Nippon-siki

Nippon-siki (日本式) is the oldest and least common system of Japanese romanization, also known as Nihon-siki, Nippon-shiki and Nihon-shiki depending on your choice of the spelling for Japan and style of romanization. Meaning simply "Japanese style" and proposed in 1885 by Meiji-era polymath Aikitsu Tanakadate (田中舘愛橘), Nippon-siki never quite caught up to Hepburn in popularity, but did largely form the basis of the government's later Kunrei romanization method. Nippon-siki maintains the best correspondance to written Japanese, but for the foreign reader is slightly more obscure than Kunrei (and considerably worse than Hepburn).

Least Significant Bits

The sole difference with Kunrei is a relic of the differences between the kana syllabary and pronunciation: the sounds of the voiced versions of the pairs し/ち si/ti and す/つ su/tu have become identical, but separate kana are still maintained. For example, if the words かな kana and つかい tukai are combined, in kana the result is written かなづかい with a dakuten ゛atop to indicate that the つ "tu" is now voiced. Hepburn and Kunrei ignore the underlying kana and represent the sounds phonetically as kanazukai, same as if the original kana were "su", while Nippon retains the difference and romanizes the word as kanadukai. This also makes Nippon-siki the only system of romanization that allows 100% mapping back from and to kana.

In case the above was too confusing, here's the standard hiragana/Nippon-siki conversion table:

あ a   か ka   さ sa   た ta   な na   は ha   ま ma  や ya  ら ra  わ wa ん n 
い i   き ki   し si   ち ti   に ni   ひ hi   み mi         り ri  ゐ(i)
う u   く ku   す su   つ tu   ぬ nu   ふ hu   む mu  ゆ yu  る ru
え e   け ke   せ se   て te   ね ne   へ he   め me         れ re  ゑ(e)
お o   こ ko   そ so   と to   の no   ほ ho   も mo  よ yo  ろ ro  を o 
		 
       が ga   ざ za   だ da           ば ba   ぱ pa 
       ぎ gi   じ zi   ぢ di           び bi   ぴ pi 
       ぐ gu   ず zu   づ du           ぶ bu   ぷ pu 
       げ ge   ぜ ze   で de           べ be   ぺ pe 
       ご go   ぞ zo   ど do           ぼ bo   ぽ po 
                    
      きゃkya しゃsya ちゃtya にゃnya ひゃhya みゃmya         りゃrya 
      きゅkyu しゅsyu ちゅtyu にゅnyu ひゅhyu みゅmyu         りゅryu 
      きょkyo しょsyo ちょtyo にょnyo ひょhyo みょmyo         りょryo 
                                   
      ぎゃgya じゃzya ぢゃdya         びゃbya ぴゃpya 
      ぎゅgyu じゅzyu ぢゅdyu         びゅbyu ぴゅpyu 
      ぎょgyo じょzyo ぢょdyo         びょbyo ぴょpyo

Characters in bold differ from those in Kunrei.
Characters in (parentheses) are obsolete.

Long vowels, geminate consonants, etc are handled exactly as in Kunrei, so see that node for details.

But Wait... It's Alive!

Interestingly enough, Nippon-siki's maintenance of the difference has been resurrected in the so-called wapuro romaji used to input Japanese into word processors and computers. Most IMEs will not recognize spellings like kanazukai, since they convert this by default to the incorrect かなずかい, so they need to have the kana spelled out Nippon-style as kanadukai. However, most word processors are lenient creatures, and will happily accept non-Nipponese spellings like *kanadzukai as well.

References

sci.lang.japan AFAQ 5.3.2