B Sentence Examples

b
  • Part B outlines the new policy, which promotes sustainable agriculture, and Part C focuses on policy implementation.

    28
    19
  • If taken with other metabolites that aid in the creation of serotonin - vitamin B, niacin and magnesium, which a multivitamin should provide - 5HTP can help deal with many of the same health issues that people take tryptophan for.

    15
    12
  • In the apparatus of type B as made by Zeiss there are two microscopes attached to a base-plate, one of which views the spectrum-plate (or other object) to be measured, while the other views a scale that moves with the slide on which the spectrumplate is mounted.

    11
    9
  • But the day showed the ' B attle of Macedonian army equal to the task.

    7
    5
  • Many organic compounds of boron are known; thus, from the action of the trichloride on ethyl alcohol or on methyl alcohol, ethyl borate B(OC2H5)3 and methyl borate B(OCH 3) 3 are obtained.

    3
    1
  • The next stage (b) is connected with the suppression of the local high-places or minor shrines in favour of a central sanctuary.

    3
    1
  • Nutritional supplements that may be beneficial include large amounts of antioxidants (vitamins C, A, E, zinc, selenium, and flavenoids), as well as B vitamins and a full complement of minerals (including boron, copper, and manganese).

    19
    17
  • Any note may be a pitch note; for orchestras custom has settled upon a' in the treble clef, for organs and pianos in Great Britain c 2, and for modern brass instruments b flat'.

    3
    2
  • The exact meaning of these features is not clear, but if it be remembered (a) that the Levites of post-exilic literature represent only the result of a long and intricate development, (b) that the name "Levite," in the later stages at least, was extended to include all priestly servants, and (c) that the priesthoods, in tending to become hereditary, included priests who were Levites by adoption and not by descent, it will be recognized that the examination of the evidence for the earlier stages cannot confine itself to those narratives where the specific term alone occurs.

    2
    1
  • Although married she always remained a member of her father's house - she is rarely named wife of A, usually daughter of B, or mother of C. Divorce was optional with the man, but he had to restore the dowry and, if the wife had borne him children, she had the custody of them.

    2
    1
    Advertisement
  • At small country towns or villages, where the message traffic is light, the Wheatstone " A B C " instrument is used.

    2
    1
  • In this apparatus electric A B C currents are generated by turning a handle (placed in front of the instrument), which is geared, in the instru ment.

    2
    1
  • The disaster which aroused Nehemiah's grief was scarcely the fall of Jerusalem in 586 B.C., but a more recent one, and it has been conjectured that it followed the work of Ezra (in b above).

    0
    0
  • To start with the last before considering (a) and (b) would be futile.

    0
    0
  • Thus, in any estimate of the influence of Babylonia upon the Old Testament, it is obviously necessary to ask whether certain features (a) are of true Babylonian origin, or (b) merely find parallels or analogies in its stores of literature; whether the indebtedness goes back to very early times or to the age of the Assyrian domination or to the exiles who now returned.

    0
    0
    Advertisement
  • The later class (B) of the linear script is that used on the great bulk of the clay tablets of the Cnossian palace, amounting in number to nearly 2000.

    0
    0
  • His extant works are (a) three poems, "The Praises of Wemen" (224 lines), "On Luve" (10 lines), and "The Miseries of a Pure Scholar" (189 lines), and (b) a Latin account of the Arbuthnot family, Originis et Incrementi Arbuthnoticae Familiae Descriptio Historica (still in MS.), of which an English continuation, by the father of Dr John Arbuthnot, is preserved in the Advocates' Library, Edinburgh.

    0
    0
  • And as in Hebrew, the six letters b g d k p t are aspirated when immediately preceded by any vowel sound.

    0
    0
  • Thus " the son of the king " is more commonly expressed by b`ra dh`malka or b`reh d`malka than by bar mailed, whereas the latter type would alone be permissible in Hebrew.

    0
    0
  • The conformation of those flowers a consists essentially in the pres- ' 'A B ence of a six-parted perianth, the three outer segments of which correspond to a calyx, the three inner ones to a corolla.

    0
    0
    Advertisement
  • E Arabian Sea Ba Of G A L e Geological information incomplete Desert Deposits Quaternary Tertiary Mesozoic Palaeozoic Archaean and Metamorphic Younger Volcanic Rocks English Miles b iuHi iiiiuiiiiii after llargl,aua Geology The geology of Asia is so complex and over wide areas so little known that it is difficult to give a connected account of either the structure or the development of the continent, and only the broader features can be dealt with here.

    0
    0
  • The prostomium overhangs the mouth, and is often of considerable size and, as a rule, quite distinct from the segment following, being A„ f s / 6/ ' A B I.

    0
    0
  • B, Diagram of the nephridium of Alciope, into which opens the large genital funnel (coelo mostome).

    0
    0
  • Here, however, the buds are lateral, though produced from a budding may be defective upon one or other of the noto a b FIG.

    0
    0
  • Let AB be the major axis of the orbit, B the pericentre, F the focus or centre of motion, P the position of the body.

    0
    0
    Advertisement
  • In the case of plants the method of procedure was to grow some of the most important crops of rotation, each separately year after year, for many years in succession on the same land, (a) without manure, (b) with farmyard manure and (c) with a great variety of chemical manures; the same description of manure being, as a rule, applied year after year on the same plot.

    0
    0
  • Amongst the field experiments there is, perhaps, not one of more universal interest than that in which wheat was grown for fifty-seven years in succession, (a) without manure, (b) with farmyard manure and (c) with various artificial manures.

    0
    0
  • In 1890, at Plymouth, competitions took place of light portable engines (a) using solid fuel, (b) using liquid or gaseous fuel, grist mills for use on a farm, disintegrators, and cider-making plant for use on a farm.

    0
    0
  • In 1892, at Warwick, the competitions related to ploughs - single furrow (a) for light land, (b) for strong land, (c) for press drill and broad-cast sowing; two-furrow; three-furrow; digging (a) for light land, (b) for heavy land; and one-way ploughs.

    0
    0
  • In 1899, at Maidstone, special prizes were offered for machines for washing hops with liquid insecticides, cream separators (power and hand), machines for the evaporation of fruit and vegetables, and packages for the carriage of (a) soft fruit, (b) hard fruit.

    0
    0
  • A B In Great Britain the flea beetles (Halticidae) are one of the most serious enemies; one of these, the turnip flea (Phyllotreta nemorum), has in some years, notably 1881, caused more than 500,00o loss in England and Scotland alone by eating the young seedling turnips, cabbage and other Cruciferae.

    0
    0
  • These parasites damage the hide, B FIG.

    0
    0
  • A, Winged female; B, winged D, viviparous wingless female from in patches from old apple trees, where the insects live in the rough bark and form cankered growths both above and below ground.

    0
    0
  • A, branch bearing male cones, reduced; B, single male cone, enlarged; C, single stamen, enlarged.

    0
    0
  • A variety of the spruce, abounding in some parts of Nor way, produces a red heartwood, not easy to distinguish from that of the Norway B pine (Scotch fir), and imported with it into England as "red deal" or "pine."

    0
    0
  • A, Branch bearing (a) young female cones, (b) ripe cones, reduced.

    0
    0
  • B, Ripe cone scale with seeds, enlarged.

    0
    0
  • In the subsequent growth of ergc- pl.y- i ln b a.

    0
    0
  • Neither the rotation of the shell as a whole nor its helicoid spiral coiling is the immediate cause of the torsion of the body in the individual, for the direction of the torsion is indicated in the segmentation of the ovum, in which there is a complete A B From Lankester's Treatise on Zoology.

    0
    0
  • B, The same, partially everted by eversion of the sides, as in the Nemertine proboscis and Gastropod eye-tentacle = pleurecbolic.

    0
    0
  • The introvert is not a simple one with complete range both in eversion and introversion, but is arrested in introversion by the fibrous bands at c, and similarly in eversion by the fibrous bands at b.

    0
    0
  • G, The acrecbolic snout of a proboscidiferous Gastropod, arrested short of complete eversion by the fibrous band b.

    0
    0
  • On the other hand, many which have a siphonate mantle-skirt are not provided with an introversible mouth-bearing al- B c..

    0
    0
  • B, Sole of the foot of Pyrula tuba, to show a, the pore usually said to be " aquiferous " but probably the orifice of a gland; b, median line of foot.

    0
    0
  • B, The diblastula has become a trochosphere by the development of the ciliated ring y r (optical section).

    0
    0
  • B, The shell removed.

    0
    0
  • Posterior cephalic tentacle; and b, the eyes.

    0
    0
  • Ia, frons; b, clypeus (the pointed labrum beneath it); II, mandible; III, first maxilla; (a, base; b, sheath; c, piercer), III', inner view of sheath; IV, second maxillae forming rostrum (b, mentum; c, ligula).

    0
    0
  • B, Section through compound eye (after Miall and Denny); C, organs of smell in cockchafer; (after Kraepelin); D, a, b, sensory pits on cercopods of golden-eye fly; c, sensory pit on palp of stone-fly (after Packard); E, sensory hair (after Miall and Denny); F, ear of long-horned grasshopper; a, Front shin showing outer opening and air-tube; b, section (after Graber); G, ear of locust from within (after Graber).

    0
    0
  • To some of the Linnaean genera he dare not, however, assign a place, for instance, Buceros, Haematopus, Merops, Glareola (B risson's genus, by the by) and Palamedea.

    0
    0
  • Under the caliphate of Mamun, Saman, a Persian noble of Balkh, who was a close friend of the Arab governor of Khorasan, Asad b.

    0
    0
  • His son Asad, named after Asad b.

    0
    0
  • A=D= -_-- - - ---Island =r= b = o =ir- monument by James Edward Kelly to General Fitz John Porter; a cottage hospital (1886); a United States naval hospital (1891); a home for aged and indigent women (1877); and the Chase home for children (1877).

    0
    0
  • If a be greater than b the curve resembles fig.

    0
    0
  • This letter corresponds to the second symbol in the Phoenician alphabet, and appears in the same position in all the European alphabets, except those derived, like the Russian, from medieval Greek, in which the pronunciation of this symbol had changed from b to v.

    0
    0
  • A new form had therefore to be invented for the genuine b in Slavonic, to which there was, at the period when the alphabet was adopted, no corresponding sound in Greek.

    0
    0
  • The new symbol, which occupies the second position, was made by removing the upper loop of B, thus producing a symbol somewhat resembling an ordinary lowercase b.

    0
    0
  • The old B retained the numerical value of the Greek i as 2, and no numerical value was given to the new symbol.

    0
    0
  • According to the system of phonetic changes generally known as "Grimm's law," an original b appears in English as p, an original bh as b.

    0
    0
  • In Late Latin there was a tendency to this spirant pronunciation which appears as early as the beginning of the 2nd century A.D.; by the 3rd century b and consonantal u are inextricably confused.

    0
    0
  • He may lease the settled land, or any part of it, for any time not exceeding (a) in the case of a building lease, 99 years; (b) in the case of a mining lease, 60 years, (c) in the case of any other lease, 21 years.

    0
    0
  • This enactment applies to leases of agricultural subjects, houses, mills, fisheries and whatever is fundo annexum; provided that (a) the lease, when for more than one year, must be in writing, (b) it must be definite as to subject, rent (which may consist of money, grain or services, if the reddendum is not illusory) and term of duration, (c) possession must follow on the lease.

