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others so constructed that instead of the frame working upon a tongue, the groove is made to receive strips of very thin box-wood, upon which are divided scales of from 1 to 6 chains to an inch, and the various Ordnance scales. Mr. Stanley, of Great Turnstile, has brought out this scale, which, together with six or eight strips, is made to fit into a case, the whole cost being £2 18s. 6d., and supplied with each set are specially-prepared sheets of divided paper.

Areas by different Scales to Plan. - The scale illustrated in the plate is of so simple and reliable a character that it commends itself; and whilst it is desirable, in an office where computation on a large scale is carried on, to have computing scales of the various scales in vogue, yet it is quite possible to arrive at an accurate estimate of the area of property drawn to a different scale from that of the computer. For instance, suppose we have a plan 5 chains to an inch, the area of which it is desired to ascertain, but our computing scale is 3 chains to an inch. As an example, we will assume that the operation of computation gives a result of 6 A. 2R. OP. with the scale. Now, as 5 chains to an inch is much smaller than 3 chains, then the area will necessarily be greater, so that if we treat it as a rule-of-three sum we shall get the correct result. In examinations, I regret to say, this question has been a source of trouble and embarrassment to many students, who, even if they are happy in thinking of the proportion, quite forget that it will not be as three to five; but, as they are dealing with areas, it is as the square of three is to the square of five, so is the known area to that required. So that, having the area with the 3 chain scale of 6 A. 2 R. OP., we proceed as follows: 32:52:6 A. 2 R. OP. = 7 A. 3 R. 26 p. = area of the plan drawn to a scale of 5 chains to an inch.

The cost of a computing scale similar to the one illustrated is £1 5s.

Planimeter. There is another method of ascertaining the areas of a plan by what is known as the planimeter, invented by J. Amsler, Professor of Mathematics at Schaffhausen, and manufactured by Messrs. Elliott Brothers, of St. Martin's Lane, the cost of which is £3 3s. But it is a very delicate instrument, and the slightest dirt or rust will throw it out of gear. "It consists essentially of two arms jointed together, so as to move with perfect freedom in one plane, and a wheel which is attached to one of the arms, and turning on this arm as an axis, records by its revolutions the area of the figure traced out by a point on the arms to which it is attached, while a point on the other arm is made a fixed centre, about which the instrument revolves." For a full description of its various parts, and of the method of using it, I cannot do better than refer the reader to Heather's "Drawing and Measuring Instruments," p. 80.* Like all instruments the object of which is to save labour, the planimeter, from the very delicacy of its construction, has to be used with the greatest care; and for ordinary practice it is hardly advisable to adopt it, on account of its great liability to injury. For myself, I cannot help saying that I much prefer to take off the quantities of land either by triangles or with a computing-scale.

* Crosby Lockwood & Son, London.

INDEX.

ABNEY level, 33; how to use it, 34
Accurately marked stations, 146

Acute angle, 85
Acute-angled triangle, 86
Acre of land, 2

Adjusting the allowance for slope, 22;
for collimation, 74
Adjustment of the eidograph, 252;
of the level, 74, 174; of the pan-
tagraph, 247; for parallax, 76; of
the theodolite, 41; vertical axis, 41

Advantages of 100-feet chain, 2
Allowance for curvature, 172
Always work from left to right, 244,
Aneroid barometer, 79; levelling
with, 197

Angle, acute, 85; of buildings, 16;
chain, 24; complemental, 98; of
fences, 17; of intersection, 210;
obtuse, 85; plane, 84; plane recti-

lineal, 85; right, 86; of slope, 21
Apex, inaccessible, 217
Arc of circle, 85; vertical, 50
Arrangement of ball and socket, 46
Areas by different scales, 265
Arithmetical complement, 123; com-
putation, 125

Arrows, 3; how to use them, 12;
necessity for counting, 12; ne-
cessity to be booked, 12

As to the chain, 166
Ascertaining areas on the ground,

261

Avoid crossing fences as much as
possible, 143

BACK sight, 175

Ball and socket arrangement, 46

Barometer, aneroid, 79
Base, 93; base lines, 23

Basis of formulæ for sines, &c.,

104

Beam compass, 234; how to use it;

234

Be careful not to cut fences unne-
cessarily, 143

Begin at bottom of page to work, 140
Bench-marks, position of, 180

Best form of base line, 141; station,

139

Boning lines with laths, 139
Borders of plans, 246
Boundaries, 13; of different pro-
perty, 244

