Jtdylktuy

I've come across a quote by Teddy Roosevelt which shows his admiration for Alexander Hamilton. It uses the phrase "the touch of the purple," but supplies little hint as to what it means.

Roosevelt saw in Hamilton “the touch of the heroic, the touch of the
purple, the touch of the gallant.”

The best explanation I've found is a possible religious meaning, gleaned from the phrase's inclusion in this Wikipedia article. I am also aware that purple has a connotation of royalty or nobility in that, some centuries ago, purple dyes were extravagant and therefore used as a symbol of wealth and power. I'm not entirely convinced that either of these are the sense that Roosevelt was invoking.

Here, purple is used as noun. So, if you check the definition of purple according to the Merriam Webster especially 2 of 3 entry and particularly 2a, you will find exquisite definition of purple:

https://www.merriam-webster.com/dictionary/purple

imperial or regal rank or power

Backed by Google definition:

a crimson dye obtained from some molluscs, formerly used for fabric worn by an emperor or senior magistrate in ancient Rome or Byzantium.

Theodore Roosevelt and 'the touch of the purple'

The quotation you cite appears in Stephen Knott, Alexander Hamilton and the Persistence of Myth (2002), subsequently reprinted in The Many Faces of Alexander Hamilton: The Life and Legacy of America's Most Elusive Founding Father (2006):

On the recommendation of his friend Henry Cabot Lodge, Roosevelt wrote two volumes for John Morse's American Statesmen series. In 1887 he completed Governeur Morris and later told Morris's great-grandson that Morris and Hamilton "embodied what was best in the Federalist Party. ... They both of them had in them the touch of the heroic, the touch of the purple, the touch of the gallant." Both Roosevelt and Lodge adored Hamilton, and on a trip to London in 1886 Roosevelt could not wait to inform Lodge that James Bryce was "especially complimentary about your Hamilton."

The comment addressed to the descendant of Gouverneur Morris (also named Governeur Morris) appears in a letter from Theodore Roosevelt to the later Gouverneur Morris dated November 23, 1910, reproduced in The Letters of Theodore Roosevelt: The Days of Armageddon, 1900–1914 (1954) [combined snippets]:

My dear Morris: You could not have made a gift which I should have appreciated more, nor could you have given those books to any other man who would have appreciated them as much. Moreover, the box in which have been kind enough to have them put is just exactly right for my library. ... I shall keep your letter in the box with the three volumes. I am naturally very much pleased at your thinking of me in comparison with your great ancestor. I have always not merely admired him immensely but what is something totally different, been very greatly drawn to his personality. He and Hamilton embodied what was best in the Federalist Party, excepting of course in so far as you can say that Washington was a Federalist. They both of them had in them the touch of the heroic, the touch of the purple, the touch of the gallant, the dashing, the picturesque, which ranks the possessors among those historical characters about whom one really cares to read. It is simply fine that you continue to like my sketch of your ancestor. Since I wrote it, I have had much more experience of public life myself; and should I now rewrite it, my praise would be more heart and my criticism far more guarded.

But Roosevelt had actually alluded to "the touch of the purple" 12 years earlier, in the one-paragraph preface to the 1898 edition of Theodore Roosevelt, Gouverneur Morris (1888/1898). Here, for maximum context, is that preface in its entirety:

Gouverneur Morris, like his far greater friend and political associate, Alexander Hamilton, had about him that "touch of the purple" which is always so strongly attractive. He was too unstable and erratic to leave a profound mark upon our political developments, but he performed two or three conspicuous feats, he rendered several marked services to the country, and he embodied to a peculiar degree both the qualities which made the Federalist party so brilliant and so useful, and hose other qualities which finally brought about its downfall. Hamilton and even Jay represented better what was highest in the Federalist party. Gouverneur Morris stood for its weakness as well as for its strength. Able, fearless, and cultivated, deeply devoted to his people, and of much too tough fibre ever to be misled, into losing his affection for things American because of American faults and shortcomings, as was and is in the case with weaker natures, he was able to render distinguished service to his country. Other American ministers have been greater and more successful diplomats that Morris was ; but no one has better represented those qualities of generous daring and lofty disinterestedness which we like to associate with the name American, than did the minister who, alone among the foreign ministers, kept his residence in Paris through the "Terror." He stood for the honest payment of debts. Unlike many of his colleagues, he was a polished man of the world, whose comments on men and things showed that curious insight and power of observation which come only when to natural ability there is added special training. But he distrusted the mass of the people in other sections of the country than his own, who had not the habits of refinement and the ways of looking at life which he and his associates possessed ; and thus it happened when the federalists sank into a secessionist faction, the name of Gouverneur Morris was associated with the names of the others who at that time lacked the power, but not the will, to split a great nation into a chaos of feeble and quarrelsome little states.