    0
    0
  • If at least half of the harvest in any year is destroyed by accident, the lessee (a) in the case of a lease for several years, obtains, at the end of his lease, a refund of rent, by way of indemnity, unless he has been indemnified by preceding harvests; (b) in the case of a lease for a year only, may secure a proportional abatement of the current rent.

    0
    0
  • Branches were promoted (a) from Mukden to Antung on the Yalu, to connect with the Korean system, and (b) from Kwang-cheng-tsze to Kirin.

    0
    0
  • To it belong (a) superficial grooves or deeper slits situated on the integument near the tip of the head, (b) nerve lobes in immediate connexion with the nervous tissue of the brain, and (c) ciliated ducts penetrating into the latter and communicating with the former.

    0
    0
  • Two pairs of invaginations of B the skin, which originally are called the prostomial and metastomial disks, grow round the intestine, finally fuse together, and form the skin and mus- cular body-wall of the future Nemertine, which afterwards becomes ciliated, frees itself from the pilidium investment and develops into the adult worm without further metamorphosis.

    0
    0
  • If these conditions are not fulfilled sufficiently, the ammeter will not give the same indications for the same current if that current has been reached (a) by increasing from a smaller current, or (b) by decreasing from a larger current.

    0
    0
  • Let -I- B, - B, be two smaller trunnions which project out from the sides of the two strips connecting together a pair of rings CC. The rings and the connecting strips constitute the circuit which is to be rendered movable.

    0
    0
  • Its consonants are k, g, ng, ch, j, n, t, d, n, p, b, m, y, r, l, w, s, h.

    0
    0
  • The processes of soap manufacture may be classified (a) according to the temperatures employed into (I) cold processes and (2) boiling processes, or (b) according to the nature of the starting material - acid or oil and fat - and the relative amount of alkali, into (1) direct saturation of the fatty acid with alkali, (2) treating the fat with a definite amount of alkali with no removal of unused lye, (3) treating the fat with an indefinite amount of alkali, also with no separation of unused lye, (4) treating the fat with an indefinite amount of alkali with separation of waste lye.

    0
    0
  • From the properties of the ellipse, A is the pericentre or nearest point of the orbit to the centre of attraction and B the apocentre or most distant point.

    0
    0
  • Since the distance of a body from the observer cannot be observed directly, but only the right ascension and declination, calling these a and 6 we conceive ideal equations of the form a = f (a, b, c, e, f, g, t) and 5=0 (a, b, c, e, f, g, t), the symbols a, b,.

    0
    0
  • The oldest mention of Robin Hood at present known occurs in the second edition - what is called the B text - of Piers the Plowman, the date of which is about 1377.

    0
    0
  • Henry started with methyl iodide, the formula of which we write in the form CI a H b H c H d.

    0
    0
  • The same methyl iodide gave with potassium cyanide, acetonitril, which was hydrolysed to acetic acid; this must be C(Coch) a H b H c H d.

    0
    0
  • This acid with silver nitrite gave nitroacetic acid, which readily gave the second nitromethane, CH a (NO 2) b H c H d, identical with the first nitromethane.

    0
    0
  • B aeyer has suggested that his hypothesis may also be applied to explain the instability of acetylene and its derivatives, and the still greater instability of the polyacetylene compounds.

    0
    0
  • The space a must allow for the inclusion of a copper spiral if the substance contains nitrogen, and a silver spiral if halogens be present, for otherwise nitrogen oxides and the halogens may be condensed in the absorption apparatus; b contains copper oxide; c is a space for the insertion of a porcelain or platinum boat containing a weighed quantity of the substance; d is a copper spiral.

    0
    0
  • The magnesite (a) serves for the generation of carbon dioxide which clears the tube of air before the compound (mixed with fine copper oxide (b)) is burned, and afterwards sweeps the liberated nitrogen into the receiving vessel (e), which contains a strong potash solution; c is coarse copper oxide; and d a reduced copper gauze spiral, heated in order to decompose any nitrogen oxides.

    0
    0
  • Eliminating a and b between these relations, we derive P k V k /Tk= 8R, a relation which should hold between the critical constants of any substance.

    0
    0
  • Van der Waal's equation (p-I- a/v 2) (v - b) = RT contains two constants a and b determined by each particular substance.

    0
    0
  • To reduce these figures to a common standard, so that the volumes shall contain equal numbers of molecules, the notion of molecular volumes is introduced, the arbitrary values of the crystallographic axes (a, b, c) being replaced by the topic parameters' (x, ?i, w), which are such that, combined with the axial angles, they enclose volumes which contain equal numbers of molecules.

    0
    0
  • From B the curve of equilibrium (BD) between rhombic and liquid sulphur proceeds; and from C (along CE) the curve of equilibrium between liquid sulphur and sulphur vapour.

    0
    0
  • He claimed descent from the caliph Abubekr, and from the Khwarizm-Shah Sultan `Ala-uddin b.

    0
    0
  • B, The proboscis of one still more highly magnified.

    0
    0
  • B, A section through the same; a, the invaginated proboscis; b, proboscis sheath; c, beginning of the neck; d, lemniscus.

    0
    0
  • Dulceti, 1339, and b, On Mercator's projection, according to modern maps.

    0
    0
  • The Somali, however, declare themselves to be of Arab origin, alleging their progenitor to have been a certain Sherif Ishak b.

    0
    0
  • Climate (B) is the steady winter climate of Edmonton district.

    0
    0
  • The earliest literary papyrus is that known, from the name of its former owner, as the Prisse papyrus, and now preserved at Paris, containing a work composed in the reign of a king of the fifth dynasty, and computed to be itself of the age of upwards of 2500 years B,C. The papyri discovered in Egypt have often been found in tombs, and in the hands, or swathed with the bodies, of mummies.

    0
    0
  • The cheek-teeth (premolars and molars) form a A B C FIG.

    0
    0
  • The Zohar pretends to be a compilation made by Simon b.

    0
    0
  • If a and b are cardinal numbers, and a+I =b+1, then a =b.

    0
    0
  • For superior education there is (1) the university of Constantinople, with its four faculties of letters, science, law and medicine; and (2) special schools, including (a) the normal school for training teachers, (b) the civil imperial school, (c) the school of the fine arts and (d) the imperial schools of medicine.

    0
    0
  • The artillery is divided into (a) field artillery, horse artillery, mountain artillery and howitzer regiments; (b) fortress artillery; (c) artillery depots.

    0
    0
  • In this manner an annuity of £T159,500 was set free, of which £Ti i,000 per annum was allotted as " extraordinary sinking fund " to series A and £T49,500 per annum each to series B, C and D; the lottery bonds were originally excluded from this arrangement, and special compensation was granted to these later.

    0
    0
  • Series B, C and D (series A having already been completely redeemed by the action of the sinking fund) were replaced by the creation of new 4% bonds to a nominal amount of £T32,738,772, with a sinking fund of 0.45% per annum, bearing identical rights and privileges, and ranking immediately after, the priority bonds.

    0
    0
  • The rates at which the series were respectively exchanged against the new unified bonds were £loo series B against £70 unified, £loo series C against £42 unified and £too series C against £37, 10s.

    0
    0
  • Table B shows the total indebtedness of the Ottoman Empire, exclusive of tribute loans.

    0
    0
  • Dresden was the last great victory of the First Empire, By noon on the 27th August the Austrians and Russians were completely beaten and in full retreat, the French pressing hard behind them, but meanwhile Napoleon himself again succumbed G Beereri B eip \ ii g?

    0
    0
  • On the i i th and 12th of Battles December there were engagements of a less severe before character, and finally on the 13th of December Soult B, or Battles ayonne of with 35,000 men made a vehement attack up the the Nive, right bank of the Nive against Hill, who with about Dec. 10-13, 14,000 men occupied some heights from Villefranque 1813.

    0
    0
  • In 734 their king Sanip(b)u was a vassal of Tiglathpileser IV., and his successor, P(b)udu-ilu, held the same position under Sennacherib and Esarhaddon.

    0
    0
  • Under the influence of an applied electric force, he imagined that the B part of the first molecule was liberated at the anode, and that the A part thus isolated united with the B part of the second molecule, which, in its turn, passed on its A to the B of the third molecule.

    0
    0
  • In this manner, the B part of the last molecule of the chain was seized by the A of the last molecule but one, and the A part of the last molecule liberated at the surface of the cathode.

    0
    0
  • It will deal briefly (I) with the general idea and the historical evolution of ecclesiastical vestments, (2) with the vestments as at present worn (a) in the Roman Catholic Church, (b) in the Oriental Churches, (c) in the Reformed Churches, (d) in the Anglican Church.

    0
    0
  • They comprise (a) the older works surrounding the town; (b) a group of coast batteries on the high ground of Cape Bizerta or Guardia, 4 m.

    0
    0
  • D, Lunaria biennis, showing the septum B, Lepidium sativum.

    0
    0
  • Engler's Versuch einer Entwickelungsgeschichte der Pflanzenwelt (Leipzig, 1879-1882), we should have in Siberia (a) the arctic region; (b) the sub-arctic or coniferous region - north Siberian province; (c) the Central-Asian domain - Altai and Daurian mountainous regions; and (d) the east Chinese, intruding into the basin of the Amur.

    0
    0
  • Pro-deltidium attached A B C FIG.

    0
    0
  • A, Larva which has just left brood-pouch; B, longitudinal section through a somewhat later stage; C, the fully formed embryo just before fixing - the neo-embryo of Beecher.

    0
    0
  • B, C, D, Stages showing the turning forward of the second or mantle segment.

    0
    0
  • The declaration is to the effect that the clergyman has not received the presentation in consideration of any sum of money, reward, gift, profit or benefit directly or indirectly given or promised by him or any one for him to any one; that he has not made any promise of resignation other than that allowed by the Clerical Resignation Bonds Act 1828; that he has not for any money or benefit procured the avoidance of the benefice; and that he has not been party to any agreement invalidated by sec. 3 sub-sec. 3 of the act which invalidates any agreement for the exercise of a right of patronage in favour or on the nomination of any particular person, and any agreement on the transfer of a right of patronage (a) for the retransfer of the right, or (b) for postponing payment of any part of the consideration for the transfer until a vacancy or for more than three months, or (c) for payment of interest until a vacancy or for more than three months, or (d) for any payment in respect of the date at which a vacancy occurs, or (e) for the resignation of a benefice in favour of any person.

    0
    0
  • In particular the square of a determinant is a deter minant of the same order (b 11 b 22 b 33 ...b nn) such that bik = b ki; it is for this reason termed symmetrical.

    0
    0
  • In the theory of surfaces we transform from one set of three rectangular axes to another by the substitutions 'X=' by+ cz, Y = a'x + b'y + c'z, Z =a"x+b"y-l-c"z, where X 2+Y2+Z2 = x2+ y2+z2.

    0
    0
  • There are then 2n(n-I) quantities b rs .

    0
    0
  • Let the determinant of the b's be Ab and B rs, the minor corresponding to b rs .

    0
    0
  • We may therefore form an orthogonal transformation in association with every skew determinant which has its leading diagonal elements unity, for the Zn(n-I) quantities b are clearly arbitrary.

    0
    0
  • Assuming then 01 to have the coefficients B1, B2,...B,, and f l the coefficients A 1, A21...A,n, we may equate coefficients of like powers of x in the identity, and obtain m+n homogeneous linear equations satisfied by the m+n quantities B1, 2, ...B n, A 1, A 2, ...A m.

    0
    0
  • Further, let 1 -1-b i x+ b 2 x 2' +...

    0
    0
  • Again, if a i, a 2, a 3 ...a m, be the t " roots of -1, b 1 = b 2 =...

