Correct spelling, explanation: the words gauge and gage have the same origin and are essentially two different spellings of the same word, often used interchangeably in various contexts. Both words trace their etymology back to the Old North French word gauger, meaning to measure or to judge. This Old North French term, in turn, has roots in the Old French word gaugier, which means to measure or to weigh. The two spellings have persisted into modern English, with gauge being more widely accepted and used, particularly in American English. Gage is considered an alternate spelling and may be found in specific contexts or regions, but it is less common in general usage.

Definition of gauge:
1. Noun, measuring instrument or device used to assess the size, dimensions, pressure, temperature, thickness, or other properties of an object or substance
The mechanic used a tire pressure gauge to check the air pressure in each of the car’s tires before the long road trip.
The meteorologist observed the barometric gauge closely to predict changes in weather patterns and anticipate upcoming storms.
2. Verb, to measure or estimate, often against a standard
The tailor carefully gauged the dimensions of the fabric before cutting to ensure a precise fit for the custom-made suit.
To determine the water depth, the marine biologist used a sonar device to gauge the distance between the research vessel and the ocean floor.

Collocations with gauge:
Some most commonly used collocations include:
1. Rail gauge: the distance between the inner sides of two parallel rails on a railway track, which can vary between different regions and countries.
The standard rail gauge varies between countries, affecting international train travel.
2. Bore gauge: a precision tool used to measure the internal diameter of a hole, often used in machining and manufacturing.
The machinist used a bore gauge to check the precise diameter of the engine cylinders.
3. Wire gauge: a system for classifying the thickness or diameter of wires, commonly used in electrical engineering to ensure compatibility and safety.
The electrician selected the appropriate wire gauge for the circuit to ensure safety and efficiency.
4. Economic gauge: indicators or measurements used to assess the health and performance of an economy, such as unemployment rates, GDP growth, or inflation.
Analysts use various economic gauges, such as unemployment rates and GDP growth, to assess the health of an economy.

Correct spelling, explanation: while gage and gauge are often used interchangeably, there are considerations based on context and regional preferences. Gauge is the preferred spelling in both British and American English. Gage is an alternate spelling that is more commonly used in American English, particularly in specific technical or specialized contexts. If you’re writing for a specific audience or publication, it’s a good idea to check their style guide or preferences regarding the spelling of gage or gauge but be aware that gauge is more widely recognized.