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Mark Spahn
science forum addict
Joined: 07 Jul 2005
Posts: 62
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 Posted: Sun May 21, 2006 9:21 am Post subject:
gold balls
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In an article in the May 2006 Harper's magazine, Michael Hudson says in an article titled "The New Road to Serfdom: an illustrated guide to the coming real estate collapse" (page 43):
The eighteenth-century philospher Richard Price identified this miracle
of compound interest and observed, somewhat ruefully, that had he
been able to go back to the day Jesus was born and save a single penny
-- at 5 percent interest, compounded annually -- he would have earned
himself a solid gold sphere 150 million times bigger than Earth.
Actually, Price worded his statement a little more clearly (Does "150 million times bigger" refer to diameter, or volume?):
"Money bearing compound interest increases at first slowly. But, the rate of increase being continually accelerated, it becomes in some time so rapid, as to mock all the powers of the imagination. One penny, put out at our Saviour's birth to 5 per cent compound interest, would, before this time, have increased to a greater sum, than would be contained in a hundred and fifty millions of earths, all solid gold. But if put out to simple interest, it would, in the same time, have amounted to no more than seven shillings and four pence half-penny.
$B!HJ#Mx$r;:$`2_J>$O=i$a$O=y!9$KA}Bg$9$k!#$7$+$7!"A}BgN($O@d$($:2CB.$5$l$k$N$G!"$"$k4|4V$N8e$K$O!"A[A|$r@d$9$kB.$5$K$J$k!#%-%j%9%H@8CB$NG/$K(B5$B!s$NJ#Mx$GB_$7=P$5$l$?(B1$B%Z%K!<$O!":#F|$G$O$9$G$K!"$9$Y$F=c6b$+$i$J$k(B1$B2/(B5000$BK|8D$NCO5e$K4^$^$l$F$$$k$h$j$b!"$b$C$HBg$-$J3[$KA}Bg$7$F$$$k$G$"$m$&!#$7$+$7!"C1Mx$GB_$7=P$5$l$?$H$9$l$P!"F1$84|4V$K(B7$B%7%j%s%0(B4$B%Z%s%9H>$K$7$+!"A}Bg$7$J$$$G$"$m$&(B.$B!I!J86Cm!K(B
?Geld, das Zinseszinsen tragt, wachst anfangs langsam; da aber die Rate des Wachstums sich fortwahrend beschleunigt, wird sie nach einiger Zeit so rasch, das sie jeder Einbildung spottet. Ein Penny, ausgeliehen bei der Geburt unsers Erlosers auf Zinseszinsen zu 5%, wurde schon jetzt zu einer grosren Summe herangewachsen sein, als enthalten ware in 150 Millionen Erden, alle von gediegnem Gold. Aber ausgelegt auf einfache Zinsen, wurde er in derselben Zeit nur angewachsen sein auf 7 sh. 4 1/2 d. "81
[Marx: Das Kapital, S. 3302 ff. Digitale Bibliothek Band 11: Marx/Engels, S. 6616 (vgl. MEW Bd. 25, S. 407 ff.)]
And in 1772 Price wrote:
"A shilling put out to 6% compound interest at our Saviour's birth" (presumably in the Temple of Jerusalem) "would... have increased to a greater sum than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn's orbit."
$B$=$N!X8eJ'$$$K$+$s$9$k9M;!!Y%m%s%I%s!"#1#7#7#2G/!"$G$O!"H`$O99$K6u9b$/HtfF$9$k!#!V%-%j%9%H@8CB$N;~!W!J$9$J$o$A$*$=$i$/$O%(%k%5%l%`$N@DF<$G!K!V#6!s$NJ#Mx$GB_$5$l$?#1%7%j%s%0$O!"A4B@M[7O$,EZ@1$N50F;$ND>7B$KEy$7$$D>7B$r$b$D0l$D$N5e$KJQ$($i$l$?>l9g$KJqMF$7$&$k$G$"$m$&$h$j$b$b$C$HBg$-$$3[$N6b$K!"A}Bg$7$F$$$k$G$"$m$&(B
?1 sh., ausgelegt bei der Geburt unsers Erlosers (also wohl im Tempel von Jerusalem) ?zu 6% Zinseszinsen, wurde angewachsen sein zu einer grosern Summe als das ganze Sonnensystem einbegreifen konnte, wenn in eine Kugel verwandelt von einem Durchmesser gleich dem der Bahn des Saturn.$B!H(B
Okay. Let's check the price of gold in these two examples. Do we get a similar price in each case?
