The first electric meter was invented quite by accident. Its creator was tinkering with an arc lamp when he noticed the peculiar way a spring had fallen off of it, as if affected by rotating electric fields. View Slideshow 
__1888: __Oliver B. Shallenberger receives a patent for the electric meter. There's no free lunch. You'll get an electric bill.
When Thomas Edison started selling electricity for illumination in 1882, he charged per lamp. He soon replaced that with a complicated chemical ampere-hour meter.
It was an electrolytic jar with two zinc plates immersed in a zinc-sulfate solution. Electricity flowing through the jar dissolved zinc off the positive plate and deposited it on the negative plate. Workers had to remove the electrodes every month and weigh them to see how much zinc had been transferred from one plate to the other.
It was messy, it was inefficient, and it wasn't very accurate. Even though Edison also developed a motor-type meter, his interest in chemistry caused him to prefer the chemical version. Blind spot.
Electrical polymath Elihu Thomson devised a walking-beam meter in 1888. It was a complicated, Rube Goldberg-type apparatus. A heating element in the circuit warmed a small alcohol-filled bottle on a seesaw lever. The alcohol warmed, evaporated and flowed into a matching bottle on the other side. When there was more alcohol in the opposite bottle, it would sink and start heating up to reverse the process. Each time the bottles rocked, they ticked off a notch on the meter. Not exactly a robust design.
Shallenberger was an Annapolis graduate who left the Navy in 1884 to join the Westinghouse company. He was working on a new arc lamp one day in 1888, when a spring fell out and landed on a ledge inside the lamp. Before an assistant could reach in to replace it, the ever-observant Shallenberger noticed the spring had rotated.
He soon determined that the lamp's rotating electric fields had caused the spring to turn. Shallenberger realized he could use the effect to turn wheels in a meter to measure electrical charge. Not only could he use it, he did ... and built an alternating-current ampere-hour meter in just three weeks.
The Shallenberger meter was a key part of George Westinghouse's AC electrical system. (Nikola Tesla later pointed out to Shallenberger that the induction meter was a type of AC motor.)
The meter went into commercial use within months, selling 120,000 units in 10 years. The ampere is a measure of current, and the ampere-hour a measure of charge. So power companies that used these meters charged by the charge.
Thomson invented a commutator watt-hour meter (that measured the energy consumed), also in 1888, and brought it to market the following year. It worked on both alternating- and direct-current systems, but fell by the wayside in the late 1890s when the induction watt-hour meter came into general use, where it remains to this day.
Source: Dave's Old Watthour Meter Webpage
Gallery: Measuring the History of Electricity
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June 29, 1888: Handel Oratorio Becomes First Musical Recording
April 11, 1888: Concertgebouw, Home of Nearly Perfect Acoustics, Opens
