement of the point H in the figure, resolved in the direction of R, is r cos 0sh sin 0.

The work is therefore R(r cos 0sh sin 0)+ G cos 8

The factor (P+P) cos 0h sin 0 is called the vIrtual coefficient of the two screws which define the types of the wrench and twist, respectively.

Is cos 4,, the vertical through the new position of G will fall to the left of J and gravity will tend to restore the body to its former position.

If the point of suspension have an imposed simple vibration f = a cos at in a horizontal line, the equation of small motion of the bob is mx= mg-l-,

To find the forced oscillation due to a periodic force we have tl+k+ux-f cos(rjt+e).

The solution is x=A cos nl+B sinai, y=C cos nt-ED sin at, (9)

If M be the total mass, the potential energy is V=Mgh cos 0, if OZ be drawn vertically upwards.

If we write C cos =H,C sin =K, (17)

Then airf dos OiVi cos Oi; (16)

Double Hookes Coupling.It has been shown in 66 that the velocity ratio of a pair of shafts coupled by a universal joint fluctuates between the limits cos 0 and 1/cos 0.

Hence, by the principle just stated, P cos OXfer= R

A more accurate though still approximate expression for the force on the frame due to the acceleration of the piston whose weight is W is given by w2r cos 0 + r cos 20

The eastern shores of the Aegean, which the earliest historical records represent to us as the seat of a brilliant civilization, giving way before the advance of the great military empires (Lydia and afterwards Persia), are almost a blank in Homer's map. The line of settlements can be traced in the Catalogue from Crete to Rhodes, and embraces the neighbouring islands of Cos and Calymnos.

In honour of the former, the Durga-puja is celebrated ' This notion not improbably took its origin in the mystic cos - mogonic hymn, Rigv.

Many of the islands of the Mediterranean, from which the ancients drew their supplies of wine, such as Chios, Cos, Tenedos, Crete and Cyprus, still produce considerable quantities of wine, but the bulk of this is scarcely to the modern European taste.

The circumference of the edge is 27rr, so that the resultant of this tension is a force 27rrT cos a acting vertically upwards on the liquid.

Equating this force with the resultant of the tension 7rpgr 2 h = 21rrT cos a, or h = 2T cos a/pgr.

Hence the resultant of the surface-tension is 2l T cos a.

Equating the forces pghla =2/T cos a, whence It= 2T cos a/pga.

Resolving horizontally we find T (COS 02 - COS 01)+2gp (y22-3/12) =0, whence cos 02 = COS gpy12 - gpy22, 2T 2 T or if we suppose P 1 fixed and P2 variable, we may write cos constant - Zgpy2/T.

Hence in all cases except that in which the angles a l and a 2 are supplementary to each other, the force is attractive when a is small enough, but when cos a i and cos a 2 are of different signs, as when the liquid is raised by one plate, and depressed by the other, the first term may be so small that the repulsion indicated by the second term comes into play.

If d is the distance between the plates at the edge of the film and II the atmospheric pressure, the pressure 2T of the liquid in the film is II - d cos a, and if A is the area of the film between the plates and B its circumference, the plates will be pressed together with a force 2AT cos a +BT sin a, and this, whether the atmosphere exerts any pressure or not.

In the next place, there is the surface-tension acting downwards, but at an angle a with the vertical, across the circular section of the bubble itself, whose circumference is 21ry, and the downward force is therefore 2lryT cos a.

Hence equating the forces which act on the portion included between ACB and PRQ, ry2p-27ryT cos a= - F (9).

Differentiating equation 9 with respect to s we obtain, after dividing by 27 as a common factor, pyds - T cos a ds + Ty s i n ad s =o...

Suppose, therefore, that the equation of the boundary is r =a+a cos kz, (I) where a is a small quantity, the axis of z being that of symmetry.

Taking the case where the motion is strictly in two dimensions, we may write as the polar equation of the surface at time t r =a cos nB cos pt, (4) where p is given by p2 = (n3_ n)..

