Note by John Cartlitch on the remedy for guineas and Irish halfpence

If a ℔ Troy of Gold be cut into $44⁤\frac{1}{2}$ guineas, then the weight of each guinea will be $129⁤\frac{39}{89}$ grains, or $129⁤\frac{438}{1000}$.

If 20 grains remedy be allowed per ℔, aguinea may weigh from $129⁤\frac{79}{89}$ grains or $129⁤\frac{8876}{10000}$ for the heaviest, to $128⁤\frac{88}{89}$ for the Lightest.

$44⁤\frac{1}{2}$ guineas each weighing 130 grains, will weigh exactly 25 grains above a pound Troy:

And $44⁤\frac{1}{2}$ guineas each weighing 129 grains will be $19⁤\frac{1}{2}$ grains lighter than a ℔ Troy. So that a guinea should alway weigh betwixt 129 and 130 grains.

If a ℔ Troy of Gold be cut into $44⁤\frac{1}{2}$ guineas, and each gain be valued at £1:1. then $\begin{array}{lll}\begin{array}{c}1\mathrm{oz.}\\ 1.{\mathrm{d}}^{\mathrm{wt}}\\ 1\mathrm{gr.}\end{array}\}& \text{ of Gold is worth }& \{\begin{array}{c}\stackrel{\pounds }{3}:17:10⁤\frac{1}{2}\\ 0:3:10⁤\frac{29}{40}\\ 0:0:1⁤\frac{101}{105}\end{array}\end{array}$

Hence in practise, ℔ odd grains may be always valued at 2d; the error in adwt amounting only to $1^{\mathrm{d}}⁤\frac{1}{4}$. but in an oz. it will be $2\prime :1^{\mathrm{d}}⁤\frac{1}{2}$.

According to the Warrant for Coining Copper for Ireland, an Irish halpenny should weigh $4⁤\frac{12}{13}$ drams; and the remedy per ℔ Averdupois (being $130$) is $1⁤\frac{11}{15}$ half-penny.

Average of the lightness per ℔ upon ℔ whole Coinage in 1736 is $9⁤\frac{9558}{10000}$ grains; And this fraction is a profit to the bank of 14 oz. 1dwt & 18 grains of Gold = £54: 18: 4

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