📚 Year 8 WJEC Geography: Formula & Theorem Quick Reference Handbook | 八年级 WJEC 地理：公式定理速查手册
This quick‑reference handbook brings together the essential formulas, laws and key relationships you will meet in Year 8 WJEC Geography. Understanding these core ideas will help you read maps, analyse population change, explain weather patterns and interpret river and coastal processes. Each entry is presented with a clear statement, an explanation of how it works and a practical example where beneficial.
这本速查手册汇集了八年级 WJEC 地理课程中必须掌握的公式、定律和关键关系。理解这些核心概念将帮助你阅读地图、分析人口变化、解释天气规律以及理解河流与海岸过程。每个条目都包含清晰的陈述、工作原理说明，并在适当处给出实用示例。
1. Map Scale | 地图比例尺
The map scale tells you how much the real world has been reduced to fit on a sheet of paper or a screen. It is expressed as a ratio or a representative fraction, such as 1:50 000. This means that 1 cm on the map represents 50 000 cm (or 0.5 km) on the ground.
地图比例尺告诉你真实世界被缩小了多少才能放进一张纸或屏幕上。它表示为比或分数形式，例如 1:50 000，意味着地图上 1 厘米代表地面上 50 000 厘米（或 0.5 公里）。
Scale = Map Distance ÷ Actual Distance (using the same units)
比例尺 = 图上距离 ÷ 实际距离（使用相同单位）
25 000 map equals 4 × 25 000 cm = 100 000 cm = 1 km. Always convert the final answer to a sensible unit such as metres or kilometres.
要计算两点间的实际距离，先量出图上距离（厘米），再乘以比例尺分母。比如，在 1:25 000 地图上量得 4 厘米，实际距离 = 4 × 25 000 厘米 = 100 000 厘米 = 1 公里。最后记得把答案换算成米或公里等合适的单位。
2. Gradient | 坡度（梯度）
Gradient measures the steepness of a slope. It is the ratio between the vertical rise (the change in height) and the horizontal distance. A road sign warning of a 1:10 gradient means that for every 10 metres you travel horizontally, you climb 1 metre vertically.
坡度衡量的是斜坡的陡峭程度，即垂直升高（高度变化）与水平距离的比值。道路标志上如标有 1:10 的坡度，表示每水平前进 10 米，垂直升高 1 米。
Gradient = Vertical Difference (m) ÷ Horizontal Distance (m)
坡度 = 高差（米） ÷ 水平距离（米）
On a contour map, first identify two points and read their contour values to get the vertical difference. Next, measure the straight‑line distance between them and convert it to metres using the map scale. Divide the vertical difference by the horizontal distance to obtain the gradient. The result is often simplified to a ratio that starts with ‘1 in …’.
在等高线地形图上，先确定两个点，读取各自的等高线数值获得高差。然后量取两点间的直线距离，用比例尺换算成米。用高差除以水平距离得到坡度。结果常简化成以“1 比 几”开头的比例形式。
3. Population Density | 人口密度
Population density describes how crowded a place is. It is the average number of people living in one square kilometre (km²) of land. A high density indicates many people in a small area, while a low density shows that people are spread out.
人口密度描述一个地方的拥挤程度，指平均每平方公里土地上居住的人数。高密度意味着小区域内人口众多，低密度则表示人口分布稀疏。
Population Density = Total Population ÷ Total Land Area (km²)
人口密度 = 总人口 ÷ 土地总面积（平方公里）
e formula helps geographers compare how intensively different regions are settled and can be applied to countries, cities or any defined area.
如果一座城市有 200 万人口、面积 800 平方公里，那么人口密度 = 2 000 000 ÷ 800 = 2 500 人/平方公里。该公式帮助地理学者比较不同地区的居住密集程度，适用于国家、城市或任意划定区域。
4. Rate of Natural Increase | 自然增长率
Natural increase (RNI) shows how much a population is growing due only to births and deaths, not counting migration. It is expressed as a percentage. A positive RNI means more people are being born than dying; a negative RNI signals natural decrease.
