log

The log stays with the car.

9229His new log home was nice, but not extravagant.

6948She glanced back over her shoulder at the log house on the hill.

4125I sat her on a fallen log by side of the dirt track.

3121A tiny yellow flower peeped from under the log and she leaned down to examine it.

2313Her hand shaking, she checked the log to see it had last been accessed by General Greene twenty-five hours ago.

166I've found old rock fences, and there's an old log cabin falling into ruins not too far from here.

1518You've got to know he had that log house built.

1415She hadn't been able to log onto Dusty's computer, because he kept it locked out.

125The log house was further on, and up a steep incline – a sentinel overlooking the valley.

126She smoothed the folds of her skirt nervously and waited for him to open the subject, but he was silent until they reached the log house.

112The thick log walls insulated them from some of the noise, but the storm was fierce.

114Across from them was the log house — home.

114There was no food in the cottage, so she turned a small log into cans of soup.

1110The log house on the hill?

1111There was a log listing mileage and dates in a variety of different handwritings.

1012To do so, you need to log in.

64Another thirty minutes and she would be at the old log cabin.

54It would be perfect hideaway - old log cabin in excellent condition - breathtaking scenery.

55She leaned over the log and retrieved the book.

55"Who will sing us a song?" said the master woodman as he threw a fresh log upon the fire.

55Before winter I built a chimney, and shingled the sides of my house, which were already impervious to rain, with imperfect and sappy shingles made of the first slice of the log, whose edges I was obliged to straighten with a plane.

55In the winter he had a fire by which at noon he warmed his coffee in a kettle; and as he sat on a log to eat his dinner the chickadees would sometimes come round and alight on his arm and peck at the potato in his fingers; and he said that he "liked to have the little fellers about him."

46They tried to make their way forward to the opposite bank and, though there was a ford one third of a mile away, were proud that they were swimming and drowning in this river under the eyes of the man who sat on the log and was not even looking at what they were doing.

46Jule took her hand and led her through the large log house with its earthy décor.

47In fact, the entire design of the living area was more open and roomy than the new log home where they now lived.

47The Tennents erected the Log College (on the Neshaminy, about 20 m.

47She sat on a thick log. He disappeared into the shadows of the jungle, and she pulled her knees to her chest, listening. He was silent while the branches overhead hissed and rasped against one another and the cries of distant birds drifted to her.

48It should know what the food on my fork weighs, run a chemical analysis of every bite I take, and log it in my Digital Echo file for my future reference.

48In an effort to release the log jam, Dean gave his stepfather a hand with the moving.

49I amused myself one winter day with sliding this piecemeal across the pond, nearly half a mile, skating behind with one end of a log fifteen feet long on my shoulder, and the other on the ice; or I tied several logs together with a birch withe, and then, with a longer birch or alder which had a hook at the end, dragged them across.

33Someone was building a log house so close that they could overlook her farm.

34Even the thunder of the underworld sounded weird. Katie glanced towards the sky, silently cursing the rain. She made her way over a fallen log and waited for Deidre before continuing.

34A log tripped her, and she rolled partway down the other side of the hill then bounded to her feet.

34Settled into a backdrop of wooded hills, was the little log cabin.

34JAMES ABRAM GARFIELD (1831-1881), twentieth president of the United States, was born on the 19th of November 1831 in a log cabin in the little frontier town of Orange, Cuyahoga county, Ohio.

34You can get a login name by clicking on "Log in" at the upper right.

34The Sawhorse stopped at the same time and stared at the other with its queer protruding eyes, which were mere knots in the log that formed its body.

34The statement is not there because you want the log per se but because the logging of the actions is what documents how much you need to pay.

34He came here a-fishing, and used an old log canoe which he found on the shore.

34Sometimes through the monotonous waves of men, like a fleck of white foam on the waves of the Enns, an officer, in a cloak and with a type of face different from that of the men, squeezed his way along; sometimes like a chip of wood whirling in the river, an hussar on foot, an orderly, or a townsman was carried through the waves of infantry; and sometimes like a log floating down the river, an officers' or company's baggage wagon, piled high, leather covered, and hemmed in on all sides, moved across the bridge.

34The house, with its bare, unplastered log walls, was not overclean--it did not seem that those living in it aimed at keeping it spotless--but neither was it noticeably neglected.

35He sauntered over to her and rested one foot on the log.

20Seated on a log in a small dell she was surrounded by a crowd of spellbound children listening to her tales.

20Our first night in your new log house.

22During the separation the New Side established the college of New Jersey at Elizabethtown (now Elizabeth) in 1747, and the Log College of the Tennents was merged into it.

22LOG(a word of uncertain etymological origin,possibly onomatopoeic; the New English Dictionary rejects the derivation from Norwegian lag, a fallen tree), a large piece of, generally unhewn, wood.

22Kelway invented an electrical log in 1876.

22The screw or rotatory log of Edward Massey, invented in 1802, came into general use in 1836 and continued until 1861.

10The rotator was connected to the log by a rope 6 ft.

10You won't have to go eat the other foods; the system will remember every meal you have had and will log your headaches.

12Napoleon looked up and down the river, dismounted, and sat down on a log that lay on the bank.

12In one smooth movement he jerked the machete from the log and chopped the twine in two.

13Petya was carried out like a log and laid in the larger of the two traps.

13The log walls of the barn and its snow-covered roof, that looked as if hewn out of some precious stone, sparkled in the moonlight.

13You might have said something in my defense last night, instead of sitting there like a lump on a log.

00I had a few drinks at dinner and I was sleeping like a log.

00Dean looked at the odometer and then at the mileage log.

00Again she swung the ax, and this time it went half way through the log.

00Grasping the handle of the machete, she half fell, half leaped behind the log.

00She brought the machete down with a dull thud, anchoring the blade in the log.

00To "heave the log," a man holds the log-reel over his head (at high speeds the man and portable reel are superseded by a fixed reel and a winch fitted with a brake), and the officer places the peg in the log-ship, which he then throws clear and to windward of the ship, allowing the line to run freely out.

00In normal circumstances the log is hove every hour.

00In a steam vessel running at high speed on an ocean route, with engines working smoothly and uniformly, a careful officer with correct line and glass can obtain very accurate results with the common log.

