It is generally accepted that LTM has an unlimited capacity. It is possible to lose things through processes such as decay and interference but the loss does not occur because of capacity limitations.
Researchers generally agree that STM has a limited capacity. If someone gives you a phone number to remember, it is impossible to recall it without rehearsal because STM has a limited capacity and items can get displaced.
Jacobs devised one of the earliest attempts at measure the capacity of STM in 1887 called the digit span technique*. Jacobs found that on average, people could recall about 7 digits in this immediate serial recall task*.
Wrote a famous article in 1956, called 'The Magical Number 7, Plus or Minus 2' in which he proposed that we can hold about 7 items in our STM, but there is a range of capacity between 5 and 9 items.
Miller believed that our immediate memory span is determined by the number of 'chunks' of information we can hold rather than the number of individual letters or numerals.
Also, memory span can be increased by chunking.
Some psychologists have criticised Miller's concept of chunking for being too vague. Simon (1974) found that the span as measured in chunks depends on the amount of information contained in the chunk. He experimented with the immediate serial recall technique with one-syllable, two-syllable and three syllable, and for two and eight word phrases.
He found that the span in chunks was less with larger chunks, i.e eight word phrases, than with smaller chunks.
Glanzer and Razel (1974) used the recency effect rather than the digit span as a measure of the capacity of STM. They found that the recency effect 2.2 items when the stimulus material consisted of single, unrelated words, but increased to 1.5 sentences (i.e considerably more single words) when unfamiliar sentences were presented and to 2.2 proverbs when familiar proverbs (e.g. 'a stich in time saves nine') were used.