自然增长率反映仅由出生和死亡（不含迁移）带来的人口增长，用百分比表示。正值表示出生多于死亡，负值表示人口自然减少。
RNI (%) = (Birth Rate - Death Rate) ÷ 10
自然增长率(%) =（出生率 － 死亡率）÷ 10
le. Dividing by 10 converts this figure into a percentage. For instance, if the birth rate is 25 per 1 000 and the death rate is 8 per 1 000, RNI = (25 - 8) ÷ 10 = 1.7%.
出生率和死亡率通常以每年每千人中的数量给出。两者相减得到每千人中的净变化，再除以 10 就转换为百分比。例如，出生率 25‰，死亡率 8‰，则自然增长率 = (25 - 8) ÷ 10 = 1.7%。
5. Net Migration Rate | 净迁移率
Net migration shows whether more people are moving into an area than leaving it. A positive net migration means the area gains population through migration, while a negative figure means more people are moving out. It complements natural increase to give total population change.
净迁移反映迁入某地的人口是否多于迁出的人口。正值表示该地因人口迁移而增加人数，负值表示迁出的人多于迁入。它和自然增长共同决定一个地方的总人口变化。
Net Migration Rate = (Immigrants - Emigrants) ÷ Total Population × 1 000
净迁移率 =（迁入人数 － 迁出人数）÷ 总人口 × 1 000
hile 400 people emigrate in a year, the net migration rate is (600 - 400) ÷ 50 000 × 1 000 = +4 per 1 000. This means the town gained 4 people per 1 000 from migration.
结果以每千人中的人数表示，便于和出生率、死亡率比较。如果一个镇有 5 万人，一年内迁入 600 人、迁出 400 人，净迁移率 = (600 - 400) ÷ 50 000 × 1 000 = +4‰，表明该镇每千人因迁移净增 4 人。
6. Urbanisation Level | 城市化水平
The urbanisation level measures the proportion of a country’s total population that lives in towns and cities. It is a simple percentage that helps geographers understand how developed or rural a country still is.
城市化水平衡量一个国家总人口中居住在城镇的人口比例。这个简单的百分比有助于地理学者了解一个国家的发展程度或乡村色彩仍有多浓。
Urbanisation Level (%) = (Urban Population ÷ Total Population) × 100
城市化水平(%) =（城镇人口 ÷ 总人口）× 100
45 million urban dwellers, the urbanisation level is (45 million ÷ 60 million) × 100 = 75% o be tracked over time to show how quickly a country is moving from rural to urban living.
例如，如果一个国家有 6000 万人口，其中 4500 万为城镇居民，城市化水平 = (4500 万 ÷ 6000 万) × 100 = 75%。还可以追踪城市化速度的变化，反映一个国家由乡村向城市生活转变的快慢。
7. Environmental Lapse Rate | 气温直减率
In the troposphere, temperature usually falls as altitude increases. The average environmental lapse rate tells us by how many degrees Celsius the air temperature drops for every 100 metres of vertical ascent. This principle is vital for understanding mountain climates and why upland areas are cooler.
在对流层中，气温通常随高度升高而下降。平均气温直减率告诉我们每上升 100 米，气温下降多少摄氏度。这一原理对理解山地气候以及为何高地地区更凉爽至关重要。
Average Lapse Rate ≈ 0.65 °C per 100 m (or 6.5 °C per 1 000 m)
平均气温直减率 ≈ 每 100 米降低 0.65 °C（即每 1000 米降低 6.5 °C）
00 × 0.65) = 24 - 9.75 = 14.25 °C. The actual value can vary with humidity, but the average figure gives a useful first estimate.
如果海边小镇在海平面处测得气温 24 °C，那么在附近海拔 1500 米的山顶，登山者可预计气温约为 24 - (1500 ÷ 100 × 0.65) = 24 - 9.75 = 14.25 °C。实际数值会因湿度有所变化，但平均值给出了有用的初步估算。
8. Water Balance Equation | 水量平衡方程
The water balance is a basic accounting tool for the hydrological cycle over a drainage basin. It states that the amount of water entering a basin through precipitation is distributed among runoff, evapotranspiration and changes in storage. This helps hydrologists understand river flows and water availability.