    0
    0
  • If m be infinite and 1 + b i x + b 2 x 2 +...

    0
    0
  • We write;L 22 = a 1 a 2 .b 1 n-2 b2s 3 n - 3 3 n-3 3 n-3 3 a 3 = a 1 a 2 .b 1 b 2 .c 1 c2, and so on whenever we require to represent a product of real coefficients symbolically; we then have a one-to-one correspondence between the products of real coefficients and their symbolic forms. If we have a function of degree s in the coefficients, we may select any s sets of umbrae for use, and having made a selection we may when only one quantic is under consideration at any time permute the sets of umbrae in any manner without altering the real significance of the symbolism.

    0
    0
  • Such an expression as a l b 2 -a 2 b i, which is aa 2 ab 2 aa x 2 2 ax1' is usually written (ab) for brevity; in the same notation the determinant, whose rows are a l, a 2, a3; b2, b 2, b 3; c 1, c 2, c 3 respectively, is written (abc) and so on.

    0
    0
  • For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.

    0
    0
  • In other words, B, b may be regarded as different or alternative symbols to A, a.

    0
    0
  • In either case (AB) =A 1 B 2 -A 2 B 1 = (A/2)(ab); and, from the definition, (ab) possesses the invariant property.

    0
    0
  • Since (ab) = a l b 2 -a 2 b l, that this may be the case each form must be linear; and if the forms be different (ab) is an invariant (simultaneous) of the two forms, its real expression being aob l -a l b 0.

    0
    0
  • This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.

    0
    0
  • In general it will be simultaneous covariant of the different forms n 1 rz 2 n3 a, b x, ?

    0
    0
  • For the quartic (ab) 4 = (aib2-a2b,) alb2 -4a7a2blb2+64a2 bib2 - 4a 1 a 2 b 7 b 2 + a a b i = a,a 4 - 4ca,a 3 +6a2 - 4a3a3+ aoa4 = 2(a 0 a 4 - 4a1a3 +e3a2), one of the well-known invariants of the quartic.

    0
    0
  • For the cubic (ab) 2 axbx is a covariant because each symbol a, b occurs three times; we can first of all find its real expression as a simultaneous covariant of two cubics, and then, by supposing the two cubics to merge into identity, find the expression of the quadratic covariant, of the single cubic, commonly known as the Hessian.

    0
    0
  • If we have a symbolic product, which contains the symbol a only in determinant factors such as (ab), we may write x 2, -x 1 for a 1, a 2, and thus obtain a product in which (ab) is replaced by b x, (ac) by c x and so on.

    0
    0
  • In particular, when the product denotes an invariant we may transform each of the symbols a, b,...to x in succession, and take the sum of the resultant products; we thus obtain a covariant which is called the first evectant of the original invariant.

    0
    0
  • The first transvectant, (f,f') 1 = (ab) a x b x, vanishes identically.

    0
    0
  • Further, in the case of invariants, we write A= (1, i') 2 and take three new forms B = (i, T) 2; C = (r, r`) 2; R = (/y).

    0
    0
  • The discriminant is the resultant of ax and ax and of degree 8 in the coefficients; since it is a rational and integral function of the fundamental invariants it is expressible as a linear function of A 2 and B; it is independent of C, and is therefore unaltered when C vanishes; we may therefore take f in the canonical form 6R 4 f = BS5+5BS4p-4A2p5.

    0
    0
  • Ternary and Higher Forms.-The ternary form of order n is represented symbolically by (aixl+a2x2+a3x3)' =a'; and, as usual, b, c, d,...

    0
    0
  • We can see that (abc)a x b x c x is not a covariant, because it vanishes identically, the interchange of a and b changing its sign instead of leaving it unchanged; but (abc) 2 is an invariant.

    0
    0
  • When R =0, and neither of the expressions AC - B 2, 2AB -3C vanishes, the covariant a x is a linear factor of f; but, when R =AC - B 2 = 2AB -3C =0, a x also vanishes, and then f is the product of the form jx and of the Hessian of jx.

    0
    0
  • When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.

    0
    0
  • Remark, too, that we are in association with non-unitary symmetric functions of two systems of quantities which will be denoted by partitions in brackets ()a, ()b respectively.

    0
    0
  • Solving the equation by the Ordinary Theory Of Linear Partial Differential Equations, We Obtain P Q 1 Independent Solutions, Of Which P Appertain To S2Au = 0, Q To 12 B U =0; The Remaining One Is Ab =Aobl A 1 Bo, The Leading Coefficient Of The Jacobian Of The Two Forms. This Constitutes An Algebraically Complete System, And, In Terms Of Its Members, All Seminvariants Can Be Rationally Expressed.

    0
    0
  • It Is Important To Notice That The Expression (0) A (0'Ls) B (01)A(0'18 1)B (812)A (0'18 2)B (Op).

    0
    0
  • T Aw 6(23)B A Series Of 2(W 2) Or Of 2(W I) Forms According As W Is Even Or Uneven.

    0
    0
  • For w = i the form is A i ai+Bib i, which we may write aob l -albo = ao(I) b -(I)abo; the remaining perpetuants, enumerated by z I - 2' have been set forth above.

    0
    0
  • For the case 8=1, 0' =2, the condition is a i r 1 72 = A032=0; and the simplest perpetuant, derived directly from the product A 1 B 21 is (I)a(2)b-(21)b; the remainder of those enumerated by z3 I z.

    0
    0
  • To represent the simplest perpetuant, of weight 7, we may take as base either A2B 1 B 2 or A l A 2 B2, and since Ai+Bi =o the former is equivalent to A 2 ArB 2 and the latter to A 2 B i B2; so that we have, (1 -f-aix) (1 + a2x).

    0
    0
  • By the rules adopted we take A?B 2 B 3, which gives (12)a(32)b - (1)a(321)b+ao(3212)b, the simplest perpetuant of weight 7; and thence the general form enumerated by the generating function 1 -z.1-z2.1 - z3 ?

    0
    0
  • The calculation results in -A,113 B2Bi+2A2B3B2Bi-AzB3BaBi+A4B3B1-2AlB3B2B1 -MB2B2131+MB33231+A213MB1 + A 2 B a Bi -2A2B3B2B +A2B1B1=0.

    0
    0
  • The general form of covariant is therefore (ab) h i (ac) h2 c) (b h3 a i bb2c'e3...abia?2b?3...

    0
    0
  • To assist us in handling the symbolic products we have not only the identity (ab) cx + (bc) a x + (ca) bx =0, but also (ab) x x+ (b x) a + (ax) b x = 0, (ab)a+(bc)a s +(ca)a b = 0, and many others which may be derived from these in the manner which will be familiar to students of the works of Aronhold, Clebsch and Gordan.

    0
    0
  • The borate, Pb 2 B 6 0 1 u 4H20, is obtained as a white precipitate by adding borax to a lead salt; this on heating with strong ammonia gives PbB2044H2.

    0
    0
  • The most famous of these are B euves de Comarchis, Ernaud de Girone, Garin d'Anseun, Aimer le chaff, so called from his long captivity with the Saracens.

    0
    0
  • When the direction of any vector quantity denoted by a symbol is to be attended to, it is usual to employ for the symbol either a block letter, as H, I, B, or a German capital, as j,, 3?

    0
    0
  • If V denote the potential, F the resultant force, X, Y, Z, its components parallel to the co-ordinate axes and n the line along which the force is directed, then - sn = F, b?= X, - Sy = Y, -s Surfaces for which the potential is constant are called equipotential surfaces.

    0
    0
  • These two positions are sometimes called the first and second (or A and B) principal positions of Gauss.

    0
    0
  • Hence if the induction per square centimetre at any point is denoted by B, then in empty space B is numerically equal to H; moreover in isotropic media both have the same direction, and for these reasons it is often said that in empty space (and practically in air and other nonmagnetic substances) B and H are identical.

    0
    0
  • The magnetic flux per square centimetre at any point (B, B, or 0) is briefly called the induction, or, especially by electrical engineers, the flux-density.

    0
    0
  • The induction may therefore be specified as B lines per square centimetre.

    0
    0
  • I = (B - H)/47r, (24) or B = H +41rI.

    0
    0
  • Hence B =µH and I =KH.

    0
    0
  • Moreover, it is not constant, being an apparently arbitrary function of H or of B; in the same specimen its value may, under different conditions, vary from less than 2 to upwards of 5000.

    0
    0
  • The total magnetic induction or flux corresponds to the current of electricity (practically measured in amperes); the induction or flux density B to the density of the current (number of amperes to the square centimetre of section); the magnetic permeability to the specific electric conductivity; and the line integral of the magnetic force, sometimes called the magnetomotive force, to the electro-motive force in the circuit.

    0
    0
  • The angle B is indicated by the position of the spot of light upon the scale, and the horizontal intensity of the earth's field H E is known; thus we can at once determine the value of H P, from which the magnetization I of the body under test may be calculated.

    0
    0
  • The inner coil is supplied, through the intervening apparatus, with current from the battery of secondary cells B,; this produces the desired magnetic field inside the tube.

    0
    0
  • Since the induction B is equal to H 47rI, it is easy from the results of experiments such as that just described to deduce the relation between B and H; a curve indicating such relation is called a curve of induction.

    0
    0
  • The current passes through the rocking key K, which, when thrown over to the right, places a in contact with c and b with d, and when thrown over to the left, places a in contact with e and b with f.

    0
    0
  • On the other hand, the form of the third curve, with its large intercepts on the axes of H and B, denotes that the specimen to which it relates possesses both retentiveness and coercive force in a high degree; such a metal would be chosen for making good permanent magnets.

    0
    0
  • Ii shows the relation of B to H in a specimen which has never before been magnetized.

    0
    0
  • Denoting by W the work in ergs done upon a cubic centimetre of the metal (=_fHdB or f HdI), he finds W =nips approximately, where n 47r is a number, called the hysteretic constant, depending upon the metal, and B is the maximum induction.

    0
    0
  • Steinmetz's formula may be tested by taking a series of hysteresis curves between different limits of B,' measuring their areas by a pianimeter, and plotting the logarithms of these divided by 47r as ordinates against logarithms of the corresponding maximum values of B as abscissae.

    0
    0
  • But though a formula of this type has no physical significance, and cannot be accepted as an equation to the actual curve of W and B, it is, nevertheless, the case that by making the index e =1.6, and assigning a suitable value to r t, a formula may be obtained giving an approximation to the truth which is sufficiently close for the ordinary purposes of electrical engineers, especially when the limiting value of B is neither very great nor very small.

    0
    0
  • After pointing out that, since the magnetization of the metal is the quantity really concerned, W is more appropriately expressed in terms of I, the magnetic moment per unit of volume, than of B, he suggests an experiment to determine whether the mechanical work required to effect the complete magnetic reversal i Phil.

    0
    0
  • Baily showed that hysteresis ceased to increase when B was carried beyond 23,000.

    0
    0
  • This value of B corresponds to I =1640, the saturation point for soft iron.

    0
    0
  • Shimizu 3 indicate that Steinmetz's formula holds for nickel and annealed cobalt up to B =3000, for cast cobalt and tungsten steel up to B =8000, and for Swedish iron up to B =18,000, the range being in all cases extended at the temperature of liquid air.

    0
    0
  • Curves of magnetization (which express the relation of I to H) have a close resemblance to those of induction; and, indeed, since B = H+47r1, and 47rI (except in extreme fields) greatly exceeds H in numerical value, we may generally, without serious error, put I = B /47r, and transform curves of induction into curves of magnetization by merely altering the scale to which the ordinates are referred.