It may be shown that if the distance of the carried point from the centre of the rolling circle be mb, the equation to the epitrochoid is x = (a+b) cos 0 - mb cos (a+b/b)0, y = (a +b) sin 9 - mb sin (a +b/b)0.

Therefore any epicycloid or hypocycloid may be represented by the equations p = A sin B+,' or p---A cos B,,G, s = A sin B11.

The intrinsic P equation is s =4a sin 4,, and the equation to the evolute is s= 4a cos 1P, which proves the evolute to be a similar cycloid placed as in fig.

The radius of curvature at any point is readily deduced from the intrinsic equation and has the value p=4 cos 40, and is equal to twice the normal which is 2a cos 2B.

The cartesian equation in terms similar to those used above is x = a6+b sin 0; y=a-b cos 0, where a is the radius of the generating circle and b the distance of the carried point from the centre of the circle.

Idyll vii., the Harvest Feast (eaXUVla), is the most important of the bucolic poems. The scene is laid in the isle of Cos.

It is quite uncertain whether the bucolic poems were written in the pleasant isle of Cos among a circle of poets and students, or in Alexandria and meant for dwellers in streets.

The usual view is that Theocritus went first from Syracuse to Cos, and then, after suing in vain for the favour of Hiero, took up his residence permanently in Egypt.

Some have supposed on very flimsy evidence that he quarrelled with the Egyptian court and retired to Cos, and would assign various poems to the " later-Coan " period.'

The equations of surfaces of equal angular motion would be of the form r =R (i --6 cos 2 0), where e is proportional to the square of the angular motion, supposed small, and R increases as e diminishes.

The value of l may be easily shown to be (r i -Er 2)1r/2 (r i t r 2)a-+-c cos a, where the positive sign is to be taken for a crossed belt and the negative sign for an open belt.

In determining the dimensions of corresponding drums of cone pulleys it is evident that for a crossed belt the sum of the radii of each pair remains a constant, since the angle a is constant, while for an open belt a is variable and the values of the radii are then obtained by solving the equations r 1 = l/ir - c(a sin a + cos a) + 2c sin a, r 2 = l/7r - c(a sin a +cos_a) - lc sin a.

The value of a is in general small, and an approximate solution may be obtained by substituting two or three terms of the expansions for sin a and cos a.

F B is the evolute of this circle, and for any radius DE at an angle a and corresponding tangent EG terminated by the evolute, the perpendicular distance of G from the line AD is c(cos a+a sin a).

If now a line be drawn from A to the bisector H of the side BC, it will meet the vertical through G in I and IJ =c(cos a+a sin a)/ur.

It forms, with the islands of Psara, Nikaria, Leros, Calymnus and Cos, a sanjak of the Archipelago vilayet.

This painting was executed for the temple of Asclepius at Cos, from which it was taken to Rome by Augustus in part payment of tribute, and set up in the temple of Caesar.

A steady flow of knowledge from East to West began in the 7th century B.C. A Babylonian sage named Berossus founded a school about 640 B.C. in the island of Cos, and perhaps counted Thales of Miletus (c. 639-548) among his astro- pupils.

And after losing Oropus, Amphipolis, Cardia, Chios, Cos, Rhodes, Byzantium, shall we fight about the shadow of Delphi?"

The equation to the tangent at 0 is x cos 0/a+y sin 0/b = 1, and to the normal ax/cos 0 - by/sin 0=a2 - b'.

On entry into the crystal the original polarized stream is resolved into components represented by a cos(- a) cos T, a sin (1P - a)cos T, T =27rt/r, and on emergence we may take as the expression of the waves cos (p - a) cos T, sin (4, - a) cos (T - p).

The resultant of these is = 2a cos 2 (k 2 - k i)z cos {nt - 1(k2 -Fk2)z}, = 2a sin 2 (k 2 - ki)z cos {nt - z (k i + k2)z}, which shows that for any fixed value of z the light is plane polarized in a plane making an angle 1(k 2 - ki)z = ir(X i - X7 1)z, with the initial plane of polarization, X 1 and being the wave-lengths of the circular components of the same frequency.

