Semicolon followed by a dash;—What is it?
A modern discussion of compound points
Following the lead of Nicholson Baker in a review of M.B. Parkes's Pause and Effect published in The New York Review of Books, Keith Houston, Shady Characters: The Secret Life of Punctuation, Symbols & Other Typographical Marks (2013) refers to the ;— combination as a semi-colash. Houston reports that this form of punctuation doubling, which also involved the commash (,—) the colash (:—), and less often the stop-dash (.—) arose in the seventeenth century, citing examples from as early as 1622 (in an edition of Othello). More traditionally, these paired forms of punctuation seem most often to have been called (generically) compound points and (specifically) semicolon dash, comma dash, colon dash, and point dash.
Houston further suggest that the demise of this form of punctuation may be due to the emergence of hostile style guides:
The Chicago Manual of Style, launched in 1906, ruled against the dash hybrids from the start—except, curiously enough, the stop-dash, which was permitted only to introduce notes or asides, as in the construction "NOTE.—", though this too had been expunged by the 1969 edition. "Compound points" such as the commash were tolerated for slightly longer in British English, though by 1953 the British lexicographer Eric Partridge had also concluded "You {should} use compound points only when they are unavoidable."
This remark by Partridge is a bit surprising, given that he continues to use utterly avoidable stop-dashes to separate numbered definitions of entries in his A Dictionary of Slang and Unconventional English right through the fifth edition (1961).
A note in Mechanical Translation and Computational Linguistics, volumes 4–5 (1957) [combined snippets] indicates that compound points were not altogether unheard of even at that date:
The present analysis will include all those punctuational patterns which are commonly found in normal technical language. Included marks are the period, comma, semi-colon, colon, question mark, exclamation point, quotation mark, parenthesis, and dash. Excluded will be the hyphen, apostrophe, asterisk, multiple dashes, dots, compound points (such as comma dash, colon dash, etc.), and oblique stroke. These punctuation marks are not included in the present analysis because their influence on the sentence structure of scientific texts is believed to be small, either because of the special nature of these punctuation marks, or because of their comparative infrequency in scientific texts.
The utility of compound points
Unfortunately, Houston doesn't try to offer a serious explanation for the emergence of these combination points in the seventeenth century. Instead, he rather facetiously argues that they arose "from a tendency—or more precisely, from an irresistible, overweening need—to burden the written word with unwonted punctuation." His line of thought seems to run something like this: we don't use combination points today; ergo, they are unnecessary to us; ergo, they were always unnecessary; ergo, the only possible explanation for their ever having existed is some irrational impulse felt by our silly forebears.
In fact, however, contemporaneous authorities saw a clear difference between, for example, a comma, a semicolon, or a colon alone, and one followed by an em dash. From Josiah Bumstead, My First School-book to Teach Me to Read and Spell Words, and Understand Them (1839/1856):
We cannot read well unless we make the right pauses; and to help us in this, little marks are placed here and there among the words. These are the marks—
. , ; : ? ! —
Now, whenever you come to one of these, be sure that you make stop there; be sure that you do not go from the word before it to the word after it as you would if there were no mark between. At first you must learn from the teacher's voice what each mark means—what kind of a stop it is; she will make it, and you must make it like her.
TRUE LENGTH OF PAUSES.—Every pause should be just long enough to give the sense of the words.
...
, COMMA [&] ; SEMICOLON [&] : COLON...... These are found, not at the end [of a sentence], but before we reach the end. We must not make full stops at them. At the Comma make a short stop; at the Semicolon a longer stop; at the Colon, longer still.
...
— DASH [&] ,— COMMA and DASH [&] ;— SEMICOLON and DASH [&] :— COLON and DASH... The dash is sometimes a short stop like the comma, and sometimes a much longer one. The dash added to another mark increases the length of the pause.