    0
    0
  • The loss for any induction B within the range for which Steinmetz's law holds may be converted into that for the standard induction 2500 by dividing it by B 6 /2500'.

    0
    0
  • If H l and H2 be the values of 47rinll and 47ri' - 'Z/ l for the 2 2 same induction B, it can be shown that the true magnetizing force is H = H l - (H 2 - H 1).

    0
    0
  • The equation F = B 2 /87r is often said to express " Maxwell's law of magnetic traction " (Maxwell, Electricity and Magnetism,, §§ 642-646).

    0
    0
  • The values assigned to H were calculated from H= 2ni/r, and ranged from 3.9 to 585, but inasmuch as no account was taken of any 2 Since in most practicable experiments H 2 is negligible in comparison with B 2, the force may be taken as B 2 /87r without sensible= error.

    0
    0
  • He showed that there was, on the whole, a fair agreement between the values determined ballistic ally and those given by the formula B = 871-F.

    0
    0
  • If the pull is measured in pounds and the area in square inches, the formula may be written B =1317 X iI P/S +H.

    0
    0
  • The test-piece A, surrounded by a magnetizing coil, is clamped between two soft-iron blocks B, B'.

    0
    0
  • The yoke has two projecting pieces C, C' at unequal distances from the knife-edges, and separated from the blocks B, B' by narrow air-gaps.

    0
    0
  • The weight W is moved along the scale until the yoke just tilts over upon the stop S; the distance of W from its zero position is then, as can easily be shown, proportional to F, and therefore to B 2, and approximately to I 2.

    0
    0
  • Let m be the number of turns in use, and H 1 and H2 the magnetizing forces which produce the same induction B in the test and the standard rods respectively; then H1=H2Xm/Ioo.

    0
    0
  • The value of B which corresponds to Hem/100 can be found from the FIG.

    0
    0
  • Thus any desired number of corresponding values of H and B can be easily and quickly found.

    0
    0
  • Values of I are derived from (B -H)/477and of from B/H.

    0
    0
  • There appears to be no definite limit to the value to which the induction B may be raised, but the magnetization I attains a true saturation value under magnetizing forces which are in most cases comparatively moderate.

    0
    0
  • When the saturation value of I has been reached, the relation of magnetic induction to magnetic force may be expressed by B = H +constant.

    0
    0
  • It 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.

    0
    0
  • If a long magnetized rod is divided transversely and the cut ends placed nearly in contact, the magnetic force inside the narrow air gap will be B = H +47rI.

    0
    0
  • The force acting on the magnetism of one of the faces, and urging this face towards the other, will be less than B by 27r1, the part of the total force due to the first face itself; hence the force per unit of area with which the faces would press against each other if in contact is P = (B-27rI)I =27rT 2 +HI = (B 2 -H 2) =/81r.

    0
    0
  • The whole of the rod will therefore be subject to a compressive longitudinal stress P, the associated contraction R, expressed as a fraction of the original length, being R = P/M = (B 2 -H2)/87-M, where M is Young's modulus.

    0
    0
  • Those who support this view generally speak of the stress as " Maxwell's stress," and assume its value to be B 2 /87r.

    0
    0
  • Further, Maxwell's stress is a tension along the lines of force, and is equal to B 2 /87r only when B = H, and there is no magnetization.

    0
    0
  • Let each of the effects A, B, C, D and E be called positive when it is such as is exhibited by moderately magnetized iron, and negative when its sense is opposite.

    0
    0
  • B r (S) = strongly magnetized.

    0
    0
  • The range of + B within which Steinmetz's formula is applicable becomes notably increased at low temperature.

    0
    0
  • B =9000, at a frequency of loo per second, was only 0.254 watt per pound, as compared with 0.382 for the Swedish iron.

    0
    0
  • Its hysteresis-loss for B =9000 was o 236 per pound.

    0
    0
  • In one case the hysteresis loss per cubic centimetre per cycle was 16,100 ergs for B =1 5,900, and only 1200 ergs for B = 20,200, the highest induction obtained in the experiment; possibly it would have vanished before B had reached 21,000.2 These experiments prove that actual friction must be almost entirely absent, and, as Baily remarks, the agreement of the results with the previously suggested deduction affords a strong verification of Ewing's form of the molecular theory.

    0
    0
  • To obtain the support of the capitalists, Gaius Gracchus conceived the plan of creating friction between them and the senate, which he carried out by handing over to them the control (a) of the jury-courts, and (b) of the revenues of Asia.

    0
    0
  • B, Diagram showing the nature of this infolding.

    0
    0
  • B, Rhabdom of the same, consisting of five confluent rhabdomeres.

    0
    0
  • The figure B also shows the peculiar neural investiture formed by the cerebral arteries in Limulus and the derivation from this of the arteries to the limbs, III, IV, VI, whereas in Scorpio the latter have a separate origin from the anterior aorta.

    0
    0
  • Whilst the chances are in favour of some one homoplastic coincidence or structural agreement occurring between some member or other of a large group a and some member or other of a large group b, the matter is very different 2 a o FIG.

    0
    0
  • A, Youngest stage with no mesosomatic somites; B and C, stages with two mesosomatic somites between the prosomatic and telsonic carapaces; D, adult condition, still with only two free mesosomatic somites.

    0
    0
  • In front of it the narrow waist is formed by the soft sternal area of the praegenital somite; 2, the sternite of the 2 second opisthosomatic somite covering the posterior pair of lung-sacs; and 4, the spinning appendages (limbs) of the opisthosoma; a, inner, b, outer ramus of the appendage; I I, sternite of the eleventh --

    0
    0
  • Opisthosoma consisting of only ten somites, which have no tergal and sternal elements, the prae-genital somite contracted to form a " waist," as in the Pedipalpi; the last three narrowed to form a A B prae-1 2345 6789 io I I111I IV V VI gen Opisttaosoma Prosoma FIG.

    0
    0
  • A, Ventral view of prosoma and of anterior region of opistho soma with the appendages cut off near the base; a and b, B, Dorsal view.

    0
    0
  • The segmentation of the prosoma and the form of the appendages bear a homoplastic similarity to the head, pro-, meso-, and meta-thorax of a Hexapod with mandibles, maxillary palps and three pairs of walking legs; while the opistho io i e d c b o a S' S" 2 I VT V S IV III II I Opisthosoma Prosoma FIG.

    0
    0
  • Tofieldia, an arctic and alpine genus of small herbs with a slender scape springing from a tuft of narrow ensiform leaves and bearing a raceme of small green flowers; Narthecium (bog-asphodel), herbs with a habit similar to Tofieldia, but with larger golden-yellow flowers; and Colchicum, a genus with about 30 species including b the meadow saffron or autumn crocus (C. autumnale).

    0
    0
  • He not only freed it from all trammels of geometrical construction, but by the introduction of the symbol b gave it the efficacy of a new calculus.

    0
    0
  • To group (a) belong territorial differences in regard to ownership of land and rights of fishing at sea; to group (b) belong pecuniary claims in respect of acts wrongfully done to one or more subjects of one state by, or with the authority of, another state.

    0
    0
  • Of a more distinctly national tendency are the lyrics of John Kriza b and John Erdelyi, but the reputation of the latter was more especially due to his collections of folk-lore made on behalf of the Kisfaludy society.

    0
    0
  • To say, for instance, that X is equal to A -B, is the same thing as to say that X is a quantity such that X and B, when added, make up A; and the above five statements of necessary connexion between two statements of equality are in fact nothing more than definitions of the symbols -, m of, =,, and loga.

    0
    0
  • If, for instance, we state that A=X - B, this is really a statement that X=Ad-B.

    0
    0
  • When we are familiar with the treatment of quantities by equations, we may ignore the units and deal solely with numbers; and (ii.) (a) and (ii.) (b) may then, by the commutative law for multiplication, be regarded as identical.

    0
    0
  • In the case of addition, for instance, suppose that we are satisfied that in a+b+c+d+e we may take any two, as b and c, together (association) and interchange them (commutation).

    0
    0
  • Let X and Y be the related quantities, their expressions in terms of selected units A and B being x and y, so that X=x.A, Y = y.

    0
    0
  • An equation of the form ax=b, where a and b do not contain x, is the standard form of simple equation.

    0
    0
  • Therefore, if (n-i) 1P+11 is divisible by (p+I)!, 'n 1P+11 is divisible b y (p +i) !.

    0
    0
  • If a of the stock are of one type, b of another, c of another,.

    0
    0
  • Suppose that there are a number of arrangements of r terms or elements, the first of which a is always either A or not-A, the second b is B or not-B, the third c is C or not-C, and so on.

    0
    0
  • If, in this latter case, the proportion of cases in which b is B to cases in which b is not-B is the same for the group of pN individuals in which a is A as for the group of (I-p)N in which a is not-A, then the frequencies of A and of B are said to be independent; if this is not the case they are said to be correlated.

    0
    0
  • If the frequency of each A is independent of the frequency of each B, then the attributes a and b are independent; otherwise they are correlated.

    0
    0
  • The values of the first ten of Bernoulli's numbers are B1= t, B2= 1, B3 =412, B4 =30, B5 =6 = 6 9 1 B7 = l, B =3 =4 4 fl, IV.

    0
    0
  • The results in (b) apply also if n is a negative integer.

    0
    0
  • We want to express (23/13) 3 in the form a l b, where b is nearly equal to i.

    0
    0
  • It could not escape notice that one and the same symbol, such as -1 (a - b), or even (a - b), sometimes did and sometimes did not admit of arithmetical interpretation, according to the values attributed to the letters involved.

    0
    0
  • They are (a+b)-?-c=a+(b+c) (A) (aXb)Xc=aX(bXc) (A') a+b=b+a (c) aXb=bXa (c') a(b c) =ab-Fac (D) (a - b)+b=a (I) (a=b)Xb=a (I') These formulae express the associative and commutative laws of the operations + and X, the distributive law of X, and the definitions of the inverse symbols - and =, which are assumed to be unambiguous.

    0
    0
  • Let i denote a definite region of space; and let a, b, &c., stand for definite parts of i.

    0
    0
  • Let a+b denote the region made up of a and b together (the common part, if any, being reckoned only once), and let a X b or ab mean the region common to a and b.

    0
    0
  • It can be proved by geometry that (aA-H3B) +yC = aA+(aB+- y C) = (a + 1 3+ 7) P, where P is in fact the centroid of masses a, 13, y placed at A, B, C respectively.

    0
    0
  • X is, in general, a determinate point, the barycentre of aA, 3B, &c. (or of A, B, &c. for the weights a, 0, &c.).

    0
    0
  • From A Merely Formal Point Of View, We Have In The Barycentric Calculus A Set Of " Special Symbols Of Quantity " Or " Extraordinaries " A, B, C, &C., Which Combine With Each Other By Means Of Operations And Which Obey The Ordinary Rules, And With Ordinary Algebraic Quantities By Operations X And =, Also According To The Ordinary Rules, Except That Division By An Extraordinary Is Not Used.

    0
    0
  • If A 1 = X a i e i, B i = /if i e i, the distributive law of multiplication is preserved by assuming A1B1=E(a0 i 3)eiej; it follows that A 1 B 1 = - B 1 A 1, and that A l 2 = o.

    0
    0
  • The symbol AB, from this point of view, is called the inner product of A and B, as distinguished from the outer product IAB.

