Enigma 229 is from the Ladies Diary of 1738 (when Beddome was 21) page 352. See here. The answer is revealed on page 356 (see below).
From dirty form, and filthy dress set free,
At length I enjoy a pleasing liberty:
From spots refin'd, and every blemish clear,
Ladies, like you, I'm innocent and fair.
I, quaker-like, am neat and plainly dust,
Yet oft in me the beauish fop's exprest.
Sometimes in black my mournful body's bound,
With costly gold sometimes I'm edg'd around.
No monstrous form, no horrid shape I bear,
Unarm'd I go, yet oft when I appear,
The stoutest souls are seiz'd with panic fear.
Th' insolvent debtor often I surprize,
Nor mind the wife's complaint, or children's cries.
With unrelenting force I seize the prey,
And to a gaol the lawful prize convey.
To vagabonds, whores, and such-like paltry stuff,
To pilfering knaves and rogues I'm always rough,
But unprovok'd, I'm peaceable enough.
The jarring feuds of friends I oft compose,
And settle peace between the greatest foes.
Love is my natural product;
I inspire An amorous warmth, and kindle mutual fire.
Like wide-mouth'd fame, thro' distant realms I fly,
Sometimes I tell the truth, and sometimes lye.
All this I do, but still my chiefest care
Is to oblige and please the charming fair.
Ladies, on you submissive I attend,
Your faithful servant, and your bosom friend.
In bulk I'm small, of all your slaves the least;
Yet trusted most, and still esteem'd the best.
Let servile fools at humble distance stand,
My office is to wait at your right hand.
There I attend from every drudgery free,
And even my mistress often stoops to me.
Whilst fortune smiles and crowns me with success,
I'm honour'd with each female's fond caress;
But if she frown, and I successless prove,
At once I lose both their respect and love.
Then all the marks of fem'nine rage I bear,
My tender tides they mangle, bruise, and tear,
And cast my feater'd limbs to rot i'th' open air.
Ye cruel dames, your utmost efforts try,
To name the thing you deal so coarsely by.
Answer (choose with cursor to see): "paper"