Roosevelt also used the expression "the touch of the purple" in his review of Edward Arlington Robinson's "The Children of the Night" in The Outlook (August 12, 1905):

The "twilight of the poets" has been especially gray in America ; for poetry is of course one of those arts in which the smallest amount of work of the very highest class is worth an infinity of good work that is not of the highest class. The touch of the purple makes a poem out of verse, and if it is not there, there is no substitute. It is hard to account for the failure to produce in America of recent years a poet who in the world of letters will rank as high as certain sculptors and painters rank in the world of art.

And in a letter dated January 9, 1899, to Henry Cabot Lodge, reproduced in The Letters of Theodore Roosevelt: The Years of Preparation, 1868–1900 (1951) [combined snippets]:

Dear Cabot:—I think that on the whole your last chapter is the best thing you have done. ...

As for Bay's [George Cabot Lodge's] poems, as you know, I think he has "the touch of the purple" in him. My favorites in his book are "The Song of the Wave"; "The Song of the Sword"; "The Mothers of Men"; "The Norsemen"; and the First and Fifth Sonnets—especially the Fifth, although I am not absolutely clear what it is about!

To top things off, Roosevelt used the expression a fifth time in a letter dated November 30, 1908, to George Cabot Lodge, reprinted in John W. Crowley, "'Dear Bay': Theodore Roosevelt's Letters to George Cabot Lodge," in New York History (April 1972):

Dear Bay: I have read "Herakles" half thru already. You have the touch of the purple, all right! I am immensely imprest by the poem.

Roosevelt also uses the shorter term "the purple" in a letter to Anna Roosevelt Cowles dated June 28, 1896:

I have been so absorbed by my own special work and it's ramifications that I have time to keep very little in touch with anything outside of my own duties; I see but little of the life of the great world; I am but little in touch even with our national politics. The work of the Police Board has absorbed all the time and energy I could give to such work at all. There is nothing of the purple in it; it is as grimy as all work for municipal reform over here must be for some decades to come; and it is inconceivably arduous, disheartening and irritating, beyond almost all other work of the kind, because of the special circumstances of the case. I have to contend with the hostility of Tammany, and the almost equal hostility of the Republican machine; I have to contend with the folly of the reformers and the indifference of decent citizens; above all I have to contend with the singularly foolish law under which we administer the Department.

In this last instance, "the purple" seems to allude to "points of honor" or "exalted service"—a meaning somewhat echoed in Roosevelt's instances of "the touch of the purple."

Conclusions

As other answerers have noted, "purple" can allude to imperial, regal, aristocratic, or lordly rank, power, or quality. Merriam-Webster's Eleventh Collegiate Dictionary (2003) lists two relevant definitions:

purple n ... 2 a: imperial or regal rank or power b : high rank or station

And The American Heritage Dictionary of the English Language (2010) has this relevant definition:

purple n. ... 3. Imperial power; high rank: born to the purple.

The expression "born to the purple" is in fact quite old in English, appearing at least as early as 1727 in a translation of the Abbé de Vertout, The History of the Revolution in Sweden, volume 2:

The Mayors of the Palace were Elected by the French alone; i. e. by the Body of the Nobility : They themselves made Choice of the General, under whose Banner they were to fight. Fredegarias has even transmitted to us the Form of that Election: But as for our Kings, they must be born to the Purple, they must be Princes of the Blood; and even it is to be observed, that in Marculph's Formulæ, the Name of Kings was often given to them, as soon as they were born.

In contrast, the first five instances of the expression "the [or that] touch of the purple" that a Google Books search turns up occur during the period 1898–1910, and all appear in writings by Theodore Roosevelt. The next-earliest instance of "touch of the purple" that Google Books brings up occurs many years later in a literal context: "Add a touch of the purple to the yellow to get a toned yellow brown."

Given that "the touch of the purple" seems to have originated (and more or less ended) as a set phrase with Theodore Roosevelt, I think its meaning is probably peculiar to him. In trying to get at what precisely Roosevelt had in mind when he used it, we need to take into account its suitability in both political contexts (as applied to Gouverneur Morris and Alexander Hamilton) and poetic ones (as applied to George Cabot Lodge and Edward Arlington Robinson).

In my opinion, "imperial," "regal," "aristocratic," and "lordly" offer a somewhat incomplete description of what Roosevelt intended to convey with the phrase "the touch of the purple." I think he probably did think of it as meaning, in part, "having an aristocratic sensibility"—one imbued with the confidence, manners, sophistication, and tastes of the high-born. But I think he probably also understood it to comprehend having the intellect and aspirations of the high-minded, the discriminating, the judicious, the honorable, and the public-spirited—all of which may have been aspects of Roosevelt's own conception of greatness.

In any event, "the touch of the purple" seems to have had a distinctive meaning for Roosevelt that made it appropriate in different situations. But it isn't clear that that meaning or complex of meanings survived him.

I take it to mean an aristocratic or lordly quality; he sees in Hamilton something lofty, as if he towers above others.