    0
    0
  • The outer and inner products of two extensive quantities A, B, are in many ways analogous to the quaternion symbols Vab and Sab respectively.

    0
    0
  • These may be compared and contrasted with such quaternion formulae as S(VabVcd) =SadSbc-SacSbd dSabc = aSbcd - bScda+cSadb where a, b, c, d denote arbitrary vectors.

    0
    0
  • One of the most important questions in investigating a linear algebra is to decide the necessary relations between a and b in order that this product may be zero.

    0
    0
  • Even in ordinary algebra the notation for powers and roots disturbs the symmetry of the rational theory; and when a schoolboy illegitimately extends the distributive law by writing -V (a+b)a+J b, he is unconsciously emphasizing this want of complete harmony.

    0
    0
  • Study), and B I c (G.

    0
    0
  • In this they were completely successful, for they obtained general solutions for the equations ax by = c, xy = ax+by+c (since rediscovered by Leonhard Euler) and cy 2 = ax e + b.

    0
    0
  • The Inter-Allied Commission entrusted with the details was ordered to divide the disputed area into Zone A, mainly south of the river Drava (Drau) and Zone B,.

    0
    0
  • Zone B, with Klagenfurt, now automatically passed to Austria.

    0
    0
  • Against Bulgaria the Yugoslav delegation claimed considerable frontier rectifications - (a) the Strumnica salient, which threatened the Vardar railway from the east, (b) the district of Kochana (Tocana) and the Bregalnitsa (Bregalnica), (c) a strip of territory running parallel with the old Serbo-Bulgarian frontier the whole way from Zajecar to Kyustendil, and (d) the town of Vidin on the Danube and the salient between it and the Timok.

    0
    0
  • Pre-Darwinian zoologists had been aware of the class of facts thus interpreted by Fritz Muller, but the authoritative view on the subject had been that there is a parallelism between (a) the series of forms which occur in individual development, (b) the series of existing forms from lower to higher, and (c) the series of forms which succeed 'one another in the strata of the earth's crust, whilst an explanation of this parallelism was either not attempted, or was illusively offered in the shape of a doctrine of harmony of plan in creation.

    0
    0
  • The most important work in this direction has been done by Fritz Muller (Filr Darwin), by Herman Muller (Fertilization of Plants by Insects), Grade b.

    0
    0
  • We will now apply the integrals (2) to the case of a rectangular aperture of width a parallel to x and of width b parallel to y.

    0
    0
  • The form of (3) shows immediately that, if a and b be altered, the co-ordinates of any characteristic point in the pattern vary as a-'- and b-1.

    0
    0
  • The brightness (corresponding to B) midway between the two central points AA' is 8106 of the brightness at the central points themselves.

    0
    0
  • Thus if A be selfluminous, the illumination is a maximum at B, where all the secondary waves agree in phase.

    0
    0
  • When the interval is very small the discrepancy, though mathematically existent, produces no practical effect, and the illumination at B due to P is as important as that due to A, the intensities of the two luminous sources being supposed equal.

    0
    0
  • This is necessarily a question of degree; but it does not require detailed calculations in order to show that the discrepancy first becomes conspicuous when the phases corresponding to the various secondary waves which travel from P to B range over a complete period.

    0
    0
  • The illumination at B due to P then becomes comparatively small, indeed for some forms of aperture evanescent.

    0
    0
  • The extreme discrepancy is that between the waves which travel through the outermost parts of the object-glass at L and L'; so that if we adopt the above standard of resolution, the question is where must P be situated in order that the relative retardation of the rays PL and PL' may on their arrival at B amount to a wave-length (X).

    0
    0
  • The path of a ray from the wave-surface AoBo to A or B is determined by the con dition that the optical distance, µ ds, is a minimum; and, as AB is by supposition a wave-surface, this optical distance is the same for both points.

    0
    0
  • Thus f t2 ds (for A) = f A ds (for B)..

    0
    0
  • The path of a ray from the wave-surface A 0 B 0 to the point A is changed; but in virtue of the minimum property the change may be neglected in calculating the optical distance,as it influences the result by quantities of the second order only in the changes of refrangibility.

    0
    0
  • B) - f S,u ds (along The new wave-surface is formed in such a position that the optical distance is constant; and therefore the dispersion, or the angle through which the wave-surface is turned by the change of refrangibility, is found simply by dividing (5) by the distance AB.

    0
    0
  • These directions, in which the retardation between A and B is exactly mnX, may be called the principal directions.

    0
    0
  • Then the relative retardation of the extreme rays (corresponding to the edges A, B of the grating) is mnX.

    0
    0
  • B is the point at which the effect is required, distant a+b from 0, so that AB= b, AP=s, PQ ds.

    0
    0
  • When a, b, X are regarded as constant, the first factor may be omitted, - as indeed should be done for consistency's sake, inasmuch as other factors of the same nature have been omitted already.

    0
    0
  • The position of Q corresponding to a given value of V, that is, to a band of given order, is by (19) BQ= aa b AD=V?

    0
    0
  • By means of this expression we may trace the locus of a band of given order as b varies.

    0
    0
  • The occurrence of sin 4 as a factor in (6) shows that the relative intensities of the primary light and of that diffracted in the direction B depend upon the condition of the former as regards polarization.

    0
    0
  • 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.

    0
    0
  • At B, where the ray leaves the drop, the deviation is the same as at A, viz.

    0
    0
  • There it was that the community formed by Yahya b.

    0
    0
  • The effect of overwork upon an organ or tissue varies in accordance with (a) the particular organ or tissue concerned, (b) the amount of nourishment conveyed to it, and (c) the power of assimilation possessed by its cells.

    0
    0
  • Its scope may be briefly indicated as including (a) duties exercised elsewhere by the Borough Councils, and by the London County Council (although that body is by no means powerless within the City boundaries); and (b) peculiar duties such as control of markets and police.

    0
    0
  • With the exception of the townships and a district of Emtonjaneni magistracy known as " Proviso B," 1 mainly occupied by Boer farmers, all the land was vested in the crown and very little has been parted with to Europeans.

    0
    0
  • Two of these (UBI, L B 15) were attached to the Austrian submarine force.

    0
    0
  • A and B are pear-shaped glass vessels connected by a long narrow india-rubber tube, which must be sufficiently strong in the body (or strengthened by a linen coating) to stand an outward pressure of 1 to 2 atmospheres.

    0
    0
  • The apparatus, after having been carefully cleaned and dried, is charged with pure and dry mercury which must next be worked backwards and forwards between A and B to remove all the air-bells.

    0
    0
  • It can be considerably shortened, the two vessels A and B brought more closely together, and the somewhat objectionable india-rubber tube be dispensed with, if we connect the air-space in B with an ordinary air pump, and by means of it do the greater part of the sucking and the whole of the lifting work.

    0
    0
  • It is expressly directed by the act of 1898 above referred to, that in regard to succession, inheritance, marriage, caste or any religious usage or institution, the law to be administered in Burma is (a) the Buddhist law in cases where the parties are Buddhists, (b) the Mahommedan law in cases where the parties are Mahommedans, (c) the Hindu law in cases where the parties are Hindus, except so far as the same may have been modified by the legislature.

    0
    0
  • His elder brother Ram Rai was passed over p was put to death for refusal to embrace Islam b.

    0
    0
  • A group (B), comprising copper, is, substantially, attacked only in the presence of oxygen or air.

    0
    0
  • This is proved by taking any two points A and B at the same level, and considering the equilibrium of a thin prism of liquid AB, bounded by planes at A and B perpendicular to AB.

    0
    0
  • As gravity and the fluid pressure on the sides of the prism act at right angles to AB, the equilibrium requires the equality of thrust on the ends A and B; and as the areas are equal, the pressure must be equal at A and B; and so the pressure is the same at all points in the same horizontal plane.

    0
    0
  • This is proved by taking the two points A and B in the same vertical line, and considering the equilibrium of the prism by resolving vertically.

    0
    0
  • In this case the thrust at the lower end B must exceed the thrust at A, the upper end, by the weight of the prism of liquid; so that, denoting the cross section of the prism by a ft.

    0
    0
  • Afterwards, when the metal has risen above B, to the level KK', the additional thrust is the weight of the cylinder of diameter KK' and height BH.

    0
    0
  • For if the ship turns through a small angle 0 about the line FF', then b1, b 2, the C.G.

    0
    0
  • Ballasted with G at B, the righting couple when the ship is heeled through 0 is given by W.BM.

    0
    0
  • The time rate of increase of momentum of the fluid inside S is )dxdydz; (5) and (5) is the sum of (I), (2), (3), (4), so that /if (dpu+dpu2+dpuv +dpuw_ +d p j d xdyd z = o, (b)` dt dx dy dz dx / leading to the differential equation of motion dpu dpu 2 dpuv dpuv _ X_ (7) dt + dx + dy + dz with two similar equations.

    0
    0
  • Taking the axis of x for an instant in the normal through a point on the surface H = constant, this makes u = o, = o; and in steady motion the equations reduce to dH/dv=2q-2wn = 2gco sin e, (4) where B is the angle between the stream line and vortex line; and this holds for their projection on any plane to which dv is drawn perpendicular.

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

    0
    0
  • 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?

    0
    0
  • 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.

    0
    0
  • The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.

    0
    0
  • 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 '?"

    0
    0
  • 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.

    0
    0
  • As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.

    0
    0
  • 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!

    0
    0
  • Ja - 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.

    0
    0
  • Helmholtz, of the efflux of a jet between two edges A and A 1 in an infinite wall, is obtained by the symmetrical duplication of the above, with n = 1, b = o, a' = - oo, as in fig.

    0
    0
  • Generally, by making a' = -oo, the line x'A' may be taken as a straight stream line of infinite length, forming an axis of symmetry; and then by duplica tion the result can be ob A tained, with assigned n, a, and b, of the efflux from a symmetrical converging FIG.

    0
    0
  • Thus with a' =o, a stream is split symmetrically by a wedge of angle ' zr/n as in Bobyleff's problem; and, by making a = oo, the wedge extends to infinity; then chnS2= u, sh nS2= b n u.

    0
    0
  • Over the ellipsoid, p denoting the length of the perpendicular from the centre on a tangent plane, px _ pv _ _ pz 1= a2+X' b +A' n c2+A p2x2 + p2y2 p2z2 I (a2 - + X)2 (b 2 +x)2 + (0+X)2, p 2 = (a2+A)12+(b2+X)m2+(c2+X)n2, = a 2 1 2 +b 2 m 2 +c 2 n 2 +X, 2p d = ds; (8) Thence d?

    0
    0
  • When the liquid is bounded externally by the fixed ellipsoid A = A I, a slight extension will give the velocity function 4 of the liquid in the interspace as the ellipsoid A=o is passing with velocity U through the confocal position; 4 must now take the formx(1'+N), and will satisfy the conditions in the shape CM abcdX ¢ = Ux - Ux a b x 2+X)P Bo+CoB I - C 1 (A 1 abcdX, I a1b1cl - J o (a2+ A)P and any'confocal ellipsoid defined by A, internal or external to A=A 1, may be supposed to swim with the liquid for an instant, without distortion or rotation, with velocity along Ox BA+CA-B 1 -C1 W'.

    0
    0
  • The extension to the case where the liquid is bounded externally by a fixed ellipsoid X= X is made in a similar manner, by putting 4 = x y (x+ 11), (io) and the ratio of the effective angular inertia in (9) is changed to 2 (B0-A0) (B 1A1) +.a12 - a 2 +b 2 a b1c1 a -b -b12 abc (Bo-Ao)+(B1-A1) a 2 + b 2 a1 2 + b1 2 alblcl Make c= CO for confocal elliptic cylinders; and then _, 2 A? ?

