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TO THE SECOND EDITION.

IN this Edition, alterations have been made in several paragraphs, with the view of removing obscurities in the statements or reasonings. The only additions made are contained in Articles 54*, 54**, 54***, in the latter parts of Articles 64 and 65, and in Article 93**. The original numeration of the Articles in the First Edition is preserved unaltered.

1. Ordinary experience on the transmitting power of Air

2. Ordinary experience on diminution and retardation of

Sound by distance

PAGE

1

3

SECTION II.

PROPERTIES OF AIR, ON WHICH THE FORMATION AND TRANSMISSION

OF SOUND DEPEND.

Articles 3-17. Pages 4-20.

3. Equality of Pressure of Air in all directions.

4. Absence of Friction among the particles of Air

5. Statement of the three Laws affecting the pressure of Air

6. Construction of the Barometer

7. Measure of Atmospheric Pressure

8. Height of Homogeneous Atmosphere, dry or humid

9. Measure of Elastic Forco of Air under different cir-

5

5

6

8

10

10. With given Temperature, Elastic Force of Air is pro-

portional to its Density

14

ABT.

11. Height of Homogeneous Atmosphere with given Tem-

perature is independent of its Density

12. Symbols, and Units of Measure

PAGE

15

15

14. Dependence of Elastic Force of Air and of Height of

Homogeneous Atmosphere on Temperature

17

15. Rise or Fall of Atmospheric Temperature, produced by

sudden Contraction or Expansion

16. Alteration of the Law connecting Elastic Force or

Pressure with Density, by the circumstance last

mentioned

17. Collection of the Laws affecting the Pressure of Air

17

19

. 20

SECTION III.

THEORY OF UNDULATIONS, AS APPLIED TO SOUND; AND INVESTIGA-

TION OF THE PASSAGE OF A WAVE OF AIR THROUGH A CYLINDRI-

CAL PIPE, OR OF A PLANE WAVE THROUGH THE ATMOSPHERE

GENERALLY.

19. The idea of a Wave first entertained and developed by

Newton

20. Newton's treatment of Waves of Air

21. Algebraical treatment of Waves of Air travelling along

a tube, and formation of the Partial Differential Equa-

tion, neglecting small quantities

.

ART.

23. General Solution of the Equation.

24. One term of the solution indicates a Wave travelling

Forwards: the velocity is independent of the cha-

racter of the wave

25. The other term represents a Wave travelling Back-

wards.

PAGE

33

34

26. The differential equation of articlo 21 being linear, if

any number of different solutions be found, the sum

of these solutions will also be a solution: this indi-

cates the possibility of co-existence of waves, each

of which singly is possible: but the theorem docs

not apply when the equation contains higher powers

of the differential coefficients

27. Plane wave in Air of Three Dimensions

28. Limitations on the Form of the Functions in the Solu-

tion

29. Forms proper for the Functions representing Continu-

ous Series of Similar Waves

38

30. Introduction of the terms, 'length of wave,' 'period of

wave,' 'frequency of wave;' relation between their

values and that of 'velocity of wave;' remarks on

the 'amplitude of vibration,' and its independence of

the other quantities

31. The Solitary Wavo, and Functions proper to represent

it; and Interpretation of their effect

32. Formation of the Equation when small quantities are

not neglected; and approximate Solution.

39

40

41

44

47

33. Progressive Change in the Character of the Wave

34. Conjectured Change of Character of Wave when it has

travelled very far

...55

SECTION IV.

INVESTIGATION OF THE MOTION OF A WAVE OF AIR THROUGH THE

ATMOSPHERE CONSIDERED AS OF TWO OR THREE DIMENSIONS.

ART.

Articles 34-59. Pages 56-128.

34*. Outline of the method to be employed; and cautions

requiring attention in regard to the order of terms to

be rejected

35. Investigation of the Elastic Force at any point of the

37. Introduction of the Characteristic Function F

38 Inferences from the value of F, when its form has been

found ..

39. Application to a Plane Wave of Air

40. Combination of two plane waves from two sources

41. Theory of the simple echo

PAGE

56

66

68

69

72

42. Various forms permissible in the expression defining a

plane wave of air

43. Remarks on the Partial Differential Equations which

occur in the investigations that next follow

80

44. Symmetrical Divergent Wave, with motions of all par-

ticles parallel to one plane.

45. Motion of the particles in this problem.

Divergent wave, with Oscillation of the Center of each

divergent wave in the direction of z; all motions

being parallel to the plane of yz

47. Interpretation of the expression for radial displace-

ment in this problem; the particles, originally in a

circle whose center is the center of divergence, will

always be found in a circle of the same diameter,

whose center oscillates

8888

. 83