Now Fresnel's formulae were obtained by assuming that the incident, reflected and refracted vibrations are in the same or opposite phases at the interface of the media, and since there is no real factor that converts cos T into cos (T+p), he inferred that the occurrence of imaginary expressions for the coefficients of vibration denotes a change of phase other than 7r, this being represented by a change of sign.

If this be so, it is clear that the factor A / - 1 denotes a change of phase of 42, since this twice repeated converts cos T into cos (T+ir) = - cos T, and hence that the factor a+b A l - I represents a change of phase of tan1 (b/a).

Rs is reduced to s (cos for cons, c 0 r p u s).

We've always had trouble getting airplay ' cos of the politics we're involved with.

Well you're not alone ' cos there's bare of us and we don't all fit the stereotype.

In our defense it was cos BB had been absolutely appalling at sleeping!

Everyday I wipe up the puddle of wee around the toilet and have to stop myself slipping cos you haven't used the bathmat.

I used a bowline ' cos it's compact and secure.

Cos they're much prettier, and they don't carry red briefcases.

Will need a brolly too cos it looks like it might rain!

I mean fancy not entering a compo just ' cos you think there's no point.

Was not good, had to walk back to the college, it was OK cos I had a strategically placed bag!

And if you're not a student, don't worry cos you're welcome anyway.

She just recently cried cos she can''t eat the cakes and chocolates that we had.

I know, cos we get the practice sessions at home!

That didn't really happen last night cos Pennant was playing as an extra right back and Milner as an extra left back.

It's funny actually cos it's so smart compared to the original one and I always quite liked that.

Wake by self in time, which is lucky, cos the alarm I set on my palm was on English time.

I was teased a little but it wasn't too bad cos I had good friends.

The quantity cos f cos l is called the Schmid factor.

Maybe thats cos I'm used to Nokia phones.

The tunes are tighter and more traditionally songlike after this, which is a shame cos sprawling instrumental meltdowns are much more fun.

We first compute the Jacobian; = cos, = sin, = - r sin, = r cos.

I also smile when I see Mike the managers face after a gig cos he's really proud of them all.

Of insurance cos established fact that Gamble Insurance to their new Pennsylvania ohio Delaware.

But I do n't fink you will, cos, like, I really fancy you, know what I mean?

So that means that the value of x is given by cos( q) multiplied by the hypotenuse.

Oh, and he's not a racist but the races should not intermarry - ' cos God says so.

The site liaison COs were happy with the proposal but expressed concern about introducing the new arrangement before the availability of a school-wide inventory.

To serve, slice and place on a simple salad of cos lettuce.

Owen Meany, cos he knows a lot more than he lets on!

Look I'll call you later, cos he's getting a bit restless.

Oh I'd better not dive the whale shark cos the book says I can't.

I freaked out completely at the sight of the open wound cos Im really squeamish at the best of times.

It was more of a shock that my Dad accepted cos he was a very staunch hindu.

It's good to carry a card but your SOS talisman is great cos paramedics or anyone with medical knowledge recognize the symbol immediately.

They started getting whiny at the end, we decided to walk instead of take the monorail cos the queue was so large.

If this be represented by Cos - x (bt - x - S),.

Thalysia, a thanksgiving festival, held in autumn after the harvest in the island of Cos (see Theocritus vii.).

In order to adapt this formula to logarithms, we introduce a subsidiary angle p, such that cot p = cot l cos t; we then have cos D = sin 1 cos( - p) I sin p. In the above formulae our earth is assumed to be a sphere, but when calculating and reducing to the sea-level, a base-line, or the side of a primary triangulation, account must be taken of the spheroidal shape of the earth and of the elevation above the sealevel.

If Q be on the circle described upon OA as diameter, so that u = a cos 4,, then Q' lies also upon the same circle; and in this case it follows from the symmetry that the unsymmetrical aberration (depending upon a) vanishes.

If the equation of this line, referred to new coordinate axes in the plane area, is written xcos a+y sin a - h=o, (3) R = f f p(h - x cos a - y sin a)dxdy, (4) zR= f fpx(h - xcos a - y sin a)dxdy, (5) yR = f f py(h - x cos a - y sin a)dxdy.

