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The analytic method sought to express the moon's motion by integrating the differential equations of the dynamical theory.

74Integrating the expression for an angle of wrapping 0, we obtain the relation log € Ti/T2= µ9, where T 1 and T2 are the end tensions.

54A recording drum or integrating apparatus may be arranged on the pulley frames.

32Integrating by parts, we find v i.

34q,,) tobe generated instantaneously from rest by the action of suitable impulsive forces, we find on integrating (II) with respect tot over the infinitely short duration of the impulse ~-=Q.

22After the establishment of universal gravitation as the primary law of the celestial motions, the problem was reduced to that of integrating the differential equations of the moon's motion, and testing the completeness of the results by comparison with observation.

22capstone project integrating the two disciplines.

10marc format provides a means of integrating metadata into existing systems.

10The expression for the change of intrinsic energy E between any given limits poOo to po is readily found by substituting these values of the specific heats in equations (II) or (13), and integrating between the given limits.

00It is easy, however, to correct the formula for these deviations, and to make it thermodynamically consistent with the characteristic equation (13) by substituting the appropriate values of (v-w) and L =H -h from equations (13) and (is) in formula (21) before integrating.

00Integrating tightly with all other dataflow modules, the result is the instant availability of essential management information throughout your company.

00The enthalpy values were obtained by integrating the specific heat capacity polynomial for each compound.

00Chapter fourteen presents a couple of " case studies, " integrating material from previous chapter fourteen presents a couple of " case studies, " integrating material from previous chapters.

00Integrating of teams into the project Our Network includes the seven experienced teams, with mutually complementary skills and research tasks.

00The amplified sensor signals are converted to digital data with a microprocessor-controlled integrating A/D converter.

00The motion proposed by the NEC will seriously curtail democracy, which is central to integrating students into the national union.

00IESS is a leading provider of advanced electronic products and systems for customers integrating electronics into their products.

00enthalpy data were obtained by integrating the specific heat capacity polynomial for each compound.

00Example 2: fieldwork in science and environment Here the CETL demonstrates excellence in integrating fieldwork with class-based teaching.

00Java enterprise technologies Microsoft got a jump-start with integrating Web services into the.NET framework.

00The next step is to create page mock-ups, which represent the actual site, by integrating the design sketches with the layout grids.

00Integrating with other technologies: video-conferencing; PDAs; SMS; electronic voting; body morphing and avatars.

00This work has contributed a user model and tailoring mechanism to the W3C SMIL language for integrating multimedia.

00Integrating the automatic layout of Euler Diagrams with the layout of graphs and less structured diagrammatic notations.

00Ordinary differential equations: first order, first degree ode 's of separable type and the integrating factor method.

00Methods of solution of first-order odes: separable, integrating factor, homogeneous.

00The enthalpy values were obtained by integrating the specific heat polynomial for each compound.

00And starting in September of this year we began integrating ship-based and ground-based radars into our test against intercontinental ballistic missiles.

00reflectance measurements are made using either a scanning spectrophotometer fitted with an integrating sphere accessory, or a diode array spectrophotometer.

00Total Transmittance Measurements are made using a scanning spectrophotometer fitted with an integrating sphere accessory.

00spectrophotometer fitted with an integrating sphere accessory.

00Total Reflectance Measurements are made using either a scanning spectrophotometer fitted with an integrating sphere accessory, or a diode array spectrophotometer.

00integrating a subwoofer into your system to produce a seamless sound is a challenge for any home cinema enthusiast.

00LSPs must be capable of balancing and integrating economic, social and environmental goals to deliver genuinely sustainable communities.

00With the values above of u, v, w, u', v', w', the equations become of the form p x + 4 7rpAx -Fax -{-hy-}-gz =o, - p - dy+ 4?pBy + hx+ay+fz =o, P d p + TpCZ +f y + yz = o, and integrating p p 1+27rp(Ax2+By2+CZ2) +z ('ax e +ay e + yz2 2 f yz + 2gzx + 2 hx y) = const., (14) so that the surfaces of equal pressure are similar quadric surfaces, which, symmetry and dynamical considerations show, must be coaxial surfaces; and f, g, h vanish, as follows also by algebraical reduction; and 4c2 (c 2 - a2)?

00Starting from any ordinate ue,o, the result of integrating with regard to x through a distance 2h is (in the example considered in § 61) the same as the result of the operation 3h(I + 4E + E 2), where E r denotes the operation of changing x into x+h (see Differences, Calculus oF).

00Integrating a subwoofer into your system to produce a seamless sound is a challenge for any home cinema enthusiast.

00Integrating DC with CHP When integrating DC with CHP, beneficial synergies ensue.