00In Thomas Walker's harpoon or frictionless log, introduced in 1861, the wheelwork was enclosed in a cylindrical case of the same diameter as the body of the rotator or fan, and the latter was brought close up to the register, forming a compact machine and avoiding the use of the 6-ft.

00The log should be washed in fresh water when practicable, to prevent oxidization of the wheels, and be lubricated with suitable oil through a hole in the case.

00These logs were towed from the ship, but with quick passages and well surveyed coasts, the need arose for a patent log which could be readily consulted from the deck, and from which the distance run under varying speeds could be quickly ascertained.

00- The AI Harpoon Ship Log.

00log (fig.

00- The Cherub Log.

00- Walker's Neptune Log.

008 the ball bearings are shown unscrewed from the body of the log, with eye, cap and spindle.

00To enable the indications of the log register on the taffrail to be recorded in the chart room or any other part of the vessel as desired, a chart room electric register has been introduced.

00By means of an electric installation between the log register aft and the electric register in the chart room, every tenth of a mile indicated by the former is recorded by the latter.

00II represents the arrangement fitted to the Neptune log; with the Cherub log, a small piece of line is introduced between the governor and the eye of the register.

00The former bears a general resemblance to the Cherub log, but the dial plate is horizontal and the faces turn upwards.

00The Bliss resembles the Rocket log in shape, and is secured to the taffrail by a rope or slung.

00Constant use, increased friction (m o r e especially at high speeds), and damage to the rotator will alter an ascertained log error; head or following seas, strong winds, currents and tidal streams also FIG.

00of Neptune Log.

00A Log Book is a marine or sea journal, containing, in the British navy, the speed, course, leeway, direction and force of the wind, state of the weather, and barometric and thermometric observations.

00- Ball Bearings of Neptune Log in Skeleton Case.

00- Rocket Log.

00The deck log book, kept by the officers of the watch, is copied into the ship's log book by the navigating XVI.

00- Dial-plate of Neptune Log.

00- Neptune Log fitted with Governor.

00In the British mercantile marine all ships (except those employed exclusively in trading between ports on the coasts of Scotland) are compelled to keep an official log book in a form approved by the Board of Trade.

00A mate's log FIG.

00- Bliss Log.

00Benjamin's youth was passed upon the ancestral farm, and as opportunity afforded he attended school in the log school-house near his home.

00On the summit La Salle built store-houses and log huts, which he surrounded by intrenchments and a log palisade.

00His father, Ebenezer Webster (1739-1806), was a sturdy frontiers - man; when, in 1763, he built his log cabin in the town of Salis - bury there was no habitation between him and Canada.

00His general formula for getting at the number of units in any sensation is S = C log R, where s stands for the sensation, R for the stimulus numerically estimated, and c for a constant that must be separately determined by experiment in each particular order of sensibility.

00See Azel Ames, The May-Flower and Her Log (Boston, 1901); Blanche McManus, The Voyage of the Mayflower (New York, 1897); The General Society of Mayflower: Meetings, Officers and Members, arranged in State Societies, Ancestors and their Descendants (New York, 1901).

00The logarithmic formulae for these concentration cells indicate that theoretically their electromotive force can be increased to any extent by diminishing without limit the concentration of the more dilute solution, log c i /c 2 then becoming very great.

00On the analogy between this case and that of the interface between two solutions, Nernst has arrived at similar logarithmic expressions for the difference of potential, which becomes proportional to log (P 1 /P 2) where P2 is taken to mean the osmotic pressure of the cations in the solution, and P i the osmotic pressure of the cations in the substance of the metal itself.

003 log (1 +aiox +aol)/+...+apgxPyq+....

00Now log (1+ï¿½X1 +/22X2+/ï¿½3X3 +ï¿½ï¿½ï¿½) =E log (1+/2aix1+22aix2-1-/23ax3+...) whence, expanding by the exponential and multinomial theorems, a comparison of the coefficients of ï¿½n gives (n) (-)v1+v2+v3+..

00+1.0v4Dp4+...; and thence p010+ v d01 - (ï¿½ 2d 20+ 2 ï¿½ vd 11 +v 2 d02) +ï¿½ï¿½ï¿½ = log (1+IuD10+PDc.1+...+ï¿½pv4Dp4+...).

00The sum of the corresponding numbers multiplied by 332600 gives Log.

00Then, from the formula a 3 - Mo - [20.12773] - n - 15.59814 Log.

00a in metres = 1 117653 Log.

00a2 Since e= I -72= V the above expression for N may be written 4 7r nt + 1/m 2 - I N = 11t1-I (2011-- I in - Jnt2 - I I/ 4 7r C = 111 2 - I 1/111 t - log (in + Im 21) - I, from which the value of N for a given dimensional ratio can be calculated.

00When the ellipsoid is so much elongated that I is negligible in relation to m'-, the expression approximates to the simpler form N=412 (log 201-I).

00It is shown in the paper that the greatest possible force which the isthmus method can apply at a point in the axis of the bobbin is F = 11, 137 I, log i n b/a, I, being the saturation value of the magnet pores, a the radius of the neck on which the cones converge, and b the radius of the bases of the cones.

00(iii.) (a) If p = log i n, then n = (b) If a = n, then n =a'.

00In the same way we regard log l 02, not as a new kind of number, but as an approximation.

00We know that log l oN(I+9) = log l oN+log 10 (I+0), and inspection of a table of logarithms shows that, when 0 is small, log 10 (I+B);s approximately equal to X0, where X is a certain constant, whose value is.

00If therefore we choose a quantity e such that log e I o X X= I, log i oe = X, which gives (by more accurate calculation) e=2.71828..., we shall have lim(loge(I+0))}/0=I, and conversely 'lim' {ex+0 - e x } 143= The deduction of the expansions log e (' +x) = x - Zx 2 + 3x 3 - ..., e x = I +.x+x2/2!+x3/3!-}-..., is then more simply obtained by the differential calculus than by ordinary algebraic methods.

00is approximately equal to -J(27rn).(nle) n; the approximation may be improved by Stirling's theorem log e 2 +log e 3 +...

00The cartesian equation is x = ti' (c2-y'")+ 2c log [{c-?/ (c.2- y2)}/{c+?i (c2+y2)il, and the curve has the geometrical property that the length of its tangent is constant.