    0
    0
  • Sources of Apocalyptic. - The origin of Apocalyptic is to be sought in (a) unfulfilled prophecy and in (b) traditional elements drawn from various sources.

    0
    0
  • An /,, B other method is to boil one FIG.

    0
    0
  • A and B, mycelium (m), the mix t ure over the affe c ted with haustoria (h).

    0
    0
  • Extraction of cane juice by diffusion (a process more fully described under the head of beetroot sugar manufacture) is adopted in a few plantations in Java and Cuba, in Louisiana Etr cti o n and the Hawaiian Islands, and in one or two factories y f i in Egypt; b u t hitherto, except under exceptional conditions (as at Aska, in the Madras Presidency, where the local price for sugar is three or four times the London price), it would not seem to offer any substantial advantage over double or triple crushing.

    0
    0
  • Outline of the ventral surface to show the external apertures and nervous system; a, rosette-organ; b, uterine pore; c, terminal sucker; e, vaginal pore; g, male gonopore; n, o, p, nervous system.

    0
    0
  • B, Archigetes sieboldi; X 60 (from Leuckart).

    0
    0
  • B, head showing the suckers, proboscides and excretory canals; X 25.

    0
    0
  • The ovum first divides into (a) a granular cell, and (b) a cell full of refringent spherules.

    0
    0
  • In the United States, Belgian furnaces of type (a) are built to contain 864 retorts; of type (b), to contain 300 to 400 retorts; and of type (c), preferably about 600 retorts.

    0
    0
  • In regard to methods and apparatus, mention should be made of his improvements in the technique of organic analysis, his plan for determining the natural alkaloids and for ascertaining the molecular weights of organic bases b y means of their chloroplatinates, his process for determining the quantity of urea in a solution - the first step towards the introduction of precise chemical methods into practical medicine - and his invention of the simple form of condenser known in every laboratory.

    0
    0
  • Details of their history are not known, but they seem to have gained power at one time even over the aakhmids of Hira; and to have ruled over Bahrein as well as Yemama until the battle of Shi'b ul Jabala, when they lost this province to Hira.

    0
    0
  • Azraqi again was followed by Fakihi, who wrote a History of Mecca in 885, 2 and `Omar b.

    0
    0
  • This evidence is confirmed by (a) the canon of Theodore of Edessa (800) allowing metropolitans of China, India and other distant lands to send their reports to the catholikos every six years; (b) the edict of Wu Tsung destroying Buddhist monasteries and ordering 300 foreign priests to return to the secular life that the customs of the empire might be uniform; (c) two 9th-century Arab travellers, one of whom, Ibn Wahhab, discussed the contents of the Bible with the emperor; (d) the discovery in 1725 of a Syrian MS. containing hymns and a portion of the Old Testament.

    0
    0
  • Much of the earlier electrometallurgical work was done with furnaces of the (a) type, while nearly all the later developments have been with those of class (b).

    0
    0
  • A further examination of the epistle shows that it must have been written towards the close of the B&erla An of Acts xxviii.

    0
    0
  • Ibrahim, the last of the Deys (1702-1705), destroyed the house of Mural, and absorbed the beyship in his own office; but, when he fell in battle with the Algerians, Hussein b.

    0
    0
  • In the Le Bel-Henninger form a series of bulbs are connected consecutively by means of syphon tubes (b) and having platinum gauzes (a) at the constrictions, so that when a certain amount of liquid collects in any one bulb it syphons over into the next lower bulb.

    0
    0
  • If M 1, M2, and P 1, P 2 be the molecular weights and vapour pressures of the components A and B, then the ratio of A to B in the distillate is M 1 P 1 /M 2 P 2.

    0
    0
  • Although, as is generally the case, one liquid (say A) is more volatile than the other (say B), i.e.

    0
    0
  • P 1 greater than P2, if the molecular weight of A be much less than that of B, then it is obvious that the ratio M 1 P 1 /M 2 P 2 need not be very great, and hence the less volatile liquid B would come over in fair amount.

    0
    0
  • A dissolved in B and B dissolved in A, since both of these solutions emit vapours of the same composition (this follows since the same vapour must be in equilibrium with both solutions, for if it were not so a cyclic system contradicting the second law of thermodynamics would be realizable).

    0
    0
  • On distilling such a mixture pure A will come over first, followed by mixtures in which the quantity of B continually increases; consequently by a sufficient number of distillations A and B can be completely separated.

    0
    0
  • B, Udonella caligorum, attached to the ova of the copepod Caligus.

    0
    0
  • A, Dorsal view showing the nervous system and digestive system; a, mouth; b, pharynx; c, d, e, gut; E, post-genital union of two limbs of gut; f, excretory pore; g, vaginal pore; h, j, k, brain and nerves; 1, dorsal nerves; m, ventral nerves; n, adoral sucker; o, posterior sucker; p, hooks on posterior sucker; r, vitello-intestinal duct.

    0
    0
  • B, Ventral view showing the The further history of the animal is only known in a few cases.

    0
    0
  • A, The free-swimming embryo.- B, A sporocyst containing young rediae.

    0
    0
  • In Cheilostomata with a rigid frontal wall A, of Membranipora; B, of an Jullien showed that proimmature zooecium of Cribrilina trusion and retraction were p.m., Parietal muscles.

    0
    0
  • This appears to indicate B that the Polyzoa are remotely allied to other phyla in which this type of larva prevails, and in particular to the Mollusca and Chaetopoda, as well as to the Rotifera, which are regarded as persistent Trochospheres.

    0
    0
  • None, however, was of equal im- b ortance with the first, and their details are given vaguely by t.

    0
    0
  • A further peculiarity of the use of C in Latin is in the abbreviation for the district Subura in Roma and its adjective Suburanus, which appears as SVC. Here C no doubt represents G, but there is no interchange between g and b in Latin.

    0
    0
  • In other dialects of Italy b is found representing an original voiced guttural (gw), which, however, is regularly replaced by v in Latin.

    0
    0
  • For a moment, when the tide of Western civilization swept over Japan, the NO seemed likely to b permanently submerged.

    0
    0
  • The other volumes dealt with (a) iron and steel, (b) copper and brass, their smelting, conversion and assaying, and chemical experiments thereon.

    0
    0
  • In modern Greek the ancient b (d) has become the voiced spirant (8), though it is still written b.

    0
    0
  • Probably these were the original genii of the necropolis, and in fact the same lean animal figured passant is s;b " jackal" or "fox."

    0
    0
  • Let us suppose that a molten mixture of two substances A and B, which at a sufficiently high temperature form a uniform liquid, and which do not combine to form definite compounds, is slowly cooled until it becomes wholly solid.

    0
    0
  • The phenomena which succeed each other are then very similar, whether A and B are two metals, such as lead and tin or silver and copper, or are a pair of fused salts, or are water and common salt.

    0
    0
  • If a mixture of A and B be melted and then allowed to cool, a thermometer immersed in the mixture will indicate a gradually falling temperature.

    0
    0
  • If we determine the freezing-points of a number of mixtures varying in composition from pure A to pure B, we can plot the freezing-point curve.

    0
    0
  • It consists of two branches AC and BC, which meet in a lowest point C. It will be seen that as we increase the percentage of B from nothing up to that of the mixture C, the freezing-point becomes lower and lower, but that if we further increase the percentage of B in the mixture, the freezing-point rises.

    0
    0
  • This process goes on until the state of the remaining liquid is represented by the point C. Now crystals of B begin to form, simultaneously with the A crystals, and the composition of the remaining liquid does not alter as the solidification progresses.

    0
    0
  • The corresponding changes in the case of the mixture Tuvw are easily understood - the first halt at U, due to the crystallization of pure B, will probably occur at a different temperature, but the second halt, due to the simultaneous crystallization of A and B, will always occur at the same temperature whatever the composition of the mixture.

    0
    0
  • There are thus two eutectic alloys B and D, and the alloys with compositions between B and D have higher melting-points.

    0
    0
  • It is probable that all the alloys of compositions between B and D, when they begin to solidify, deposit crystals of the compound; the lower eutectic B probably corresponds to a solid complex of mercury and the compound.

    0
    0
  • Then take two suspended gilt pith balls and touch them (a) both against one tray; they will be found to repel each other; (b) touch one against one tray and the other against the other tray, and they will be found to attract each other.

    0
    0
  • This mass is equal to 47rabcp,u; therefore Q = A47rabcp s and b =pp, where p is the length of the perpendicular let fall from the centre of the ellipsoid on the tangent plane.

    0
    0
  • Hence the density v is given by 47rabc (x2/a4+y2/b4-I-z2/c4), and the potential at the centre of the ellipsoid, and therefore its potential as a whole is given by the expression, adS Q dS V f r 47rabc r' (x2/a4-I-y2/b4+z2/c4) Accordingly the capacity C of the ellipsoid is given by the equation 1 I J dS C 47rabc Y (x 2 +y 2 + z2) V (x2/a4+y2/b4+z2/c4) (5) It has been shown by Professor Chrystal that the above integral may also be presented in the form,' foo C 2 J o J { (a2 + X) (b +X) (c 2 + X) } (6).

    0
    0
  • Thus if the ellipsoid is one of revolution, and ds is an element of arc which sweeps out the element of surface dS, we have dS = 27ryds = 27rydx/ (Ts) = 27rydx/ (b y) = 2 p2 dx.

    0
    0
  • The metal slips are so placed that, as the disk revolves, the middle brush, connected to one terminal of the condenser C, is alternately put in conductive connexion with first one and then the other outside brush, which are joined respectively to the battery B and galvanometer G terminals.

    0
    0
  • This can be done by placing at B an equal negative point-charge -q in the place which would be occupied by the optical image of A if PO were a mirror, that is, let -q be placed at B, so that the distance BO is equal to the distance AO, whilst AOB is at right angles to PO.

    0
    0
  • Take a point B in CA such that CB CA =r 2, or CB =r 2 /d.

    0
    0
  • If then we put a negative point-charge -qr/d at B, it follows that the spherical surface will be a zero potential surface, for q rq 1 (24).

    0
    0
  • The area BCDdb under the path represents the external work done by the substance in expanding from B to D, which is analytically represented by the integral of pdv taken along the given path.

    0
    0
  • If the substance in any state such as B were allowed to expand adiabatically (dH = o) down to the absolute zero, at which point it contains no heat and exerts no pressure, the whole of its available heat energy might theoretically be recovered in the form of external work, represented on the diagram by the whole area BAZcb under the adiabatic through the state-point B, bounded by the isometric Bb and the zero isopiestic bV.

    0
    0
  • The change of the intrinsic energy in passing from one state to another, as from B to C is represented by the addition of the heat-area H= Bczz', and the subtraction of the work-area W = BCcb.

    0
    0
  • If, starting from E, the same amount of heat h is restored at constant pressure, we should arrive at the point F on the adiabatic through B, since the substance has been transformed from B to F by a reversible path without loss or gain of heat on the whole.

    0
    0
  • If we consider any short length of the stream bounded by two imaginary cross-sections A and B on either side of the plug, unit mass of the fluid in passing A has work, p'v', done on it by the fluid behind and carries its energy, E'+ U', with it into the space AB, where U' is the kinetic energy of flow.

    0
    0
  • In passing B it does work, p"v", on the fluid in front, and carries its energy, E"+ U", with it out of the space AB.