00While there are many different methods for integrating a new cat into your home, these five tips are gathered from methods that have worked for other cat owners.

00Cost - While the initial cost of integrating biofuels into everyday life seem enormous, once that expense is addressed, the use of biofuels would be much less expensive than traditional fuel.

00He believed in designing to the scale of the human and integrating buildings gracefully within the landscape.

00Other tasks in games might include walking the dog and integrating the puppy with other dogs.

00Russell specializes in integrating his scientific background with his knowledge of holistic health to create wellness programs that promote optimum health for both people and pets.

00Pendants, brooches, cuff links, anklets, and earrings are also available, integrating the symbolism of the claddagh into anyone's jewelry preferences.

00Google Latitude - Not really a necessity, but absolutely cool, the Google Latitude app lets you share your current location and even permits integrating with Google Maps.

00Infants born prematurely have more difficulty integrating and interpreting visual information even when their acuity is normal.

00Carlson, Jon, et al. Family Therapy Techniques: Integrating and Tailoring Treatment.

00They are a means of integrating recent and past learning and of establishing psychological equilibrium.

00Childhood nightmares are a normal process of coping with new challenges and integrating new life experiences into the child's understanding of the world.

00J. "Integrating Research on Temperament and Childhood Psychopathology: Its Pitfalls and Promise."

00Other groups such as Unmata can be seen on YouTube integrating contemporary music and dance forms such as electronica and hip-hop with basic forms straight from Arab belly dancing.

00Taking any style from the past 100 years and integrating it with a modern personalized cut.

00Integrating both writing and reading practice, build on fluency when you start teaching comprehension skills.

00Integrating technology into your homeschool curriculum gives kids the exposure they need for future computer success.

00They focus on integrating your child to a learning environment and working on necessary life skills.

00This cliffhanger demonstrated how Deb/Jane were integrating as one person.

00Many practitioners of alternative health strongly recommend consulting with a your primary care provider about physical problems and integrating alternative remedies as a supplement to general care.

00Integrating yoga, creativity, music and fun, YogaKids emphasizes healthy minds and bodies through active participation in YogaKids classes.

00Hatha Yoga is all yoga that consists of working on a series of different yoga poses (asanas), and integrating breathing work into the poses (pranayama).

00Integrating children with autism into the educational environment is one area in which many strategies and innovations have been developed.

00Exposure to the right toys can help your child have fun while integrating new sensations into her daily life.

00People on the spectrum may have difficulty integrating several small pieces of information to form a whole concept.

00As the above examples show, cost benefits of EAPs are worth integrating into your company.

00They end up integrating a form of hip-hop dancing called "crumping" into their routines, a strategy that ends up setting their squad apart from the others as they compete for a TV spot with pop star Rihanna.

00Meal replacement products, such as Slim Fast food items, promote quick weight reduction by means of integrating their products into your daily intake.

00Integrating some unique music players can really personalize your page and set it apart from all your friends.

00Integrating music on MySpace is similar to using MySpace music videos.

00Werewolves have intrigued us for many centuries; integrating the myth and legend into popular culture making werewolf fantasy art increasingly popular.

00This is one of the reasons that some people prefer Blogger over Wordpress, because integrating Adsense into your Blogger site is extremely easy.

00Whether you're just using audio (like the popular NPR broadcasts) or are integrating video (like the YOGAmazing instructional podcasts) it's all your choice based on your abilities and feelings on the matter.

00Regardless of the source, integrating a forum into your site is the first step to leveraging the truly interactive potential of the web.

00Taking the time to learn advanced HTML codes before jumping into things like CSS and Javascript can make integrating those Web 2.0 techniques a much easier process.

00Google Checkout is also a very stable platform to build an e-commerce site with, integrating into almost any website with ease.

00Thus the contribution to the total impulsive pressure exerted on the area dS in time dt from this cause is mu X udtdS X (11 3 m 3 /,r 3)e hm (u2+v2+w2 )dudvdw (I o) The total pressure exerted in bringing the centres of gravity of all the colliding molecules to rest normally to the boundary is obtained by first integrating this expression with respect to u, v, w, the limits being all values for which collisions are possible (namely from - co too for u, and from - oo to + oo for v and w), and then summing for all kinds of molecules in the gas.

01Integrating (27) again, (31) y =g(zTt2t 2) = zgt(T -t); and denoting T-t by t', and taking g= 32f/s2,) y =16tt', (32 which is Colonel Sladen's formula, employed in plotting ordinates.

01If we proceed instead by the method of integrating the equation H -h =6(v-w)dp/d6, we observe that the expression above given results from the integration of the terms -dh/R0 2 +w(dp/d9)/R9, which were omitted in (25).