00(2) (3) Suppose the density p varies as some nth power of the depth below 0, then (7) and the lowering of the surface is 2 ° - z=klog po - z= - k log(1 - k) - zt12 k (20) Po as before in 17).

00For instance, in a uniplanar flow, radially inward towards 0, the flow across any circle of radius r being the same and denoted by 27rm, the velocity must be mfr, and 0=m log r,, y=m0, +4,i =m log re ie, w=m log z.

00(7) Interchanging these values =m log r, 4, = mO, 4,+4,i =m log rei e (8) gives a state of vortex motion, circulating round Oz, called a straight or columnar vortex.

00If other vortices are present, any one may be supposed to move with the velocity due to the others, the resultant stream function being = gy m log r =log IIrm; (9) the path of a vortex is obtained by equating the value of 1P at the vortex to a constant, omitting the rm of the vortex itself.

00The expression for w in (i) § 29 may be increased by the addition of the term im log z =-m0 + im log r, (1) representing vortex motion circulating round the annulus of liquid.

00A relative stream line, along which 1/,' = Uc, is the quartic curve y-c=?![2a(r-x)], x = 4a2y2-(y g)4, r- 4a2y2 +(y c) 4, 7) 4 a (y-c) 4a(y and in the absolute space curve given by 1', dy= (y- c)2, x= 2ac_ 2a log (y -c) (8) 2ay y - c 34.

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.

00(b-a.0-a) (6) (Q) AI (a-a .0b) ch n2= ch log (Q) n cos 114+i sh log (9) re sin n9 = 2(r+ fi n) = b - a ' ju -a (7) a-a' l u-b nf2 = sh log (cos nO +1 ch log (" sin 110 =2(?"

002n u (a -b.b -a')' not requiring the integration of (II) and (12) If 0=a across the end J J' of the jet, where u = oo, q= Q, b-a' a-b ch 7/2,=cos na = I, , sh 162 = i sin na = i,, a - a a-a Then a-a'+(a+a) cos 2na-[a+a'+(a-a) cos 2najcos 2110 (a-a') sin' 2na X cos 211a - cos 2110 Along the wall AB, cos nO =o, sin n0= I, a> u> b, ch n2= i sh log (q) n= i?

00`ia a - a u-b sh nf2= i ch log (Q) n =i a-b ?

00m _ c Q du dO dt - rrqu 2r qu AB _ Q du L bq (u -a') +V (b -a')1,l (a -u)11/ndu) L 1,1 (a-a/),,1 (u-b), f u Along the wall Bx, cos n0 =I, sin n0 =o, b >u>o ch nSt = ch log () n=, , fb-a?, ?

00Ja - u ?I a -a b -u' sh nS2=sh log (Q)=?a - b a - a' b - u' At x where = co, u = o, and q= go, (O n b - a ' a + a -b a' cio) - ?a-a'?b a-a' q In crossing to the line of flow x'A'P'J', b changes from o to m, so that with q = Q across JJ', while across xx the velocity is qo, so that i n = go.

005, I ch S2 = u a, sh C2= ' u (I) (I and along the jet APJ, oo > u=aerslc>a, sh S2=i sin 0 =iu=ie zrs/o, (2) PM sin 0 ds = f e ds = 1 = 1 sin 0, (3) cos 272a - cos 2n0 = 2Q - ?ib L a b2 s i n' 27ta u-b A (a- (u -a.u -b') sin 2110 - 2 a-a .u-b ?l (u -a.u -a') = s in 2na u-b 2n b) A (ab.ba') p l u -bJ (u -a.u -a') sh nS2=i sin 110=i then the radius sin 2170 (30) A', cos nO= i, sin n0=o, n 1 ' b-a' ch nS2= ch log (9) = Va -a' n shnS2= shlog (Q) q _ o> u>a'.

00From A to B, a>u >b, 0=0, ch S2= ch log Q=cos a-i sin 2a a-b I sh S2= sh log Q= I (a u-b-a/) s i n a Q = (u-b) cos a-2(a-a') sin 2 a+1,/ (a-u.u- a')sin a (8) u-b ds _ ds d4 _ Q dw Q du - Q d 4) du q du (u-b) cos a-2(a- a') sin 2 a (a-u.0 - a') sin a (9) it j- -j' AB _f a(2b - a - a')(u-b)-2(a-b)(b-a')+2V (a - b.

00with A' =0 over the surface of the paraboloid; and then' = ZU[y 2 - pJ (x2 + y2) + px ]; (9) =-2U p [1/ (x2 + y2)-x]; (io) 4, = - ZUp log [J(x2+y2)+x] (II) The relative path of a liquid particle is along a stream line 1,L'= 2Uc 2, a constant, (12) = /,2 3, 2 _ (y 2 _ C 2) 2 2 2 2' - C2 2 x 2p(y2 - c2) /' J(x2 +y 2)= py ` 2p(y2_c2)) (13) a C4; while the absolute path of a particle in space will be given by dy_ r - x _ y 2 - c2 dx_ - y - 2py y 2 - c 2 = a 2 e -x 1 46.

00Now (x1 - x21) (y 1 +y21) = xl l +x2y2 + - (' r 1 2 - x2y1) = FG-x3y3+iV X3, yi+3 7 21_FG-x3y3+2V X3 xl+x21 X12 +X22 (x 1 +x 2 i) = - i{(q' - q)x3+r'y3]+irx3(y1+y21), = FG - x3y3 +ZJ X3 dt2log(x1+x22) - - (q g) x 3- r y3+rx3 F2x32 (12) d dl2 log V x1 ± x2 2 (q'-q)x3-(r'-r) y3FrFF2-x 2 3 ' (13) requiring the elliptic integral of the third kind; thence the expression of x1-f -x21 and yl-}-y21.

00It consists of two thick trunks placed upright, their upper ends mortised into a horizontal log which projects beyond them at either side.

0021rry/dx units, and the potential V at a point on the axis at a distance x from the annulus due to this elementary charge is ll2 2?rrc V=2 j o (r2+x2) dx=47rrvj log e (2l+1,/ r2 +412 ') - loge'} If, then, r is small compared with 1, we have V =47rry log e llr.

00But the charge is Q = 21rra, and therefore the capacity of the thin wire is given by C =1/2 log e llr (2).