水量平衡是对流域水文循环的基本核算工具，指出通过降水进入流域的水量在径流、蒸散发和储水量变化之间进行分配。这有助于水文学者理解河流流量和可用水资源。
P = Q + E + ΔS
降水量 = 径流量 + 蒸散发量 + 储水量变化
Where P is precipitation, Q is stream runoff, E is evapotranspiration and ΔS is the change in water stored in the ground, lakes and vegetation. Over a long period, storage changes may average out to near zero, so runoff plus evapotranspiration roughly equals precipitation.
式中 P 代表降水量，Q 代表河流径流量，E 代表蒸散发量，ΔS 代表土壤、湖泊和植被中储水量的变化。长时间尺度的平均储水变化接近零，所以径流量加蒸散发量大致等于降水量。
9. Hjulström Curve (Erosion–Transport–Deposition) | 尤尔斯特伦曲线（侵蚀—搬运—沉积）
The Hjulström curve is not a formula but a fundamental theorem that links water velocity to the erosion, transport and deposition of sediment particles of different sizes. It shows that fine clay and silt particles need surprisingly high velocities to be eroded because they are cohesive, while sand erodes at moderate speeds. Once a particle is moving, a lower velocity is needed to keep it in suspension than was needed to pick it up.
尤尔斯特伦曲线虽非公式，却是一个联系水流速度与不同粒径沉积物侵蚀、搬运和沉积规律的基础定理。它显示细小的黏土和粉砂由于具有黏结性，反而需要相当高的流速才能被侵蚀，而沙粒在中等流速下即可侵蚀。一旦颗粒开始运动，维持其悬浮所需的流速远低于起动流速。
Threshold velocities: Erosion curve lies above transport curve; finest and largest particles require highest erosion speeds.
临界流速：侵蚀曲线位于搬运曲线之上；最细和最大的颗粒都需要最高的侵蚀速度。
Geographers use the Hjulström diagram to explain river landforms. When a river slows down on the inside of a meander, it drops the larger particles first, building a point bar. Where the river speeds up, erosion cuts the outer bank, forming a river cliff. Understanding this curve helps predict where material will be picked up and where it will be laid down.
地理学者借助尤尔斯特伦图解释河流地貌。在河曲内侧水流减缓，首先卸下较大颗粒，形成凸岸坝；而在水流加速处，侵蚀切割外侧河岸，形成凹岸陡壁。理解这条曲线有助于预测物质的起动和堆积位置。
10. Longshore Drift Theorem | 沿岸漂移定理
Longshore drift describes the zig‑zag movement of sediment along a coastline caused by waves approaching the shore at an angle. Swash carries sand and pebbles up the beach in the direction of the wave, and backwash pulls them straight down the slope under gravity. The net effect is a gradual transport of material parallel to the shore. This process shapes spits, bars and beaches.
沿岸漂移描述的是由斜向入射的海浪引起的泥沙沿滨线的锯齿状运动。冲流将沙石沿波浪方向推上海滩，回流在重力作用下顺着斜坡直线退下。两者的净效应是物质沿着与海岸平行的方向逐渐移动。这个过程塑造了沙嘴、拦湾坝和海滩等地貌。
Net drift direction ≈ direction of prevailing wave approach (adjusted by swash–backwash imbalance)
净漂移方向 ≈ 盛行波浪入射方向（由冲流—回流的不对称性调整）
To identify the direction of longshore drift in the field, geographers look at the shape of groynes, the build‑up of sand on one side, or use floating objects. The rate of drift depends on wave energy, beach material size and the angle of wave attack, but the fundamental principle remains the same across all coastlines.
在野外，地理学者通过观察防波堤两侧的沙粒堆积形态或使用浮子来判断沿岸漂移方向。漂移速率取决于波浪能量、滩面物质大小和波浪入射角，但其基本原理在所有海岸线上都是一致的。
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