Editing Dollar (section)

==Relationship to the troy pound==
The quantity of silver chosen in 1792 to correspond to one dollar, namely, 371.25 grains of pure silver, is very close to the [[geometric mean]] of one [[troy pound]] and one [[pennyweight]].  In what follows, "dollar" will be used as a unit of mass.  A troy pound being 5760 [[grain (unit)|grains]] and a pennyweight being 240 times smaller, or 24 grains, the geometric mean is, to the nearest hundredth, 371.81 grains.  This means that the ratio of a pound to a dollar (15.52) roughly equals the ratio of a dollar to a pennyweight (15.47).  These ratios are also very close to the ratio of a gram to a grain:  15.43.  Finally, in the United States, the ratio of the value of gold to the value of silver in the period from 1792 to 1873 averaged to about 15.5, being 15 from 1792 to 1834 and around 16 from 1834 to 1873.  This is also nearly the value of the gold to silver ratio determined by Isaac Newton in 1717.<ref>{{Cite book |title=International Monetary Conference Held . . . in Paris in August 1878| year=1879 |url=https://books.google.com/books?id=bNRAAAAAIAAJ&dq=isaac+newton+15.57+gold+silver&pg=PA570}}</ref>

That these three ratios are all approximately equal has some interesting consequences.  Let the gold to silver ratio be exactly 15.5.  Then a pennyweight of gold, that is 24 grains of gold, is nearly equal in value to a dollar of silver (1 dwt of gold = $1.002 of silver).  Second, a dollar of gold is nearly equal in value to a pound of silver ($1 of gold = 5754 3/8 grains of silver = 0.999 Lb of silver).  Third, the number of grains in a dollar (371.25) roughly equals the number of grams in a troy pound (373.24).