order than the units of analysis of the individual systems. That is, just as the phones present within an individual variety are grouped together into abstract phonemes, the phonemes present within a group of varieties could be grouped together into even more abstract diaphonemes. Weinreich exemplified the diasystemic approach by a formulaic arrangement of phoneme correspondences in three dialects of Yiddish, focusing on the vowels but arguing that the principle could work for other aspects of language. Although Weinreich did not elaborate the diasystemic approach, he did consider some theoretical pitfalls to be avoided. He recognized that phonemic mergers and splits with dissimilar results across dialects would pose a difficult challenge for the construction of a diasystem; he cautioned against positing a diasystem when the work of creating all the member systems (e.g. the work of phonemicization) was yet incomplete; and, following the lead of , he noted that the differences in phonological inventory and etymological distribution might prove problematic in the construction of diasystems. Subsequent investigation A few linguists took up Weinreich's challenge and quickly found it to be inadequate. Some of the failures had been anticipated by Weinreich himself, as described above. found an extreme example of divergent incidence in a study of two dialects of Swiss German, Luzerner and Appenzeller, which evolved independently of each other. Although each dialect had the same set of eleven short vowel phonemes, only one pair ( ~ ) was shown to have a common parent vowel in earlier stages of German. The remaining phonetic similarities between the Luzerner and Appenzeller phoneme sets were fortuitous results of multiple mergers and splits that each dialect underwent separately. , examining and , noted the need for refinements in the original proposal; different researchers did not seem to agree on definitions, disciplines of study, or objects of inquiry. The research and debate concluded that multiple dialects could not be described by a common grammar, at least not under structuralist theory. That is, it would be unfeasible to construct a single grammar for multiple dialects unless their differences were very minor or if it incorporated only a small number of dialects. Related to Weinreich's proposal were efforts in both American dialectology and generative phonology to construct an "overall system" that represented the underlying representation for all dialects of English. An example of this was the diaphonemic analysis, made by , that presumably all American varieties could