00Hence V 2 - V 1 = - A log R 2 /R 1.

00If then the outer cylinder be at zero potential the potential V of the inner one is V =A log (R 2 /R 1), and its capacity C =1/2 log R2/R1.

00Kirchhoff's expression is as follow d+47 r rd l dlog e 167x 2 + t), +t log,: t t I (4) In the above formula e is the base of the Napierian logarithms. The first term on the right-hand side of the equation is the expression for the capacity, neglecting the curved edge distribution of electric force, and the other terms take into account, not only the uniform field between the plates, but also the non-uniform field round the edges and beyond the plates.

00It is ordinarily caught in wooden traps of simple construction, being little enclosures of stakes or brush in which the bait is placed upon a trigger, with a short upright stick supporting a log of wood, which falls upon its victim on the slightest disturbance.

00Applying the above equation to a gas obeying the law pv=RT, for which the work done in isothermal expansion from a volume i to a volume r is W=RT loger, whence dW=R log e rdt, he deduced the expression for the heat absorbed by a gas in isothermal expansion H=R log er/F'(t).

00The same result follows if the work W =RT log e ?'

00done by a gas in isothermal expansion is assumed to be equivalent or proportional to the heat absorbed, H=R log e r/F'(t).

00The heat absorbed in isothermal expansion from vo to v at a temperature 0 is equal to the work done by equation (8) (since d0 =o, and 0(dp/d0)dv =pdv), and both are given by the expression RO log e (v/vo).

00If we assume that s is a linear function of 0, s= so(I +aO), the adiabatic equation takes the form, s 0 log e OW +aso(0 - Oo) +R loge(v/vo) =o

00In the case of a solid or a liquid, the latent heat of isothermal expansion may often be neglected, and if the specific heat, s, be also taken as constant, we have simply 0-00 =s log e0/00.

00In the case of an ideal gas, dp/d9 at constant volume =R/v, and dvld6 at constant pressure =R/p; thus we obtain the expressions for the change of entropy 0-4)0 from the state poeovo to the state pev, log e e/eo+R logev/vo =S log e 9/00-R (32) In the case of an imperfect gas or vapour, the above expressions are frequently employed, but a more accurate result may be obtained by employing equation (17) with the value of the specific heat, S, from (29), which gives the expression 4-¢o = Sologe0/00 - R logep/po-n(cp/B-copo/Bo)

00Writing formulae (3r) and (33) for the energy and entropy with indeterminate constants A and B, instead of taking them between limits, we obtain the following expressions for the thermodynamic functions in the case of the vapour: " =Solog e 0 - R log e p - ncp/D+A".

00G' =s'e(i - log e 0) +(dh - Dd4) - A'D+B'.

00Rearranging the terms, and dividing throughout by 0, we obtain an equation of the form R log ep= A - B/D - (s' - So)loge0+(c - b)p/D+(dh/D - d4)) (44) in which B=B" - B', and A = A'+s' - So.

00According to a later tradition, not known to Homer, the Moerae appeared to Althaea when Meleager was seven days old, and announced that the child would only live as long as the log blazing on the hearth remained unconsumed.

00Althaea thereupon seized the log, extinguished the flames, and hid it in a box.

00But, after her brothers' death, she relighted the log, and let it burn away until Meleager died.

00When, on the 2nd of May 1840, some time after the nomination by the Whig party of William Henry Harrison for the Presidency, Greeley began the publication of a new weekly campaign paper, The Log Cabin, it sprang at once into a great circulation; 40,000 copies of the first number were sold, and it finally rose to 80,000.

00In September 1841 Greeley merged his weekly papers, The Log Cabin and The New Yorker, into The Weekly Tribune, which soon attained as wide circulation as its predecessors, and was much more profitable.

00Some of the Italian terremare show quadrangular constructions made like the modern log houses, of undressed tree trunks superposed longitudinally and overlapping at the ends, as at Castione in the province of Parma.

00Legendre's formula x: (log x- I.

00The szlachta, who had had a "King Log" in SigisWladlsmund, were determined that Wladislaus should be laws " a King Bee who will give us nothing but honey" - 1632-1648.

00One close datum, if trustworthy, would be log of water = Assyrian mina implying a bath of about 2200 cub.

00The log and kab are not found till the later writings; but the ratio of hin to issaron is practically fixed in early times by the proportions in Num.

00The wholesale theory of Revillout (35) that all Hebrew and Syrian measures were doubled by the Ptolemaic revision, while retaining the same names, rests entirely on the resemblance of the names apet and epha, and of log to the Coptic and late measure lok.

00This relation between x, a, rn, may be expressed also by the equation x= log m.

00The principal properties of logarithms are given by the equations log (mn) = log m --Flogs n, loga(m/n) = toga m -logo.

00n, log.

00Thus in arithmetical calculations if the base is not expressed it is understood to be io, so that log m denotes log n m; but in analytical formulae it is understood to be e.

00The logarithms to base io of the first twelve numbers to 7 places of decimals are log 1 =0.0000000 log 5 log 2 = 0.3010300 log 6 log 3 =0.477 121 3 log 7 log 4 =0.6020600 log 8 The meaning of these results is that The integral part of a logarithm is called the index or characteristic, and the fractional part the mantissa.

00When the base is to, the logarithms of all numbers in which the digits are the same, no matter where the decimal point may be, have the same mantissa; thus, for example, log 2.5613 =0-4084604, log 25.613 =1.4084604, log 2561300 = 6.4084604, &c.

00numbers in which the integral part is o) the mantissa is still kept positive, so that, for example, log 25613 =7-4084604, 4084604, log 0025613 = 3.4084604, &c.

00., and the value of its reciprocal, log e io (by multiplication by which Briggian logarithms may be converted into Napierian logarithms) is 2.302585092994 0 45 68401 799 1 4

00The 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.

00The notation log x is generally employed in English and American works, but on the continent of Europe writers usually denote the function by lx or lg x.

00The logarithmic function is most naturally introduced into analysis by the equation log x= x ?

00This equation defines log x for positive values of x; if o the formula ceases to have any meaning.

00Thus log x is the integral function of 1/x, and it can be shown that log x is a genuinely new transcendent, not expressible in finite terms by means of functions such as algebraical or circular functions.

