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been worked out completely, and the description and theory of the ordinary optical instruments are given in much greater detail than has been usual in elementary treatises. The theory of vision through lenses is based upon Cotes' theorem, after the manner of the older English writers on Optics, Cotes and Smith. An elegant geometrical construction for the deviation of a ray at a refraction, due to Prof. P. G. Tait, furnishes an elementary theory of the rainbow. Numerous easy exercises are scattered through the text, and several typical examples are fully worked out, while the more difficult are collected at the end of the chapters. The articles marked with an asterisk may be omitted at a first reading.

Suggestions which may improve and extend the usefulness of the book and notifications of errors will be very thankfully received by the author.

R. S. HEATH.

MASON COLLEGE, BIRMINGHAM,

August, 1888.

REFLEXION AND REFRACTION OF DIRECT PENCILS.

45. Image of an object formed by refraction at a spherical surface.

46–48. Geometrical constructions.

49. Helmholtz' theorem.

CHAPTER IV.

REFRACTION THROUGH LENSES.

50. Definitions.

51–55. Refraction through any thick lens.

56. Refraction through a thin lens.

57. Refraction through a sphere. Examples.

58. Refraction through two thick lenses.

59–71. Refraction through any system of thick co-axal lenses.

72, 73. Theory of equivalent lenses.

CHAPTER V.

GENERAL THEOREMS.

CAUSTICS.

74. Minimum property of the reduced path.
75. Malus' theorem.
76. Orthotomic systems.

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