Practical Astronomy and Geodesy

68. (Prop. VI.) Investigations of formulæ for determining two
sides of a spherical triangle when there are given the other
side and two adjacent angles

69. Investigations of formulæ for expressing the relations between

an angle in any plane and its orthographical projection on

a plane inclined to that of the angle

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70. Reduction of an arc on any small circle to the corresponding
arc on a great circle parallel to it; and the converse
71. Two great circles making with each other a small angle at
their line of section, and from a point in one of these an
arc of a great circle being let fall perpendicularly on the
other, also from the same point an arc of a small circle
perpendicular to both being described; there are inves-
tigated approximative formulæ for the distance between
the two arcs and the difference of their lengths

CHAP. IV.

TRANSIT INSTRUMENT.

AZIMUTH AND ALTITUDE CIRCLE.

ZENITH

MURAL CIRCLE.

SECTOR.-EQUATORIAL INSTRUMENT.-COLLIMATOR.-REPEATING

CIRCLE. REFLECTING INSTRUMENTS.

72. Nature of the observations made for determining the places of

celestial bodies

73. The sidereal clock. Its adjustments for the purpose of in-

dicating the commencement of the sidereal day, the right

ascension of the mid-heaven, and of a star

74. Description of the micrometer

75. Determination of the value of its scale by a terrestrial object - 62

76. The same, by the diameter of the sun and by a transit of the

pole-star

77. The position micrometer

78. The micrometer microscope

79. Manner of finding the value of a run of the micrometer screw

80. Manner of obtaining the subdivisions on a circular instrument

when a micrometer microscope is used

81. Description of a transit telescope

82. The fixed wires at the focus of the object glass, and the man-

ner of enlightening them at night

83. The attached circle for obtaining altitudes approximatively

84. Description of the spirit level, and the manner of using it in

placing the axis of motion horizontal

85. Formula for computing the deviation of the axis of motion

from a horizontal position; and the corresponding correc-

tion to be applied to the observed time of a star's transit

86. Manner of determining the like deviation of the axis, from

transits observed by direct view and by reflexion

Art.

87. Manner of bringing the meridional wire to the optical axis by

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trials
88. Process for determining the error of collimation by a micro-
meter, and the manner of correcting the observed time of
a transit on account of that error
89. Method of ascertaining that the meridional wire and those
which are parallel to it are in vertical positions, and that
the wire at right angles to them is horizontal

90. Use of two, or a greater number of wires parallel to the me-
ridional wire

91. Manner of obtaining the correct time of a star's transit at the

mean wire, when the transits have not been observed at all

the wires

92. Formula for determining the distance of any wire from the

mean wire, when the transit of a star near the pole is used 72

93. Correction to be applied in finding the time of transit at the

mean wire, when a planet is observed

94. Method of placing a transit telescope very near the plane of

the meridian

95. Investigation of a formula for finding the azimuthal deviation

of a transit telescope from the meridian, by stars differing

considerably in altitude

96. The same, by transits of circumpolar stars

97. Description of a mural circle

98. Methods of verifying the horizontality of the axis, the line of

collimation, and the position of the circle with respect to

the meridian

99. Process for finding the polar point on the circle

100. Processes for finding the horizontal point -

101. Formula for obtaining the correction of a star's observed

declination, when, at the time of the observation, the star

is not on the meridian wire

102. Manner of correcting the observed declination of the moon

when her disk is not wholly enlightened

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103. The mural circles at Greenwich and at Gottingen

104. Description of the azimuth and altitude circle

105. Manner of verifying the positions of the wires

106. Methods of finding the error of collimation in azimuth and

in altitude

107. Description of the zenith sector

108. Improved zenith sector by the Astronomer Royal

109. Manner of making the observations

110. Description of a fixed equatorial instrument

111. A portable equatorial

112. Method of finding the error of the polar axis in altitude and

113. Method of determining the error of collimation

114. Method of making the axis of the declination circle perpen-

Art.

116. Employment of the instrument in finding differences of

right ascension and declination

117. Adjustment for observing a star during day-light

119. Employment of the micrometer with an equatorial, in mea-
suring angles of position, and small angular distances

120. Manner of deducing from thence the differences of declina-
tion and right ascension between two stars, and between

the moon and a star

121. Bessel's heliometer

122. Explanation of the terms north following, south following,

north preceding and south preceding

123. Description of the floating collimator

124. Manner of using the horizontal and vertical collimators
125. The spirit level collimator, and manner of using it for find-
ing the error of collimation in a transit telescope or circle

126. Description of the repeating circle

127. Manner of using the instrument in observing altitudes or

zenith distances

128. Manner of observing horizontal and oblique angles -
129. Hadley's reflecting octant, &c.

130. Manner in which, after two reflexions of light from an object,
the image of that object may be made to coincide with that
of an object seen by direct view

131. The parallax of a reflecting instrument