This is an attempt to get some scientific information about how to best use batteries (I'm going to refer to both single cells or assemblies of cells as batteries for the sake of this question) in home brew apparatus. Battery manufacturers seem to avoid giving any practical information on sizing for particular applications, so circuit designers are forced to use an empirical approach and learn from trial & error.
I'd expect to find graphs showing how long a given size battery can deliver specific currents. For example: A theoretically perfect AA battery rated at 2000mAh might have a graph with datapoints at 1 hour and 2 amps extending to 10 hours at 200mA and 100 hours at 20mA. Variations from this ideal might show that an alkaline battery might not be able to deliver anywhere near 2 amps for one hour but would be able to fit the curve at 100 hours or that a ni-mh (or lithium) battery might be able to match the curve over the entire range from 1 to 100 hours. I think this is called the C rate.
These variations in performance most likely have to do with specific battery chemistry, physical design and parameters such as internal resistance. So what we would like to do is come up with a way to roughly ascertain the suitability of a specific size battery of a certain chemistry for an application. So - what might happen to a battery short circuited momentarily be an ammeter? Some battery systems might recover from this experiment but others might not due to polarization effects that change internal resistance or other factors. One certainly would not want to attempt this with a Weston standard cell!
Many years ago, we installed & maintained burglar alarm systems using several #6 dry cells (1.5 volts - great big things - the carbon electrode was about 1" dia. and 6" long) to power a 20 milliamp alarm loop. To test the remaining life of the cell we would connect a 30 amp ammeter (we used a ruggedized panel mount meter, not a multimeter) directly across the terminals. A new cell could deliver around 20-25 amps for a second or two. A very old cell might barely move the meter. These cells would typically last between 1 and 3 years, sometimes up to 5 years. Cells in a loop with doors that were normally open (like a warehouse) would last longer than cells in a store where the doors were usually closed - open circuits draw no power.
I've recently had occasion to use 4-AA cells to power a digital audio preamp with phantom power for microphones. When using alkaline cells, battery life might only be 2-3 hours, but rechargeable ni-mh cells might last 12-15 hours. The total milliamp hour capacity of the alkaline and ni-mh cells is about the same - somewhere between 1800 and 2500mah.
This is clearly a case where the continuous current draw is much higher than the alkaline cell was designed to deliver. So if you need 150ma continuous output from AA cells, ni-mh seems to be your best bet. (the equipment manufacturer had no recommendations for which batteries to use to achieve their 12-15 hour spec) After all, lead-acid batteries come in two flavors - high current for automotive engine cranking or marine batteries for electric motors and most of us know which to use for which application.
The big problem with ni-mh cells is how long they hold a charge. Alkaline cells might be able to sit in storage 10 years, but even the best ni-cads will lose charge after about a year. This can be a problem when gear is expected to sit in the case until an emergency, at which time it is expected to work! So designers might want to spec alkaline C cells instead of AA in such cases...
I suppose one could plot a graph using a resistor with a voltmeter across the resistor and periodically recording the voltage until the battery voltage dropped to under 70% of rated voltage. It would require several fresh batteries and several different resistors to plot more than a single data point. (destructive testing)
But is this really necessary? All we want to know is the maximum current that the battery can actually deliver that meets the amp-hour rating. If I recall correctly that point might be when the internal resistance of the battery is the same as the resistance of the load. Is there an easy non-destructive way to measure this value?
Refer to: First Principles of Physics - Fuller,Brownlee,Baker - 1937 edition, Chapter XXXIV and College Physics - Sears & Zemansky - 3rd edition, Chapter 30.
The Wikipedia article https://en.wikipedia.org/wiki/Battery_(electricity) addresses some of these concerns but not all.