    0
    0
  • The introduction of the covolume, b, into the equation is required in order to enable it to represent the behaviour of hydrogen and other gases at high temperatures and pressures according to the experiments of Amagat.

    0
    0
  • The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..

    0
    0
  • I by the whole area B"DZ'VO under the isothermal 9"D and the adiabatic DZ', bounded by the axes of pressure and volume.

    0
    0
  • The difference 90-E is represented by the area 9"DdO to the left of the isometric Dd under the isothermal B"D.

    0
    0
  • The value of B is determined by observing the latent heat, Lo = F"o - F'0, which gives B =B" - B' =L0+(s' - So)00+(n+r)copo - bpo+dho (45) This constant may be called the absolute latent heat, as it expresses the thermal value of the change of state in a manner independent of temperature.

    0
    0
  • This simple result is generally true, and the corresponding expressions for G" and J" are valid, provided that c - b in formula (17) is a function of the temperature only.

    0
    0
  • Rose the third day, A, B, D, E (F omits " the third day " being a theological creed; the translation of C is uncertain).

    0
    0
  • Reinforced by Khalid b.

    0
    0
  • In the first place an inverted image (first image) is formed in the face b c, and then an image of this image is formed in a b, and it is the outline of this second image seen projected on the paper that is traced by the pencil.

    0
    0
  • None of them, in point of fact, has held its ground, and even his proposal to denote unknown quantities by the vowels A, E, I, 0, u, Y - the consonants B, c, &c., being reserved for general known quantities - has not been taken up. In this denotation he followed, perhaps, some older contemporaries, as Ramus, who designated the points in geometrical figures by vowels, making use of consonants, R, S, T, &c., only when these were exhausted.

    0
    0
  • The right sheath C (outer process of the ninth abdominal segment-9) is shown in connexion with the guide B formed by the inner processes of the 9th segment.

    0
    0
  • The stylet A (process of the 8th abdominal segment-8) is turned over to show its groove a, which works along the tongue or rail b.

    0
    0
  • The top is fitted with a rubber stopper, or in some forms with a stop-cock, while a little way down there is a bent delivery tube (b).

    0
    0
  • In 1842 he took a "double-first" and was elected fellow of B alliol, and lecturer in mathematics and logic. Four years later he took orders, and with the aim of helping forward the education of the very poor, he accepted the headship of Kneller Hall, a college which the government formed for the training of masters of workhouse and penal schools.

    0
    0
  • The slides are moved by the screws a and b, the divided heads of which serve to measure the separation of the segments.

    0
    0
  • These screws are turned from the eye-end by bevelled wheels and pinions, the latter connected with the handles a', b'.

    0
    0
  • The ring c, which carries the supports of the handles a', b', is capable of a certain amount of rotation on the tube.

    0
    0
  • Accordingly, in reading the scales A and B (attached to the slides which carry the two halves of the object-glass), it is only necessary to turn the screws until the fixed 1 The primary object was to have the object-glass mounted in steel cells, which more nearly correspond in expansion with glass.

    0
    0
  • Thus 7-12, which is really a Jewish fragment recounting the victory of Michael over Satan, has to a certain degree been adapted to a Christian environment by the insertion of the b - I 1.

    0
    0
  • Curve B shows the typical distribution of temperature in an enclosed sea, in this case the Sulu Basin of the Malay Sea, where from the level of the barrier to the bottom the temperature remains uniform or homothermic. Curve C shows a typical summer condition in the polar seas, where layers of sea-water at different temperatures are superimposed, the arrangement from the surface to 200 fathoms is termed FIG.

    0
    0
  • This is done by the little crank B on the axle of the fly-wheel, acting through the rod C, and the bent lever D, which forms a toggle-joint at E with the vertical piece of metal below it.

    0
    0
  • B is the pan on which the coin rests, at a point above the beam.

    0
    0
  • The coins are placed in a rouleau in the hopper C and the lowest one is pushed on to the pan B by a slide not shown in the figure.

    0
    0
  • B ut more important and less speculative is the hero's aspect as a national type or an amalgamation of tribal types of physical force, of dauntless effort and endurance, of militant civilization, and of Hellenic enterprise, " stronger than everything except his own passions," and " at once above and below the noblest type of man " (Jebb).

    0
    0
  • They occur (a) in crystalline igneous and metamorphic rocks as an original constituent, (b) in veins associated with igneous rocks, and (c) in sedimentary rocks either as organic fragments or in secondary concretionary forms.

    0
    0
  • The ripe ears of the last hang so as to become almost parallel with the stem; they are narrower and longer than in (b), owing to the grains being placed farther apart on the rachis; it includes the Chevalier variety, one of the best for malting purposes.

    0
    0
  • This page gives an overview of all articles in the 1911 Brittanica which are alphabetized under B to Ba.

    0
    0
  • At B there is no displacement, but at K there is displacement towards B represented by KR, i.e.

    0
    0
  • At L there is also displacement towards B and again compression.

    0
    0
  • Since the condition of the medium between A and B remains constant, even though the matter is continually changing, the momentum possessed by the matter between A and B is constant.

    0
    0
  • The total momentum moving in at B is therefore P+poU 2.

    0
    0
  • Equating this to the momentum entering at B and subtracting P' from each X+W+p(U - u)2 =poU 2.

    0
    0
  • Consequently a wave front such as b 1 tends to turn upwards, as shown in the successive positions b 2, 3 and 4.

    0
    0
  • Then the front tends to swing round and travel upwards as shown in the successive positions b I, 2, 3, and 4, in fig.

    0
    0
  • Taking the successive key-notes D, A, E, B, it is found that besides small and negligible differences, each introduces a new sharp, and so we get the five sharps, C, D, F, G, A, represented nearly by the black keys.

    0
    0
  • If we start with F as key-note, besides a small difference at we have as the fourth from it 3 X 4 = y, making with B = I R 5 an interval and requiring a new note, B flat.

    0
    0
  • If we take the new note B flat as key-note, another note, E flat, is required.

    0
    0
  • In works on sound it is usual to adopt Helmholtz's notation, in which the octave from bass to middle C is written c d e f g a b c'.

    0
    0
  • The octave above is c' d'e' f' g' a' b' c".

    0
    0
  • The points A, B, C, D are termed " nodes," and the points half-way between them " loops."

    0
    0
  • At the nodes A, B, C, D, E there is no displacement, but there are maximum volume and pressure changes.

    0
    0
  • When the displacement is represented by Ahbkc the particles on each side of B are displaced towards it 6 7 ?.

    0
    0
  • When the displacement is represented by AH'BK'C the particles on each side of B are displaced from it, giving an extension, and since the slope is again the steepest, the extension is a maximum.

    0
    0
  • The fundamental mode is that in which A and B represent the ends of the string.

    0
    0
  • A string is fixed at C on the top of a hollow box, and C" A D B um FIG.

    0
    0
  • It is evident that, in such case, the string, while vibrating as a whole between its fixed extremities, is at the same time executing subsidiary oscillations about its middle point, its points B FIG.

    0
    0
  • The material between A and B, though continually changing, is always in the same condition, and therefore the momentum within AB is constant.

    0
    0
  • At B there is only the latter kind, and since the transfer of matter is powoU, where po is the undisturbed density and wo is the undisturbed cross-section, since its velocity is U the passage of momentum per second is powoUo 2.

    0
    0
  • Let A be a point in the disturbance and B a point in the undisturbed portion.

    0
    0
  • But at B there is no torsion, and no torsion couple of one part of the wire on the next.

    0
    0
  • But if the same ends A, B be placed over oppositely vibrating segments (such as AOD, COD), the sand will be scarcely, if at all, affected.

    0
    0
  • If a tuning-fork in vibration be turned round before the ear, four positions will be found in which A B it will be inaudible, owing to the mutual interference FIG.

    0
    0
  • Thus the interval b'c" with frequencies 495 and 528, giving 33 beats in a second, is very dissonant.

    0
    0
  • But the interval b bc" gives nearly twice as many beats and is not nearly so dissonant.

    0
    0
  • Thus b"c"' and b'bc" have each 66 beats per second, yet the former is more dissonant than the latter.

    0
    0
  • Again b'c" and CG have each 33 beats per second, yet the latter interval is practically smooth and consonant.

    0
    0
  • The amplitudes of these tones are proportional to the products of a and b multiplied by X or µ.

    0
    0
  • Its meaning varies (a) according to the various definitions of deity, and especially (b) according as it is (i.) deliberately adopted by a thinker as a description of his own theological standpoint, or (ii.) applied by one set of thinkers to their opponents.

    0
    0
  • But the ambiguities arising from the points of view described in (b) are much more difficult both intellectually and in their practical social issues.

    0
    0
  • According to tradition, his wife was taken for a time into the harem of Abdallah, brother of Kotaiba the conqueror of Balkh, and became the mother of Khalid b.

    0
    0
  • The family prospered, and his grandson Yahya b.

    0
    0
  • In point of fact, there are fields of action in which A is sovereign, others in which B is sovereign, and certain others in which A and B are jointly or alternately sovereign.

    0
    0
  • Under the law prior to the act of 1889 (a) an agreement to refer disputes generally, without naming the arbitrators, was always irrevocable, and an action lay for the breach of it, although the court could not compel either of the parties to proceed under it; (b) an agreement to refer to a particular arbitrator was revocable, and if one of the parties revoked that particular arbitrator's authority he could not be compelled to submit to it; (c) when, however, the parties had got their tribunal fixed, and were proceeding to carry out the agreement to refer, the act 9 and io Will.

    0
    0
  • Let A be the dead load and B the live load, producing stress in a bar; p =B / A the ratio of live to dead load; f i the safe working limit of stress for a bar subjected to a dead load only and f the safe working stress in any other case.

    0
    0
  • Consider any section a b.

    0
    0
  • The total shear at a b is S = R-E(W1+W2 ...) where the summation extends to all the loads to the left of the section.

    0
    0
  • Let s be the perpendicular from 0, the join of C and T on the direction of S; t the perpendicular from A, the join of C and S on the direction of T; and c the perpendicular from B, the join of S and T on the direction of C. Taking moments about 0, Rx - W 1 (x+a) - W 2 (x+2a) =Ss; taking moments about A, R3a-W 1 2a-W 2 a =Tt; and taking moments about B, Rea-W I a = Cc.

    0
    0
  • Or generally, if M 1 M2 M3 are the moments of the external forces to the left of 0, A, and B respectively, and s, t and c the perpendiculars from 0, A and B on the directions of the forces cut by the section, then Ss=M11 Tt=M2andCc=M3.

    0
    0
  • B ending Moment.

    0
    0
  • The greatest shear at C for any position of the load occurs when the head of the train is at C. For any load p between C and B will increase the reaction at B and therefore the shear at C by part of p, but at the same time will diminish the shear at C by the whole FIG.

    0
    0
  • Next let the loads advance a distance a so that W2 comes to C. Then the shear at C is R(n+a)/l - WI, plus any reaction d at B, due to any additional load which has come on the girder during the movement.

    0
    0
  • But W' these are the average A 3 ' 3 C 3 13 B loads per ft.

    0
    0
  • Let a b be Ak X ?

    0
    0
  • Let W 1, W2, W3 traverse the girder from the left at fixed distances a, b.

    0
    0
  • If these are first drawn it is easy, for any position of the loads, to draw the lines B'C, B'D, B'E, and to find the sum of the intercepts which is the total bending moment under a load.

