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.

11.

Reflexion of a ray at a plane surface.

12. Projections of the incident and reflected rays on a normal plane.

13. Successive reflexion at two plane mirrors.

14-16. Laws of refraction.

17. Critical angle. Total internal reflexion.

18. Projections of the incident and refracted rays on a normal plane.

19, 20. If the angle of incidence (or refraction) increase uniformly, the

deviation increases faster and faster.

21-23. Refraction through a prism in a principal plane.

24. Minimum deviation through a prism.

25. Prism of small refracting angle.

26. Refraction by a prism, not in a principal plane.

ᎪᎡᎢ .

CHAPTER III.

REFLEXION AND REFRACTION OF DIRECT PENCILS.

27. Reflexion of a pencil at a plane surface.

28. Successive reflexion of a pencil at two parallel plane mirrors.

29, 30. Successive reflexion of a pencil at two inclined mirrors. Number

of images.

31. Vision of an object reflected in a mirror.

32. Direct refraction of a small pencil at a plane surface.

33. Appearance of an object seen under water.

34.

35, 36.

37, 38.

Reflexion and refraction of small pencils at spherical surfaces.

Direct reflexion of a small pencil at a spherical mirror.

Image of an object formed by a spherical mirror.

39-44. Direct refraction of a small pencil at a spherical surface.

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.

ᎪᎡᎢ .

77.

Caustic curves and surfaces.

78. Character of a limited pencil. Aberration.

79. Caustic of parallel rays reflected at a circle.

80. Caustic by reflexion at a circle of rays issuing from a point on the

90. Measure of dispersive power of a substance.

91. Irrationality of dispersion.

112-115.

116-119.

Vision through a lens.

Spectacles and reading glasses.

120. Vision through thin lenses. Apparent distance.

125, 126. Gauss' method of finding the magnifying power.

ART.

CHAPTER VIII.

OPTICAL INSTRUMENTS.

127, 128. Simple microscopes.

129. Wollaston's doublet.

130. Compound instruments.

131-133. The astronomical telescope.

134, 135. Galileo's telescope.

136, 137. Object-glasses.

138, 139. Eye-pieces.

140. Huyghens' eye-piece.

141. Ramsden's eye-piece.

142. The erecting eye-piece.

143, 144. Telescopes with compound eye-pieces.

145, 146. Herschel's telescope.

147-149. Newton's telescope.

150-153. Gregory's telescope.

154. Cassegrain's telescope. Example.

155, 156. The compound microscope.

CHAPTER IX.

OPTICAL INSTRUMENTS AND EXPERIMENTS.

157. The camera obscura and solar microscope.

158. The camera lucida of Wollaston.

159. Hadley's sextant.

160-163. Determination of refractive indices.

164. To find the focal length of a thin lens.

165-168. Photometry.

169-173. Methods of determining the velocity of light.