A few preliminaries...
The price of gold is normally stated as a price per troy ounce.
How many troy ounces are there in a cubic foot of gold?
foot = 30.48 cm, specific gravity of gold = 19.32, so ft^3 = (30.48 cm)^3 = 28,317 cm^3.
A cubic centimeter of water weighs 1 gram, and the specific gravity of gold means that a cubic centimeter of gold weighs 19.32 times an equal volume of water; that is, a cubic centimeter of gold weighs 19.32 g. So a cubic foot of gold weighs 28,317*19.32 = 547,084 g = 547 kg = about 1200 pounds (avoirdupois, not sterling).
A troy ounce = 31.1034768 g, so a cubic foot of gold weighs 547,084/31.1 = 17,589 troy ounces.
The formula for the volume of a sphere is (4/3)*pi*R^3, the radius of the Earth is 3,960 miles, and there are 5,280 feet in a mile, so the volume of the Earth in cubic feet is
(4/3)*pi*(3960 mi * 5280 ft/mi)^3 = 3.83*10^22 ft^3.
The volume of 150 million such Earths is 150 million times this, or
5.745*10^30 ft^3, and since each cubic foot of gold weighs 17,589 troy ounces, 150 million Earth-size gold balls amounts to 5.745*10^30*17,589 = 1.01*10^35 troy ounces of gold.
How many troy ounces of gold are there in a sphere whose radius is the distance from the Sun to Saturn (8.95*10^8 miles, says a reference)? The answer is
(4/3)*pi*(8.95*10^8 mi * 5280 ft/mi)^3 * 17,589 oz/ft^3 = 7.775*10^42 oz.
Now let's examine how much Price says these volumes of gold will cost.
In the first case (150 Earth-volumes of gold), the gold can be bought for 1 penny, compounded annually at 5%, for the number of years from Jesus's birth until 1774. Taking the year of Jesus's birth to be 4 B.C. (Are the lyrics of 'Jesus Christ Superstar' a good-enough historical source?), and remembering that there was no year Zero, the number of years is 1774-(-4)-1 = 1777 years. So the number of pence available in year 1777 is (1.05)^1777 = 4.502*10^37 pence. There are 12 pence per shilling and 20 shillings per pound sterling, so in British pounds this amount of money is 4.502*10^37 pence * (1 pound/240 pence) = 1.876*10^35 pounds. So, according to Price, 1.876*10^35 pounds of money will buy you 1.01*10^35 troy ounces of gold, which means that the price of gold (in 1777) is 1.876/1.01 = 1.857 pounds per troy ounce.
In the second case, the amount of money accumulated since Jesus's birth is (1.06)^(1772-(-4)-1) = (1.06)^1775 = 8.278*10^44 shillings * (1 pound/20 shillings) = 4.139*10^43 pounds. This amount of money will buy 7.775*10^42 oz of gold, for a price of 4.139/7.775 * 10^1 = 5.323 pounds per troy ounce.
So in one case Price says a troy ounce of gold costs 1.857 pounds, and in the other case he says it costs 5.323 pounds -- an almost 3-fold difference. (And are these prices historically accurate?) This discrepancy by Price is very suspicious. (Price has a little wiggle room with his wording "greater" rather than "equal to" or "about", but still.) Did one of us make a mistake in our arithmetic? (Somebody please check.) Am I the first person in 2006-1774 = 232 years to actually check Richard Price's calculations?