Then the quantity E cos OdS is the product of the normal component of the force and an element of the surface, and if this is summed up all over the surface we have the total electric flux or induction through the surface, or the surface integral of the normal force mathematically expressed by JE cos OdS, provided that the dielectric constant of the medium is unity.

If the sphere r, degenerate to a point, the function 2rr 1 cos 0 has the limit d 2 - r2; this is the square of the tangent to the sphere from the point, and is named the "power of the sphere at the point," or the "power of the point with respect to the sphere."

Resolving normally in the trajectory, and supposing the resistance of the air to act tangentially, (18) v(di/dt) =g cos i, where di denotes the infinitesimal decrement of i in the infinitesimal increment of time dt.

Starting with the exact equations of motion in a resisting medium, (43) d2t cos i = ds, d 2 y d 44 dt2 = -r sin i-g= -rds-g, and eliminating r, (45) dt - - cos z, or the equation obtained, as in (18), by resolving normally in the trajectory, but di now denoting the increment of i in the increment of time dt.

But, as originally pointed out by Euler, the difficulty can be turned if we notice that in the ordinary trajectory of practice the quantities i, cos i, and sec i vary so slowly that they may be replaced by their mean values,, t, cos 7 7, and sec r t, especially if the trajectory, when considerable, is divided up in the calculation into arcs of small curvature, the curvature of an arc being defined as the angle between the tangents or normals at the ends of the arc.

In fact, if we put xy=4(X+Y), X being a function of x only and Y a function of y only, we can show that we must have X = Ae gz, y =Be y "; and if we put xy= 0(X+Y) - 43(X-Y), the solutions are 4(X+Y)=4(x+y)2, and x= sin X, y= sin Y, 4(X-1-Y) =-2 cos (X+Y).

The cartesian equation to a parabola which touches the coordinate axes is 1 / ax+'1 / by= i, and the polar equation when the focus is the pole and the axis the initial line is r cos 2 6/2 = a.

The moment of the resultant force R of the wrench about this line is Rr sine, and that of the couple G is G cos 9.

Then if 0 is the centre of curvature in the plane of the paper, and BO =u, I _ cos sinew u R 1 R2 Let POQ=o, PO=r, PQ=f, BP=z, f 2 = u 2 +r 2 -2ur cos 0 (26) The element of the stratum at Q may be expressed by ou t sin o do dw, or expressing do in terms of df by (26), our 1fdfdw.

Hence X =4gp(h, 2 +h 2 2) - T{I - 2(sin a i +sin a2)}, or, substituting the values of h 1 and h2, I T2 X = - 2 (cos a, +cos a2)2 2 pga - T { I - z (sin a l +sin a 2) - T12 (cos a t +cos a 2) (cot a t +cot a 2) } the remaining terms being negligible when a is small.

Look I'll call you later, cos he 's getting a bit restless.

Oh I 'd better not dive the whale shark cos the book says I ca n't.

Been listening to the usual old stuff cos no one sends me new music anymore and I 'm too skint to buy any.

But we 're sticking with ' Dame ', ' cos it 's much snappier and quicker to type.

Too well, in fact, cos I keep having to somehow stump up the cash to get more done !

It 's good to carry a card but your SOS talisman is great cos paramedics or anyone with medical knowledge recognize the symbol immediately.

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

Dus any1 no wen da peru reunion camp is cos i can wait !

The most common of these sulphides is cobaltous sulphide, CoS, which occurs naturally as syepoorite, and can be artificially prepared by heating cobaltous oxide with sulphur, or by fusing anhydrous cobalt sulphate with barium sulphide and common salt.

The factors Af (u-v cos i) and Bf (v sin i) give the frictional resistance to sinking, per unit length of the cable, in the direction of the length and transverse to the length respectively.

Corinth, however, was allowed to go on striking staters under Antigonus Gonatas; Ephesus, Cos and the greater cities of Phoenicia retained their right of coinage under Seleucid or Ptolemaic supremacy.