Box sextant, 59; how to use it, 61
Box-wood scales, best, 230

Book, field, 6
Broken ground, 135

Brushwood, 134

Buildings, how to measure, 16; as to,

169

Bundle of laths, 5

CAP and spanner, 45

Cardiff, survey at, 142

Cart-tracks and footpaths, 133,

143

Care in checking, 160; in shifting an
arc with beam compass, 235

Centre of circle, 85

Centering-plates of theodolite, 43
Chain, how to hold it, 11; how to
use it, 12; angles, 25; advantages
of 100-feet, 2; décamètre, 3; divi-
sions of Gunter's, 3; Gunter's 66-
feet, 2; testing, 9
Chain and arrows, 2, 10
Chaining a hedge, 14
Chain-men, 10; should be instructed

in their duties, 139

Chain survey of part of Wimbledon
Park, 138

Check-lines, 24: obviated, 146; check
measurements, 230

Chord, 92
Circumferentor, 40

Circle, 85; centre of, 85; diameter
of, 85; segment of, 85; semi,

85

Clamps, 48; Troughton's arrange-
ment, 49

Clear up ground after you, 144
Clinometer, 31; rule, 32; scale, 34
Clips, 50

Close paling, 133

Closing a traverse, 159

Collimation, adjustment of, 74; line

of, 74

Colours, 242

Colour saucers, 242

Contouring, 199

Combined telescope clinometer and
prismatic compass, 35

Compass, prismatic, 38; of theodo-
lite, 50

Computation scale, 262; various
kinds of, 264

Compound levelling, 175
Conventional signs, 133, 242

Copying a plan, 254

Corroboration, 151

County boundaries, 135

Cosine, 91

Cotangent, 91

Co secant, 92

Coversed sine, 92

Cross-sections, 197

Cross-staff, 29; how to use it, 15

Crossing hedges, 12
Curve, length of, 214; impeded
point in, 215; office, 237; setting-
out, 216; setting-out with theo-
dolite, 213; with ordinates, 227;
with offsets, 224; of different radii,
221; setting out from same tan-
gent, 227

Curves of contraflexure, 222
Curvature of the earth, 171; allow-
ance for, 172; providing for, 191

DATUM, 177; ordnance, 177
Décamètre chain, 3

Declination or variation, magnetic, 160
Diameter of circle, 85

Diaphragm of level, 73; theodolite, 51
Different kinds of levelling, 181
Disc, 51

Distances, inaccessible, 25; in level-

ling, 189

Direction of line, 135

Ditch and hedge, 13, 132

Dividers, 239

Divisions of Gunter's chain, 3

Doing up a chain, 10

Do not erase figures, 169; cut down
trees, 144; spare use of theodo-
lite, 151

Double box sextant, 62

Draw scale on plan, 229
Drawing instruments, 240

Drawing pen, 237; how to hold, 237
Drawing tables, 231

Duties of follower, 11; of leader, 10

FARTH'S curvature, 171

Eidograph, 249; to adjust, 252

Enlarging and reducing plan, 247;
by square, 253

Enter every ten chains, 139
Equilateral triangle, 86

Equipment of office, 231; of survey-

or, 5

Eye-piece, 72

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Instructions to staff-holder, 104
Isosceles triangle, 86

KEEPING the level book, 185

269

LAND quantities, 256; by tri-
angles, 258; by computation

scale, 264

Lamp-posts, as to, 169
Laths, bundle of, 5
Laying out a base, 66; down survey

lines on paper, 230

Leader's duties, 10
Length of curve, 214

Level, Abney, 33; adjusting, 175;
book, 181, 185, 188; dumpy, 71;
reflecting, 33; staff, 77, 188; "Y,”
69, 70

Level ground, what is, 20
Levelling, 171; different kinds of,
181; compound, 175; plates, 49;
simple, 175; with aneroid, 197;
with theodolite, 195
Limb or lower plate, 46
Limits of offset, 18; of radii, 211
Lines, base, 23; of collimation, 74;
ranger. 31; of ranging out, 19
Logarithms, 120; division by, 122;
evolution by, 123; involution by,
123; multiplication by, 122; pro-
portion by, 122; sines, 124

Lower plate or limb, 46

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India-rubber, 241

191

Intermediate sights, 183

Merrett's quadrant, 32

Intersection of fences, 17

Minus signs in trigonometry, 100

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