The Draughtsman's Handbook of Plan and Map Drawing / Including instructions for the preparation of engineering, architectural, and mechanical drawings. - George G. André

Fig. 79.

The total length of the scale will be determined by the greatest length which it is required to read off at once, and in the following manner. Thus, let it be required to construct a scale of ¹⁄₂₄, = ¹⁄₂ inch to the foot, to show 12 feet. Here ·5 inch : x inches :: 1 inch : 12 inches; whence x = 12 × ·5 = 6 inches. This distance of 6 inches must, therefore, be set off upon the lines intended for the scale, and divided in the manner described above. Again, to construct a scale of ¹⁄₁₀₅₆₀, = 6 inches to a mile, to show 100 chains. Since 6 inches represents 5280 feet or ⁵²⁸⁰⁄₆₀ = 80 chains, the proportion becomes 6 : x :: 80 : 100; whence x = ⁶⁰⁰⁄₈₀ = 7¹⁄₂ inches. If the scale is ¹⁄₃₉₆₀ = 16 inches to a mile, = 5 chains to an inch, and the distance to be shown is 30 chains, we have 1 : x :: 5 : 30; or x = ³⁰⁄₅ = 6 inches. In a scale of 10 yards to the inch, for example, the representative fraction is 10 × 3 × 12 = ¹⁄₃₆₀. So, on the contrary, ¹⁄₃₆₀ = ³⁶⁰⁄₃₆ = 10 yards to the inch. Sometimes it is required to construct a comparative scale, that is, a scale having the same representative fraction, but containing other units. Thus suppose, for example, we have a Russian plan on which is marked a scale of archines measuring a length of 50 archines. It is required to draw upon this plan a comparative scale of yards, upon which a distance of 50 yards may be measured. The Russian archine = ·777 yard. Hence we have the proportion 50 : x :: ·777 : 1, whence x = ⁵⁰⁄₇₇₇ = 64·35 archines. Measure off this length from the Russian scale, and upon it construct the English scale in the manner already described. This scale may then be used to measure distances on the plan.

Amongst Continental nations, decimal scales are usually employed, which are far more convenient in practice than those involving the awkward ratios of miles, furlongs, chains, yards, feet, and inches. The decimal scale has also been adopted for the United States’ Coast Survey, the smallest publication scale of which is ¹⁄₃₀₀₀₀; this is also the scale of the new map of France.

In choosing a scale, regard must be had alike to the purposes for which the drawing is intended, and to the nature and the amount of detail required to be shown. Thus a larger scale is required in plans of towns than in those of the open country; and the smaller and more intricate the buildings, the larger should the scale be. Also a plan to be used for the setting out of works should be to a larger scale than one made for parliamentary purposes.

The following Tables, given by Rankine in his ‘Civil Engineering,’ enumerate some of the scales for plans most commonly used in Britain, together with a statement of the purposes to which they are best adapted.

Horizontal Scales.
Ordinary Designation of Scale.		Fraction of real Dimensions.	Use.
1.—	1 inch to a mile	¹⁄₆₃₃₆₀			Scale of the smaller Ordnance maps of Britain. This scale is well adapted for mapsto be used in exploring the country.
2.—	4 inches to a mile	¹⁄₁₅₈₄₀			Smallest scale permitted by the Standing Orders of Parliament for the depositedplans of proposed works.
3.—	6 inches to a mile	¹⁄₁₀₅₆₀			Scale of the larger Ordnance maps of Great Britain and Ireland. This scale, beingjust large enough to show buildings, roads, and other important objects distinctly in their true formsand proportions, and at the same time small enough to enable the eye of the engineer to embrace the planof a considerable extent of country at one view, is on the whole the best adapted for the selection oflines for engineering works, and for parliamentary plans and preliminary estimates.
4.—	6·366 inches to a mile	¹⁄₁₀₀₀₀			Decimal scale possessing the same advantages.
5.—	400 feet to an inch	¹⁄₄₈₀₀			Smallest scale permitted by the Standing Orders of Parliament for “enlargedplans” of buildings and of land within the curtilage.
6.—	6 chains to an inch	¹⁄₄₇₅₂		-	Scale answering the same purpose.
7.—	15·84 inches to a mile	¹⁄₄₀₀₀			Scales well suited for the working surveys and land plans of great engineeringworks, and for enlarged parliamentary plans.
8.—	5 chains to an inch, or 16 inches to a mile.	¹⁄₃₀₆₀
					(Scale 8 is that prescribed in the Standing Orders of Parliament for “crosssections” of proposed railways, showing alterations of roads.)
9.—	25·344 inches to a mile	¹⁄₂₅₀₀			Scale of plans of part of the Ordnance survey of Britain, from which the maps before mentionedare reduced. Well adapted for land plans of engineering works and plans of estates.
10.—	200 feet to an inch	¹⁄₂₄₀₀			Scale suited for similar purposes. Smallest scale prescribed by law for land or contract plans in Ireland.
11.—	3 chains to an inch	¹⁄₂₃₇₆			Scale of the Tithe Commissioners’ plans. Suited for the same purposes as the above.
12.—	100 feet to an inch	¹⁄₁₂₀₀			Scale suited for plans of towns, when not very intricate.
13.—	88 feet to an inch, or 60 inches to a mile.	¹⁄₁₀₈₀			Scale of the Ordnance plans of the less intricately built towns.
14.—	63·36 inches to a mile	¹⁄₁₀₀₀			Decimal scale having the same properties.
15.—	44 feet to an inch, or 120 inches to a mile.	¹⁄₅₂₈			Scale of the Ordnance plans of the more intricately built towns.
16.—	126·72 inches to a mile	¹⁄₅₀₀			Decimal scale having the same properties.
17.—	30 feet to an inch	¹⁄₃₆₀		-	Scales for special purposes.
18.—	20 feet to an inch	¹⁄₂₄₀
19.—	10 feet to an inch	¹⁄₁₂₀

Vertical Scales.
Ordinary Designation of Vertical Scale.		Fraction of real Height.	Horizontal Scales with which the Vertical Scale is usually combined.			Exaggeration.			Use.
						from
1.—	100 feet to an inch	¹⁄₁₂₀₀	¹⁄₁₅₈₄₀	to	¹⁄₁₀₅₆₀	13·2	to	8·8			Smallest scale permitted by the Standing Orders of Parliament for sections of proposed works.
2.—	40 feet to an inch	¹⁄₄₈₀₀	¹⁄₄₈₀₀	to	¹⁄₃₉₆₀	10	to	8·25			Smallest scale permitted by the Standing Orders of Parliament for cross sections showing alterations of roads.
3.—	30 feet to an inch	¹⁄₃₆₀	¹⁄₃₉₆₀	to	¹⁄₂₃₇₆	11	to	6·6		-	Scales suitable for working sections.
4.—	20 feet to an inch	¹⁄₂₄₀	¹⁄₃₉₆₀	to	¹⁄₂₃₇₆	16·5	to	9·9		-	Scales suitable for working sections.

The vertical scale, or scale of heights, is always much greater than the horizontal scale or scale of distances, and the proportion in which the vertical scale is greater than the horizontal, is called the exaggeration of the scale. This exaggeration is necessary, because the differences of elevation between points on the ground are in general much smaller than their distances apart, and would therefore, without exaggeration, be unapparent, and also because, in the execution of engineering works, accuracy in levels is of more importance than accuracy in horizontal positions.