00A connexion with the circular functions, however, appears later when the definition of log x is extended to complex values of x.

00A relation which is of historical interest connects the logarithmic function with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy=const., it is evident that the area included between the arc of a hyperbola, its nearest asymptote, and two ordinates drawn parallel to the other asymptote from points on the first asymptote distant a and b from their point of intersection, is proportional to log bla.

00The following fundamental properties of log x are readily deducible from the definition (i.) log xy= log x-Flog y.

00Either of these properties might be taken as itself the definition of log x.

00There is no series for log x proceeding either by ascending or descending powers of x, but there is an expansion for log (I +x), viz.

00log ('I' 2x 2 + 3 x 3 -4x 4 +..

00The function log x as x increases from o towards w steadily increases from - co towards +co.

00that x-"' log x tends to zero as x tends to 00 for every positive value of m however small.

00The exponential function, exp x, may be defined as the inverse of the logarithm: thus x =exp y if y= log x.

00Thus even when the argument is real log x has an infinite number of values; for putting 71 =o and taking positive, in which case a = o, we obtain for log the infinite system of values log +2n7ri.

00It 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.

00The next publication was due to Vlacq, who appended to his logarithms of numbers in the Arithmetica logarithmica of 1628 a table giving log sines, tangents and secants for every minute of the quadrant to ro places; there were obtained by calculating the logarithms of the natural sines, &c. given in the Thesaurus mathematicus of Pitiscus (1613).

00It contains log sines (to 14 places) and tangents (to 10 places), besides natural sines, tangents and secants, at intervals of a hundredth of a degree.

00In the same year Vlacq published at Gouda his Trigonometria artificialis, giving log sines and tangents to every ro seconds of the quadrant to ro places.

00The first logarithms to the base e were published by John Speidell in his New Logarithmes (London, 1619), which contains hYPerbolic log sines, tangents and secants for every minute of the quadrant to 5 places of decimals.

00numbers up to 1000, and log sines and tangents from Gunter's Canon (1620).

00In the following year, 1626, Denis Henrion published at Paris a Traicte des Logarithmes, containing Briggs's logarithms of numbers up to 20,001 to io places, and Gunter's log sines and tangents to 7 places for every minute.

00In the same year de Decker also published at Gouda a work entitled Nieuwe Telkonst, inhoudende de Logarithmi voor de Ghetallen beginnende van r tot io,000, which contained logarithms of numbers up to io,000 to io places, taken from Briggs's Arithmetica of 1624, and Gunter's log sines and tangents to 7 places for every minute.'

00The next great advance on the Trigonometria artificialis took place more than a century and a half afterwards, when Michael Taylor published in 1792 his seven-decimal table of log sines and tangents to every second of the quadrant; it was calculated by interpolation from the Trigonometria to 10 places and then contracted to 7.

00came into very general use, Bagay's Nouvelles tables astronomiques (1829), which also contains log sines and tangents to every second, being preferred; this latter work, which for many years was difficult to procure, has been reprinted with the original title-page and date unchanged.

00I „ Logarithms of the ratios of arcs to sines from 04 00000 to 0 4.05000, and log sines throughout the quadrant 4 „ Logarithms of the ratios of arcs to tangents from 0 4 00000 to 0 4.05000, and log tangents throughout the quadrant 4 The trigonometrical results are given for every hundred-thousandth of the quadrant (to" centesimal or 3" 24 sexagesimal).

00Logistic or Proportional Logarithms. - The old name for what are now called ratios or fractions are logistic numbers, so that a table of log (a/x) where x is the argument and a a constant is called a table of logistic or proportional logarithms; and since log (a/x) =log a-log x it is clear that the tabular results differ from those given in an ordinary table of logarithms only by the subtraction of a constant and a change of sign.

00The object of a table of log (a/x) is to facilitate the working out of proportions in which the third term is a constant quantity a.

00In most collections of tables of logarithms, and especially those intended for use in connexion with navigation, there occurs a small table of logistic logarithms in which a = 3600"(= I° or I h), the table giving log 3600 log x, and x being expressed in minutes and seconds.

00Gaussian logarithms are intended to facilitate the finding of the logarithms of the sum and difference of two numbers whose logarithms are known, the numbers themselves being unknown; and on this account they are frequently called addition and subtraction logarithms. The object of the table is in fact to give log (a =b) by only one entry when log a and log b are given.

00Corresponding to the argument log x it gives the values of log (I -Fx - 1) and log (1+x).

00He then by means of a simple proportion deduced that log (I 00000 00000 00000 I)=o 00000 00000 00000 0 434 2 944 81 90325 1804, so that, a quantity 1.00000 00000 00000 x (where x consists of not more than seventeen figures) having been obtained by repeated extraction of the square root of a given number, the logarithm of I 00000 00000 00000 x could then be found by multiplying x by 00000 00000 00000 04342 To find the logarithm of 2, Briggs raised it to the tenth power, viz.

00Adding the characteristic 3, and dividing by 10, he found (since 2 is the tenth root of 1024) log 2 = 30102 9995 6 63981 195.

00Briggs calculated in a similar manner log 6, and thence deduced log 3.

00h I Io^ - i - log e 10' the value of la being 1/2 64, and in the second process log i o 2 is in effect calculated from the formula.

00The following calculation of log 5 is given as an example of the application of a method of mean proportionals.

00Since loge(I +x) =x-2x 2 -3x 3 - 4x4+&c., we have, by changing the sign of x, log e (I - x) _ - x - zx 2 - 3x 3 - x 4 - &c.; whence g 1 +x to=2(x+ix'+1x5+&c.), e l - x and, therefore, replacing x by p +q, log e q =2 p +q +3 () 3T ?

00As particular cases we have, by putting (q= 1, log e p=2 p 1 +3 (-) 3 l5 5 +&c., and by putting q= p+1, loge(p-f-1) - logep =2 2p+1?-s(2p+1)3+5(2p+1)5-i-&c.

00From the formula for log e (p/q) we may deduce the following very convergent series for log e 2, log e 3 and log e 5, viz.: log e 2=2(7P +5Q +3R), log e 3 =2(11P+8Q +5R), log e 5=2(16P+12Q+7R), where P 1 +3?1) 3 5 s (31) &C.

00The following still more convenient formulae for the calculation of log e 2, loge3, &c. were given by J.

