What phonetic alphabet is used here?

Solution 1:

Considering its date and source, the symbols appear to be a phonetic representation of the kind that has been abandoned in most of the world, but remains entrenched in the major American dictionaries and in American primary and secondary education. See for example the American Heritage Dictionary pronunciation key, Merriam-Webster Guide to Pronunciation, or the Wikipedia United States dictionary transcription key.

The breve (˘) is not used by Random House, Merriam-Webster, or the New Oxford American Dictionary, but it is commonly used to mark a "short" vowel sound, and is used in the AHD system. The prime mark indicating stress but positioned at the end of the stressed syllable is also a mark of the AHD. Using the AHD key then, the SI prefix for giga-, meaning 10⁹, and represented as

jĭ′gä

would in IPA be something like

'dʒɪgɑ or 'dʒɪgə

akin to jig.

This pronunciation seems strange nowadays, because we have become accustomed to the 'hard g' \gɪgɑ-\ pronunciation in words like gigabyte and gigahertz. This prefix as a multiplier was uncommon outside of science and industry until fairly recently, however, and some used to prefer the 'soft g' \dʒ\ variant— endorsed by the IEEE, ANSI, and indeed the NBS, whose successor, the National Institute of Standards and Technology, sticks by this pronunciation to the present day. MW also retains the 'soft g' in its recorded pronunciation, and notes both pronunciations, but most other dictionaries seem to have dropped it in favor of the 'hard g' (\g) variety.

Famously, Doc Brown's time machine in the Back to the Future films is said to use 1.21 gigawatts of power, pronounced with the 'soft g'. This was retconned by later fans to jigowatts — ironic, because his pronunciation of gigawatt would have been unexceptional in the 1950s U.S.