    0
    0
  • Experience shows that (a) a parabola having the same ordinate at the centre of the span, or (b) a parabola having 15 ons FIG.

    0
    0
  • When the load is at F', the reaction at B' is m/l and the moment at C' is m(l-x)ll, which will be reckoned positive, when it resists a tendency of the right-hand part of the girder to turn counter-clockwise.

    0
    0
  • The loads at D', E, due to unit weight on the rail girder are (p-n)/p and n/p. The reaction at B' is {(p- n)xi+n(xi+p)}' /pi.

    0
    0
  • Also mn/mf = hk/kf 'or' mn-W (l-x)/l, which is the reaction at A due to the load at C, and is the shear at any point of AC. Similarly, po is the reaction at B and shear at any point of CB.

    0
    0
  • Let measurements along the beam be represented according to any convenient scale, so that calling L 1 and 1 1 the lengths to be drawn on paper, we have L = aL i; now let r1, r 2, r 3 be a series of radii such that r 1 = R i /ab, r 2 = R 2 /ab, &c., where b is any convenient constant chosen of such magnitude as will allow arcs with the radii, r 1, &c., to be drawn with the means at the draughtsman's disposal.

    0
    0
  • This method distorts the curve, so that vertical ordinates of the curve are drawn to a scale b times greater than that of the horizontal ordinates.

    0
    0
  • This can be regulated by altering the value of b.

    0
    0
  • In the same passage of Luke mention is made of Lysanias, tetrarch of Abilene near Damascus, in the valley of the B arada.

    0
    0
  • The wider view, according to which the hypothesis of direct transmission of physical influences expresses only part of the facts, is that all space is filled with physical activity, and that while an influence is passing across from a body, A, to another body, B, there is some dynamical process in action in the intervening region, though it appears to the senses to be mere empty space.

    0
    0
  • Now the electric force (P,Q,R) is the force acting on the electrons of the medium moving with velocity v; consequently by Faraday's electrodynamic law (P,Q,R) = (P',Q' - vc, R'+vb) where (P',Q',R') is the force that would act on electrons at rest, and (a,b,c) is the magnetic induction.

    0
    0
  • In it were found the winged lions, now in the British Museum, the fine series of sculptured bas-reliefs glorifying the deeds of Assur-nasir-pal in war and peace, and the large collection of bronze vessels and implements, numbering over 200 pieces; (b) the Central palace, in the interior of the mound, toward its southern end, erected by Shalmaneser II.

    0
    0
  • In this stage the body is composed of two layers, ectoderm (d) externally, and endoderm (c) internally, surrounding a central cavity, the archenteron (b), which communicates with the exterior by a pore (a), the blastopore.

    0
    0
  • This is due to (a) the dirty condition of the cows' udders, (b) the imperfect cleansing of the cans and of the hands of the milkers.

    0
    0
  • It is, therefore, further recommended (a) that the milk be rapidly cooled or chilled, as the lower the temperature the less do the bacteria multiply, (b) that contamination during railway transit be avoided by dustproof locked milk cans.

    0
    0
  • B, male flowers; I before; 2, after spreading of the petals...

    0
    0
  • On the 3rd of March 1905 a proposal for accepting either French or German as an alternative for either Latin or Greek in the Previous Examination was rejected by 1559 to 1052 votes, and on the 26th of May 1906 proposals distinguishing between students in letters and students in science, and (inter alia) requiring the latter to take either French or German for either Latin or Greek in the Previous Examination, were rejected b y 746 to 241.

    0
    0
  • The aim of that association is " to promote the development, and maintain the well-being, of classical studies, and in particular (a) to impress upon public opinion the claim of such studies to an eminent place in the national scheme of education; (b) to improve the practice of classical teaching by free discussion of its scope and methods; (c) to encourage investigation and call attention to new discoveries; (d) to create opportunities of friendly intercourse and co-operation between all lovers of classical learning in this country."

    0
    0
  • P. Postgate, How to pronounce Latin (Appendix B, on " Recent Progress "), (1907).

    0
    0
  • Arbogast's rule of the last and the last but one; in fact, taking the value of a to be unity, and, understanding this letter in each term, the rule gives b; c, b2; d, bc, b; e, bd, c, b c, b, &c., which, if b, c, d, e, &c., denote I, 2, 3, 4, &c., respectively, are the partitions of 1, 2, 3, 4, &c., respectively.

    0
    0
  • The Romans knew the constellation as Arctos or Ursa; the Arabians termed the quadrilateral, formed by the four stars a, 0, y, b, Na'sh, a bier, whence it is sometimes known as Feretrum majus.

    0
    0
  • Ptolemy catalogued 8 stars, Tycho 7 and Hevelius Of these, the seven brightest (a of the 1st magnitude, 0, y, of the 2nd magnitude, and b of the 3rd magnitude) constitute one of the most characteristic figures in the northern sky; they have received various names - Septentriones, the wagon, plough, dipper and Charles's wain (a corruption of " churl's wain," or peasant's cart).

    0
    0
  • Gulf of Gabes I o g Lemg.W.of Greenwicir 0 Longitude East of Greenwich B 4 D very complete sequence of formations from the Lias to those of recent date.

    0
    0
  • A, B, C, D, E, F, Terminals to which standard cell or voltages to be tested are attached.

    0
    0
  • Potassii Carbonis (salt of tartar), dose 5 to 20 grs., from which are made (a) Potassii Bicarbonas, dose 5 to 30 grs.; (b) Potassa Caustica, a powerful caustic not used internally.

    0
    0
  • Meyer in giving, for reasons which cannot be here explained, for the beginning of the 1st dynasty c. B c. 3400, for the 4th dynasty c. B.C. 2900-2750, and for the rule of the Hyksos c. B.C. 1680-1580; and in his Researches in Sinai, 1906, p. 175, Petrie proposes for Menes B.C. 5510, and for the 4th dynasty B.C. 473 1 -4454.

    0
    0
  • But it should be admitted that, especially in regard to Ephesians and Pastorals, there is a perceptible difference, (a) in style, and (b) in characteristic subject matter, from the standard epistles.

    0
    0
  • The date of the completed Luke depends (a) on whether or not we believe Luke himself or a later disciple to be the author, and (b) whether or not we believe that the author of Acts had seen Josephus' Antiquities, published in A.D.

    0
    0
  • It has, in the main, a Neutral text, less mixed in the Epistles than that of B, but not so pure in the Gospels.

    0
    0
  • This is a fairly strong case, but it falls short of demonstration because it cannot be shown that the MS. corrected by Pamphilus was still at Caesarea when it was used by x, and because it is not certain either that the chapter divisions in Acts were added by the original scribes, or that x and B were at that time in their original home, or that the chapter divisions were necessarily only to be found at Caesarea.

    0
    0
  • The case for Alexandria depends partly on the orthography of B, which resembles Graeco-Coptic papyri, partly on the order of the Pauline epistles.

    0
    0
  • At present, both in N and B, Hebrews is placed after 2 Thess., but in B there is also a continuous numeration of sections throughout the epistles, according to which I to 58 cover Romans to Galatians, but Ephesians, the next epistle, begins with 70 instead of 59, and the omitted section numbers are found in Hebrews.

    0
    0
  • Veronensis (b) of the same date (the latter being the better), and by others of less importance.

    0
    0
  • Bezae and in Syr C; (2) the Alexandrine text used by Cyril of Alexandria and found especially in CL 33; and (3) a text which differs from both the above mentioned and is therefore called by WH the Neutral text, found especially in rt B and the quotations of Origen.

    0
    0
  • They decided that the two best authorities were k and B, and that when these differed the reading of B, except when obviously an accidental blunder, was probably right.

    0
    0
  • Another group which Bousset has tried to identify is that headed by B, which he connects with the recension of Hesychius, but this theory, though widely accepted in Germany, does not seem to rest on a very solid basis.

    0
    0
  • To some extent influenced by and using Bousset's results, Schmidtke has tried to show that certain small lines in the margin of B point to a connexion between that MS. and a Gospel harmony, which, by assuming that the text of B is Hesychian, he identifies with that of Ammonius.

    0
    0
  • Nestle, however, and other scholars think that the lines in B are merely indications of a division of the text into senseparagraphs and have nothing to do with any harmony.

    0
    0
  • It is unfortunately not found in any extant MS. The second stage is that found in the quotations of Origen which is fairly well represented in B, though Origen seems at times to have used MSS.

    0
    0
  • The homiletic Midrashim are characterized by (a) a proem, an introduction based upon some biblical text (not from the lesson itself), which led up to (b) the exposition of the lesson, the first verse of which is more fully discussed than the rest.

    0
    0
  • It follows very simply from the definition of a logarithm that logo b X logo a, = 1, logo m =log.

    0
    0
  • The second of these relations is an important one, as it shows that from a table of logarithms to base a, the corresponding table of logarithms to base b may be deduced by multiplying all the logarithms in the former by the constant multiplier i/logab, which is called the modulus of the system whose base is b with respect to the system whose base is a.

    0
    0
  • A 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.

    0
    0
  • Gaussian 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.

    0
    0
  • To every geometric mean in the column of numbers there corresponds the arithmetical mean in the column of logarithms. The numbers are denoted by A, B, C, &c., in order to indicate their mode of formation.

    0
    0
  • The doctrines we are to believe (1) concerning the nature of God, (2) concerning the decrees of God and their execution - (a) in creation and providence, (b) in the covenant of works, (c) in the covenant of grace; II.

    0
    0
  • The scholastic does not b, and then passes through a four or six years' course.

    0
    0
  • The wonderful plumage of the " quetzal " (Trogon resplendens) was, it is said, reserved b y the Aztec rulers for their own exclusive use.

    0
    0
  • A and B represent the same animal, some of the organs being shown in one figure and some in the other.

    0
    0
  • The extraing to foot of rotifers; at, median blastoporic opening of antenna, united by a nerve to br, brain the cloaca leads us to a (letter omitted in B); bl, bladder, re ver y different view, which ceiving ramified kidney in B, C, D; finds negative support f, foot, and f.g, its cement-gland;.

    0
    0
  • The form of the limacon depends on the ratio of the two constants; if a be greater than b, the curve lies entirely outside the circle; if a equals b, it is known as a cardioid; if a is less than b, the curve has a node within the circle; the particular case when b= 2a is known as the trisectrix.

    0
    0
  • The area is (b 2 +a 2 /2)7r, and the length is expressible as an elliptic integral.

    0
    0
  • Ray Lankester (18) subsequently described this same form (under the name of Undulina ranarum) A B (From Lankester.) FIG.

    0
    0
  • In B the nucleus is shown.

    0
    0
  • Voltmeters may be divided into two classes, (a) electrostatic, (b) electrokinetic.

    0
    0
  • The relief is strong enough to make occupation difficult; the slopes are forested; the uplands are cleared and well occupied b farms and villages, but many of the valleys are wooded glens.

    0
    0
  • The buildings are completely ruined, but enough remains to enable us to identify the grand cruciform church (A), the cloister-court with the chapterhouse (B), the refectory (I), the kitchen-court with its offices (K, 0, 0) and the other principal apartments.

    0
    0
  • The western entrance was approached by an ante-church, or narthex (B), itself an aisled church of no mean dimensions, flanked by two towers, rising from a stately flight of steps bearing a large stone cross.

    0
    0
  • Round the cloister (B) were ranged the buildings connected with the monks' daily life.

    0
    0
  • On one side of the gate-house (B) is a long building (C), probably the almonry, Citeaux.

    0
    0