00If a= logg = - log (1-10)' 81 (1) c = 10g 80 = log 1 +sr, 126 (8) e =10g1 o = log 1 +1000 then log 2=7a-2b+3c, log 3=IIa-3b+5c, log 5=16a-4b +7c, and log 7 =2(39a - IOb+17c - d) or=19a-4b+8c +e, and we have the equation of condition, a-2b+c=d+2e.

00By means of these formulae Adams calculated the values of log e 2, log e 3, log e s, and loge?

00to 276 places of decimals, and deduced the value of log e lo and its reciprocal M, the modulus of the Briggian system of logarithms. The value of the modulus found by Adams is Mo = 0-43429 44 81 9 03251 82765 11289 18916 60508 22 943 97 00 5 80366 65661 14453 78316 58646 4920-8870 77 47292 2 4949 33 8 43 17483 18706 106 74 47 6630-3733 64167 92871 58963 90656 92210 64662 81226 58521 27086 56867 03295 9337 0 86965 88266 88331 16360 773849 0514 28443 48666 76864 65860 85135 56148 212 34 87653 43543 43573 25 which is true certainly to 272, and probably to 273, places (Proc. Roy.

00If the logarithms are to be Briggian all the series in the preceding formulae must be multiplied by M, the modulus; thus, log i o(I +x) = M(x-2x2+3x3-4x4+&c.), and so on.

00As has been stated, Abraham Sharp's table contains 61-decimal 10 b= log 24 = - log (1-160) d =10g 49 = - log (1-160) 17253 8 35 62 21868 Briggian logarithms of primes up to I ioo, so that the logarithms of all composite numbers whose greatest prime factor does not exceed this number may be found by simple addition; and Wolfram's table gives 48-decimal hyperbolic logarithms of primes up to 10,009.

00Multiplying by 50, we have 50X43,867=2,193,350, and on looking in Burckhardt's Table des diviseurs for a number near to this which shall have no prime factor greater than 10,009, it appears that 2,193,349 = 23 X 47 X 2029; thus 43,867= Au (23X47X2029 -{-1), and therefore log e 43,867 = log e 23+loge 47+logy 2029 - log e 50 +2,193,349 2 (2,193,349) 2 + (2,193,349)3 &c. The first term of the series in the second line is whence, taking out the logarithms from Wolfram's table, log e 43, 86 7 = Io 68891 76079 60568 10191 3661.

00The logarithm is then obtained by use of the formula d l d2 l d3 2 log e (x+d) = log e x-f- - x2+3 x3 - &c., in which of course the object is to render dlx as small as possible.

00His mind gradually turned from belief in the efficacy of violent measures to the acceptance of constitutional methods; and in his last book, King Stork and King Log, he spoke with approval of the efforts of politicians on the Liberal side to effect, by argument and peaceful agitation, a change in the attitude of the Russian government towards various reforms. Stepniak constantly wrote and lectured, both in Great Britain and the United States, in support of his views, and his energy, added to the interest of his personality, won him many friends.

00He wore a sharp shirt of hair next his skin, scourged himself every Friday and other fasting days, lay upon the bare ground with a log under his head, and allowed himself but four or five hours' sleep. This access of the ascetic malady lasted but a short time, and More recovered to all outward appearance his balance of mind.

00For most experimental purposes the small terms involving the factor (- p') may be neglected, and we have, approximately, PoV'=Rt log (ply).

00If L is zero or negligible, X = - P(v - v) and we have dP/dT = - P/T or dP/P = - dT/T, which on integration gives log P =log T+C, or P= kT, i.e.

00(2) If k is constant the solution is evidently B =a log r+b, where a= and b and k are determined from the known values of the temperatures observed at any two distances from the axis.

00This gives an average value of the conductivity over the range, but it is better to observe the temperatures at three distances, and to assume k to be a linear function of the temperature, in which case the solution of the equation is still very simple, namely, 0+Ze6 2 =a log r+b, (3) where e is the temperature-coefficient of the conductivity.

00The earliest recorded images of Hera preceded the rise of Greek sculpture; a log at Thespiae, a plank at Samos, a pillar at Argos served to represent the goddess.

00Definitions and sizes are given below of the most usual forms of sawn timber: A log is the trunk of a tree with the bark removed and branches lopped.

00A balk is a log hewn or sawn to a square section, and varying in size from I 1 to 18 in.

00As soon as possible after felling, logs by sawing into scantling sizes, for if the log is left to dry or season, it is liable on shrinking to split.

00The usual method is to saw a log into planks or boards by n g P y of Timber.

00After the log is converted into scantlings, or "lumber," as it is termed in America, it is stacked in the timber yard under covered sheds with open sides to enable it to "season."

00"Upsets" are the result of some crushing force or violent shock to the balk or log.

00Log >>

00Rice is threshed by beating the ears on a log; other grains, with flails on mud threshing-floors.

00If logic were treated as merely formal, the stress of the problem of knowledge fell upon the determination of the Log and processes of thepsychological mechanism.

00Assuming an equation of the form log (p/760) =a log (0/373), their results give a = S/R =4.305, or S=0.474, which agrees very perfectly with Regnault's value.

00log p= A+BO.

00log p=C log (A+BO).

00log p=A0/(B +CO).

00log p=A+Bbe+Cce..

00log p= A+B/0+C/0 2.

00log p=A+B/0+C log 0..

00log p = A+B/0 b (Unwin, 1887).

00log p=A+B log 0+C log (0+c).

00log p=A+B/(0+C)..

00Observing that this rate of diminution is approximately as the square of the reciprocal of the absolute temperature, we see that the almost equally simple formula log p=A+B/0 represents a much closer approximation to experiment.

00If we assume formulae of the simple type A+B/0 for two different substances which have the same vapour-pressure p at the absolute temperatures 0' and 0" respectively, we may write log p=A'+B'/0'= A"+B"/0", .

00(22) which is of the same type as log p =A-}-B/6, and shows that the coefficient B should be equal to L/R.

00Substituting L= Lo+ (S-s)(6-Bo), and integrating between limits, we obtain the result log e p=A+B/o+C log e 6,..

00(23) C= (S-s)/R, B = -[Lo+(s-S)90]/R, A = log e po - B /9 0 - C logeeo.