So we have a brief but seemingly definitive explanation from the middle 1800s of what ;— signified—namely, a pause longer than the normal pause that a reader would accord a semicolon. And since, according to a notice dated July 5, 1839, and appended to the second page of this volume from Bumstead's Primary School Series,
At a meeting of the Boston Primary School Committee, held on the 4th instant, it was Voted, That the book called "My First School-Book" be introduced into the Primary Schools, for the use of the third and fourth classes.
it seems literally true that any Boston schoolboy of the 1840s and 1850s could have told an interested adult why the semicolon dash and other compound points existed and what purpose each one served.
The demise of compound points
Nevertheless, what seemed fundamental to good reading in 1839 seemed superfluous to critics less than a century later, at least in the case of comma-dash combinations. From Hugh Paterson, Style Manual for Stenographers, Reporters and Correspondents:
The comma and dash is used instead of parenthesis:
He planned,--but his planning was often in vain,--that his dream be realized.
The combination of the comma and dash, as in the preceding example, is a hybrid. The object of adding two marks is to widen the separation; but there is no utility in this, for the comma, dash, and parenthesis perform, mainly, the same office, the enclosing of expressions that might be left out and the sense of the sentence be complete. Each represents a greater degree of separation, in the order named, so that, if the dash be not strong enough, the parenthesis may be used.
This comment suggests that the demise of the comma dash is primarily owing to the triumph of the open and close parentheses—marks not mentioned in Bumstead's book at all—as the preferred way to express a longer pause than contemporaneous writers understood either paired commas or paired em dashes alone convey. The effect of this change on the other compound points may have been somewhat like the effect that losing a flagship product has on a company that makes only three or four products. With the familiar and relatively frequent instances of ;— supplanted by ( and ), the continued use of ;— and :— must have fallen into doubt, especially as the timing theory of proper punctuation began losing ground to the sense argument. Benjamin Drew, Pens and Types: Or, Hints and Helps for Those who Write, Print, Or Read (1872) notes with approval the rise of this rival theory:
We have been often told, that the period denotes the longest pause; the colon, a pause one half of the length of the period; the semicolon, a pause one half the length of the colon; the comma, a pause one half the length of the semicolon, etc.; but as Greene remarks, "Points are used to mark the sense, rather than the pauses."
Greene is Samuel Greene, A Grammar of the English Language (1870), which made the argument about the purpose of punctuation marks amid a flurry of comma dashes, colon dashes, and stop dashes. Evidently, the very pseudo-mathematical precision of timing theorists' the distribution of pauses for each punctuation mark contributed to the discrediting of the whole enterprise.
Yet another influence on the demise of compound points (astutely noted by Keith Houston in his book) may have been the central role that typewriters, with their limited set of available keys played in newspaper publishing from the late 1800s onward. Pre-electric typewriters normally had only the hyphen-width dash to apply to situations calling for em dashes, so the usual method in U.S. newspaper publishing was to represent an em dash with two non-overlapping hyphen-width dashes. Whereas ";—" may have seemed clean and clarifying, ";--" begins to look like a small bug convention—and the appeal of removing either the semicolon or the double hyphens grows correspondingly stronger.
Conclusions
The compound punctuation that the poster asks about is commonly referred to as a semicolon dash. Although many modern readers find such compound points—which also include the comma dash, the colon dash, and the stop (or period) dash—baroque and mystifying, they were widely understood at the time to signal a lengthening of the marked space in the sentence beyond what either of the component punctuation marks alone would have indicated. As the comma dash gave way to parenthesis marks, and as the theory of punctuation as signaling the amount of time to pause during reading at each punctuated place in a text lost territory to the theory that punctuation conveyed the sense of the demarcated words and phrases, the need (and justification) for compound points began to fade. The limited palette of typable characters on standard typewriters might have contributed further to the demise of compound points.
Today when we see compound points in an old book, they seem quaint and arbitrary, and not at all grounded in a practical objective. But in their own time, I believe, they conveyed real information that readers had been taught from a young age to receive and interpret correctly.
Semicolon dash used to serve the same purpose as the semicolon by itself. It has fallen out of use. See for example The Inland Printer - Volume 60 - Page 61.