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共 84 题- ENCYCLOPAEDIA BRITANNICA
- ELEVENTH EDITION
- VOLUME VIII, SLICE IX
- Dyer to Echidna
- ARTICLES IN THIS SLICE:
- 1. _General Equations of Impulsive Motion._
- 2[Tau] = p1q`1 + p2q`2 + ... (15)
- A11q`1q''1 + A22q`2q`'2 + ... + A12(q`1q`'2 + q`'1q`2) + ... (17)
- 2[Tau]' = A'11p1 squared + A'22p2 squared + ... + 2A'12p - p2 + ... (19)
- In virtue of (13) this reduces to
- R = [Tau] - [kappa][chi]' - [kappa]'[chi]]`' - [kappa]"[chi]]`" - ..., (25)
- 2. _Continuous Motion of a System._
- Hence
- Hence, omitting the terms which cancel in virtue of Sec. 1 (13), we find
- For the right-hand side of (2) we have
- Comparing (6) and (7) we find
- Hence the typical Lagrange's equation may be now written in the form
- As shown under MECHANICS, Sec. 22, we derive from (10)
- 3. _Constrained Systems._
- These quantities (r, s) are subject to the relations
- A(t, q1, q2, ... q_n) = 0, B(t, q1, q2, ... q_n) = 0, &c. (28)
- A1q`1 + A2q`2 + ... = 0, B1q`1 + B2q`2 + ... = 0, &c. (33)
- 4. _Hamiltonian Equations of Motion._
- Hence the Lagrangian equations Sec. 2 (14) transform into
- If we write
- H = [Tau]' + V, (4)
- If to these we join the equations
- H = p1q`1 + p2q`2 + ... - [Tau] + V, (8)
- It follows from (11) that
- 5. _Cyclic Systems._
- If, as in Sec. 1 (25), we write
- R = [Tau] - [kappa][chi]` - [kappa]'[chi]`' - [kappa]"[chi]`" - ..., (3)
- Omitting the terms which cancel by (2), we find
- Substituting in Sec. 2 (10), we have
- The function R is made up of three parts, thus
- R = R(2,0) + R(1,1) + R(0,2), ... (9)
- If, as in Sec. 1 (30), we write this in the form
- R = [@] - [Kappa] + ss1q`1 + ss2q`2 + ..., (12)
- It is to be particularly noticed that
- Q1[delta]q1 + Q2[delta]q2 + ... = [delta][Kappa], (24)
- By means of the formulae (18), which now reduce to
- 6. _Stability of Steady Motion._
- 7. _Principle of Least Action._
- R = T - [kappa][chi]` - [kappa]'[chi]`' - [kappa]''[chi]`" - ..., (15)
- Sec. 8. _Hamilton's Principal and Characteristic Functions._
- Tš + V = H (7)
- It follows from (4) that
- 9. _Reciprocal Properties of Direct and Reversed Motions._
- If for shortness we write
- E = B_gLV x 10^(-8) volts (1)
- F = B_gLC x 10^(-1) dynes, (2)
- I. Smooth. II. Toothed.]
- E_a = 2KZ_a(pN[tau]/60mq) x 10^(-8) volts (1a)
- E_a = (2/q)(ZpN/60)[tau] x 10^(-8) volts (1b)
- Lap-loops]
- Wave-loops]
- X = A[Tau] = 0.8B_g.2l_g + f(B_t)2l_t + f(B_a)l_a + X_b + f(B_m)l_m. (3)
- Armature reaction in alternators
- FOOTNOTES:
- T = Fr = WR. (1)
- T = [Sigma]WR. (2)
- FOOTNOTE:
- FOOTNOTE:
- FOOTNOTES:
- DISEASES OF THE EAR
- FIG. 1.--Ear-ring from an Assyrian bas relief.]
- THE EARTH
- FOOTNOTE:
- X = -Ax, Y = -Ay, Z = -Cz,
- This, after integration, gives
- The data of the French arc from Formentera to Dunkirk are--
- For the Indian arc in long. 77 deg. 40' we have the following data:--
- FOOTNOTES:
- TABLE I.
- TABLE II.--_Mean Numerical Value of Resultant Current._
- FOOTNOTES:
- FOOTNOTE:
- FOOTNOTE:
- 1. All hands with three or more trumps, whatever the other cards.
- 2. Hands with _two trumps_ which contain also--
- 3. Hands with _one trump_, which contain also--
- 3. One trump and four cards of a plain suit is too weak to play.
- FOOTNOTES:
- The Presbyterian courts thus created are arranged in ascending order:--