00Omitting w and neglecting the small variation of the specific heat of the liquid, the result is simply the addition of the term (c-b)/V to formula (23) log p=A+B/B - I - C log B-f-(c-b)IV..

00It is interesting to remark that the simple result found in equation (25) (according to which the effect of the deviation of the vapour from the ideal state is represented by the addition of the term (c-b)/V to the expression for log p) is independent of the assumption that c varies inversely as the n th power of 9, and is true generally provided that c-b is a function of the temperature only and is independent of the pressure.

00This armed body, consisting of over fifty men, surrounded a log cabin and shot down two of the supposed cattle " rustlers," the latter defending themselves bravely.

00If the axes of x and y be taken horizontal and vertical (upwards), we derive x =a log (sec #+tan ~), y= a sec ~.

00From this we derive x=?oJ~, y=A log sec ~, (16),

00Shouid B/C be greater than 6, the best number of elementary combinations m I will lie between log Blog C nd log Blog C

00hyp log.

00The term jute appears to have been first used in 1746, when the captain of the "Wake" noted in his log that he had sent on shore "60 bales of gunney with all the jute rope" (New Eng.

00It came to be called Stockholm ("the isle of the log," Latin Holmia, German Holm); the true explanation of the name is not known.

00where a (a+I)y (a+n-I)(y+n-2) =y, (33= (Y+ I)(y+2),..., 132n-1 - (y+2n-3)(7+272-2)' (32= y-a, N4 = 2(y+I-a) ?..., N2 - 71(7-I-a) Y(' y + I) (7+2) (7+3)' (y+2n-2)(y+2nFrom this we may express several of the elementary series as continued fractions; thus taking a= I, 7=2, and putting x for -x, have log (I +x) = x I 2 x I 2 x 2 2 x 2 2 X 3 2 x 32x we +2 + 3 +4+5+ 6-I-7 +.

00Because of his fame as a frontier hero, of the circumstance that a part of his home at North Bend, Ohio, had formerly been a log cabin, and of the story that cider, not wine, was served on his table, Harrison was derisively called by his opponents the " log cabin and hard cider " candidate; the term was eagerly accepted by the Whigs, in whose processions miniature log cabins were carried and at whose meetings hard cider was served, and the campaign itself has become known in history as the "log cabin and hard cider campaign."

00Their funeral mourning consists of abstaining from drink and eating raw beef, and they use a wooden log for a coffin.

00Integrating 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.

00A usual value of for hemp ropes on cast-iron pulleys is 0.3, and the exponential log ratio is therefore 0 3ur cosec 20 when 9 =7r.

00For practical purposes logarithms are usually calculated to base i o, so that log l o 10 = I, log i n I oo = 2, &C.

005 3 Involves 5 And 3, And Log 2 8 Involves 2 And 8.

00Or Logo I Ooi, Log L O 1.002, Log L O 1.003.

00Logarithms.-Multiplication, division, involution and evolution, when the results cannot be exact, are usually most simply performed, at any rate to a first approximation, by means of a table of logarithms. Thus, to find the square root of 2, we have log A /2 = log (21)=1 log 2.

00We take out log 2 from the table, halve it, and then find from the table the number of which this is the logarithm.

00Hence t= log S S 0 _, and a = S(I - e1).

00The intensity 0343 (36) G"=SoD(1 - log e 0)+ Re log e p - (c - b)p - A"D+B" (37) J" =s 0 0 - S O D log e O+RD log e p - A"D+B"..

00log E = a+b /T+c log T E(t-to =c(t -t') (2t°- (t+t')) E t +E; = I O a +bt +.

00E t = bt +c log T/273, (c = Ts.).

00Et = at +ct 2 +s°(T log eT -273 log e273) (Where s = s° +2cT, and c is small.

00- If we take the analogy of a perfect gas and assume s =constant, we have dE 2 /dT 2 = - s/T, dE/dT =s log e To/T (12) E (T -r') =sT log eTo /T-sT"log e To/T (13) where T and T' are the temperatures of the junctions, and T.

00-r')=c log e T/T'-c(TT')/To..

00In 1822 John Wood (1798-1880), the first white settler, built a log cabin here, and in 1825, Quincy, then having less than ten inhabitants, was made the county-seat of Adams county, both town and county being named through Wood's influence in honour of John Quincy Adams. Wood was lieutenantgovernor of the state in 1857-1860, and acting-governor in 1860-1861.

00Jule took her hand and led her through the large log house with its earthy dÃ©cor.

00With the jury trial continuing into the coming weekâ€”far longer than originally expectedâ€”the Dawkins clan was going nowhere, thus causing a log jam of customers in the river of incoming lodgers.

00Beating his brains out trying to get that log house built and you're suspecting him of courting me.

00She held out her hand. Toby smiled grudgingly and took it. Katie led them around the island, trying to find some part of the chasm that was narrow enough to jump or a log they could roll across the gaping ravine.

00The log house was further on, and up a steep incline â€“ a sentinel overlooking the valley.

00Across from them was the log house â€” home.

00The muscles in her legs complained as she squatted behind the log, peering over the rotting bark.

00alias expansions will be announced, etc. -X logfile Log all traffic in and out of mailers in the indicated log file.

00Read the latest news Log on at Nottingham High School ON Line to read the latest news about other alumnae and the school!

00ambienceival you will discover a discreet haven with open log fires that create a homely ambiance.

00amusing to note my family now reads the studio log to find out what it is I do up here.

00If your logfile is not in one of the recognized formats, you can tell analog about your format using a log format string.

00No rolled versions are kept by default; any existing log file is simply appended.

00Whenever a log file is opened, it is always opened in append mode, so existing data is never truncated.

00Log in View Full Version: Do i need a new avatar?

00Dog races in games backgammon etc fans may log wireless content including.

00Session Log A screen you can access showing all the requests you've made during your current visit to smile banking.

00The oak beamed lounge with log fires in winter provides room to relax.

00Peering through those windows, families can be seen gathering round the log fire, with the room bedecked with evergreens and red ribbon.

00In a driving blizzard, with his inexperienced helper (Patrick Holt ), they seek shelter in a log cabin.

00The entrance hall now boasts a cozy log fire.

00log books are diaries kept by the head teacher.