01We will suppose that P is a function of r only; then integrating (~) we find ~ v2 = fPdr+const., (4)

01whence, integrating with respect to t, 3/4M (~2 +5i) + 3/4162 =f(Xdx+Ydy +NdO) +const.

01Integrating with respect to f from f =z to f=a, where a is a line very great compared with the extreme range of the molecular force, but very small compared with either of the radii of curvature, we obtain for the work (1,G (z) - 111(a))dw, and since (a) is an insensible quantity we may omit it.

01Integrating the first term within brackets by parts, it becomes - fo de Remembering that 0(o) is a finite quantity, and that Viz = - (z), we find T = 4 7rp f a, /.(z)dz (27) When c is greater than e this is equivalent to 2H in the equation of Laplace.

01Integrating by parts, we get J l'(z)d z = zI, G (z) + 3 z 3 I I (z) 3 f z3Cb(z)dz, fzqi(z)dz = J z21 '(z) + k z41 I (z) + a fz4(1)(z)dz.

01The mean brightness varies as z3 (or as r3), and the integral found by multiplying it by zdz and integrating between o and co converges.

02If the subject of examination be a luminous line parallel to n, we shall obtain what we require by integrating (4) with respect to 77 from - oo to + oo.

02E is then the co-ordinate relatively to 0 of any focal point 0' for which the retardation is R; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo.

02Integrating by parts in (II), we get J e = ikr d7 pc-11 / d (e r - ay= rJ Z d y - r / 1 dY, in which the integrated terms at the limits vanish, Z being finite only within the region T.

02Taking 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.

02(to) Integrating over the base, to obtain one-third of the kinetic energy T, 3T = 2 pf '3 4R2(3x4-h4)dx/h 3 = pR2h4 / 1 35 V 3 (II) so that the effective k 2 of the liquid filling the trianglc is given by k 2 = T/Z p R 2 A = 2h2/45 = (radius of the inscribed circle) 2, (12) or two-fifths of the k 2 for the solid triangle.

02= -dQ+1dg2, and integrating round a closed curve (udx+vdy+wdz) =0, and the circulation in any circuit composed of the same fluid particles is constant; and if the motion is differential irrotational and due to a velocity function, the circulation is zero round all reconcilable paths.

02J -1k di - d 3a dX +2(a2+X)d (a -) =o, and integrating (a 2 + X) 3 /2ad?

02The equation to these lines in terms of v and 0 is obtained by integrating dE=sd0+(Odp/de - p)dv = o .

02The equation to the lines of constant total heat is found in terms of p and 0 by putting dF=o and integrating (it).

02In thiscase the ratio of the specific heats is constant as well as the difference, and the adiabatic equation takes the simple form, pv v = constant, which is at once obtained by integrating the equation for the adiabatic elasticity, - v(dp/dv) =yp.

02Putting d0/dp=A/0 2 in equation (15), and integrating on the assumption that the small variations of S could be neglected over the range of the experiment, they found a solution of the type, v/0 =f(p) - SA /30 3, in which f(p) is an arbitrary function of p. Assuming that the gas should approximate indefinitely to the ideal state pv = R0 at high temperatures, they put f(p)=Rip, which gives a characteristic equation of the form v= Re/p - SA /30 2 .

02Denoting by So, so, these constant limiting values at p=o, we may obtain the values at any pressure by integrating the expressions (27) and (28) from co to v and from o to p respectively.

02(29) (30) The expression for the change of entropy between any two states is found by dividing either of the expressions for dH in (8) by 0 and integrating between the given limits, since dH/B is a perfect differential.

02Apparatus is added to some dynamometers by means of which a curve showing the variations of P on a distance base is drawn automatically, the area of the diagram representing the work done; with others, integrating apparatus is combined, from which the work done during a given interval may be read off directly.

02di 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.

02Now 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.

02He concludes that the integrating principle of the whole - the Spirit, as it were, of the Universe - must be something akin to, but immeasurably superior to, the " psychism " of man.

02The relation between the equilibrium pressures P and P' for solution and solvent corresponding to the same value po of the vapour pressure is obtained by integrating the equation V'dP' = vdp between corresponding limits for solution and solvent.

02Putting in these values and integrating we have, neglecting terms involving 0', P=12.06 0-0.021 O s where P is the osmotic pressure in atmospheres.

02The Mean Specific Heat, Over Any Range Of Temperature, May Be Obtained By Integrating The Formulae Between The Limits Required, Or By Taking The Difference Of The Corresponding Values Of The Total Heat H, And Dividing By The Range Of Temperature.

02Substituting L= Lo+ (S-s)(6-Bo), and integrating between limits, we obtain the result log e p=A+B/o+C log e 6,..

02

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