00The bothy has now had some visitors and the bothy log book shows that people are beginning to enjoy the new bothy.

00Brick fireplace with cast iron log burning stove on a brick fireplace with cast iron log burning stove on a brick hearth.

00There is a log burning stove in the main living room.

00Born in 1866 in a log cabin in Kentucky on July 29 th.

00cast iron log burning stove on a brick hearth.

00Large sitting room with exposed beams and fireplace with log burner, downstairs cloaks, 2 staircases.

00Log in View Full Version: Why did you steal 40,000 hotel coat hangers?

00Corydalis cashmeriana In log 28 I was repotting a fish box trough of corydalis cashmeriana In log 28 I was repotting a fish box trough of Corydalis cashmeriana and made it into two troughs.

00And uses almost ALL CPU to actually log in.

00Cozy log fires crackle in the winter, filling the air with wonderful scents of wood smoke.

00cracklebout a winter walk with crackling log fires in country inns?

00Lose yourself in a snowy forest, toast the occasion by a log fire, go cross-country skiing to work up an appetite.

00In addition the raw data is aggregated into the current monthly log file in an anonymised fashion.

00decibel scale used for sound is another common example of a log scale.

00delete the directory created in step 4. Double click on Exceed (XDMCP Broadcast) and select a Unix workstation to log onto.

00disables logging If no TransferLog directive is given then no log is written.

00Douglas fir log.

00You also MUST have a PC connected by wire to log onto the server, cool safety feature eh?

00entrycheck out previous entries and get your fave teacher to log on here.

00error log.

00Log in View Full Version: v975 steel faceplate rusting?

00We have added a feature to the log in page which allows you to request your log in details should you forget them.

00It can read a range of temperature log file formats.

00In Canadian forestry high quality red alder logs are said to be approximately equal in value to that of a Douglas fir log.

00Its traditional, cozy and friendly interior and roaring log fires attract both locals and visitors alike.

00fireplace with fitted villager log burning stove on a slate hearth.

00brick fireplace with cast iron log burning stove on a brick hearth.

00It essentially tells firestorm + to daemonize and send all diagnostic messages to a log file.

00firestorm analysts approach should be to log anything that might matter and just use the console to filter away the chaff.

00firewood log carrier tote bag, allows you to gather wood then place it in your home or hearth.

00Log in View Full Version: Orson - big hit or big flop?

00They have some water rides too - their log flume is great fun!

00They cleared the thickly forested land, built log dwellings, made merry with Highland games at Johnson Hall gatherings with the friendly Mohawks.

00However it was agreed that the press log relating to a police pension forfeiture case would be attached to the report in future.

00Drink or dine next to a blazing log fire in winter or 'Al fresco ' on our secluded patio in summer.

00gas log burning stove.

00There is a large sitting room with log fire and a library converted from a former hayloft.

00We have had a hiccup, a log jam which involves ' artistic ' sub-contractors who are slightly behind on deadlines.

00homely comforts of the lounge with the log fire for the colder evenings.

00hopped across on some stepping stones and then found a floating log which carried him to the shore.

00Log in View Full Version: Not enough horsepower!

00Accommodation Hotels, log cabins, ice hotels, ice igloos, glass igloos, ' warm rooms ' .

00Kat took the time to ponder an imponderable: How easy is it to fall off a log?

00The tram lay on it like a log. *** A poor smile, you say - But not inapt.

00Log in to cast your vote 10th April There are several new contributions this week, despite the rather inclement weather!

00informality with cozy lounges and a log fire burning on cold winter nights.

00insecure wireless networks means he doesn't even need to get inside the building to log on.

00interlocking log (not sectional) construction, a level concrete or paved base is required to enable installation.

00intimacy of the cozy living room with its blazing log fire; the adjoining dining room overlooks the garden.

00Hackers could record the keystrokes you use to log into your Internet bank account or simply erase everything on your hard disk.

00kindlealso broke up pieces of real coal, logs and kindling for the fires, log baskets and coal scuttles.

00larch pole to use as a suet log.

00Lawrence river st he points out call or log now means a went to the.

00The tests can then be taken at any time within the 3 year life span of the log book.

00lithology graphics are fundamental to all geological log drawing.

00logger that can spy on and log keystrokes without your knowldege or permission.

00log cabins who built a jet-propelled Arrow that flew circles around the American Air Force.

00Due to the loose interlocking log (not sectional) construction, a level concrete or paved base is required to enable installation.

00Streams uses Oracle's log Miner infrastructure to read redo logs.

00It will also keep a log of all your connections.

00It's full of Nelson memorabilia and interesting oldie worldly rooms and in winter has roaring log fires.

00This will display the messages sent to the error log.

00Every transaction log application is different and needs to be properly analyzed, so that strengths and weaknesses can be identified and reported.

00The word ' blog ' is short for ' web log ' is short for ' web log ' .

00log cabin to make it all the way to the White House.

00log fires in winter provides room to relax.

00log burning stove on a brick hearth.

00log files by running the dep for the first time.

00log flume at the theme park?

00log off from the Wireless Network at the end of your session.

00log on!

00On a public computer a fraudster can log on, install the key logger, then log off.

00A basic ship's log was used as a means of estimating the speed of a vessel, and so roughly calculating the longitude.

00luminaryn announcing the leading luminaries by the alderney fans may log.

00By 1838 the Beaufort wind force scale was made mandatory for log entries in all ships of the Royal Navy.

00There is an open fire place with a marble mantle and a gas log fire along one wall there are shelves with cupboards below.

00Log in & reply mapmaker Thursday 17 April 2003 10.21am Sitting on the foreshore under London Bridge?

00The median viral load decreased from 4.12 log to 2.02 log10, after a median of 15 days from initiation of therapy.

00Some, such as the Yule log and the Christmas tree, are relics of the old pagan midwinter festival.

00millionth unique user ever to log onto Nintendo's Wi-Fi Connection service.

00mossy log on the bend, then flew off.

00Narcissus bulbs that I chitted in Log 26.

00navvyly, the official school log books of the temporary wooden school in the navvies village have not survived in a readable form.

00oak beamed lounge with log fires in winter provides room to relax.

00Funeral homes and reporters can log in and post obits, I've got search, paged news and RSS.

00Comment | Permalink | in categories Log beaneater oops.

00