Mark Spahn (West Seneca, NY) |
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Barry Schwarz
science forum beginner
Joined: 30 Apr 2005
Posts: 31
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| Posted: Mon May 22, 2006 12:54 am Post subject:
Re: gold balls
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On Sun, 21 May 2006 05:21:42 -0400, "Mark Spahn" <mspahn@localnet.com>
wrote:
| Quote: | In an article in the May 2006 Harper's magazine, Michael Hudson says in an article titled "The New Road to Serfdom: an illustrated guide to the coming real estate collapse" (page 43):
The eighteenth-century philospher Richard Price identified this miracle
of compound interest and observed, somewhat ruefully, that had he
been able to go back to the day Jesus was born and save a single penny
-- at 5 percent interest, compounded annually -- he would have earned
himself a solid gold sphere 150 million times bigger than Earth.
Actually, Price worded his statement a little more clearly (Does "150 million times bigger" refer to diameter, or volume?):
"Money bearing compound interest increases at first slowly. But, the rate of increase being continually accelerated, it becomes in some time so rapid, as to mock all the powers of the imagination. One penny, put out at our Saviour's birth to 5 per cent compound interest, would, before this time, have increased to a greater sum, than would be contained in a hundred and fifty millions of earths, all solid gold. But if put out to simple interest, it would, in the same time, have amounted to no more than seven shillings and four pence half-penny.
?????????????????????????????????????????????????????????????????????5???????????1??????????????????????1?5000??????????????????????????????????????????????????????????7????4?????????????????.?????
?Geld, das Zinseszinsen tragt, wachst anfangs langsam; da aber die Rate des Wachstums sich fortwahrend beschleunigt, wird sie nach einiger Zeit so rasch, das sie jeder Einbildung spottet. Ein Penny, ausgeliehen bei der Geburt unsers Erlosers auf Zinseszinsen zu 5%, wurde schon jetzt zu einer grosren Summe herangewachsen sein, als enthalten ware in 150 Millionen Erden, alle von gediegnem Gold. Aber ausgelegt auf einfache Zinsen, wurde er in derselben Zeit nur angewachsen sein auf 7 sh. 4 1/2 d. "81
[Marx: Das Kapital, S. 3302 ff. Digitale Bibliothek Band 11: Marx/Engels, S. 6616 (vgl. MEW Bd. 25, S. 407 ff.)]
And in 1772 Price wrote:
"A shilling put out to 6% compound interest at our Saviour's birth" (presumably in the Temple of Jerusalem) "would... have increased to a greater sum than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn's orbit."
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
?1 sh., ausgelegt bei der Geburt unsers Erlosers (also wohl im Tempel von Jerusalem) ?zu 6% Zinseszinsen, wurde angewachsen sein zu einer grosern Summe als das ganze Sonnensystem einbegreifen konnte, wenn in eine Kugel verwandelt von einem Durchmesser gleich dem der Bahn des Saturn.?
Okay. Let's check the price of gold in these two examples. Do we get a similar price in each case?
A few preliminaries...
The price of gold is normally stated as a price per troy ounce.
How many troy ounces are there in a cubic foot of gold?
foot = 30.48 cm, specific gravity of gold = 19.32, so ft^3 = (30.48 cm)^3 = 28,317 cm^3.
A cubic centimeter of water weighs 1 gram, and the specific gravity of gold means that a cubic centimeter of gold weighs 19.32 times an equal volume of water; that is, a cubic centimeter of gold weighs 19.32 g. So a cubic foot of gold weighs 28,317*19.32 = 547,084 g = 547 kg = about 1200 pounds (avoirdupois, not sterling).
A troy ounce = 31.1034768 g, so a cubic foot of gold weighs 547,084/31.1 = 17,589 troy ounces.
The formula for the volume of a sphere is (4/3)*pi*R^3, the radius of the Earth is 3,960 miles, and there are 5,280 feet in a mile, so the volume of the Earth in cubic feet is
(4/3)*pi*(3960 mi * 5280 ft/mi)^3 = 3.83*10^22 ft^3.
The volume of 150 million such Earths is 150 million times this, or
5.745*10^30 ft^3, and since each cubic foot of gold weighs 17,589 troy ounces, 150 million Earth-size gold balls amounts to 5.745*10^30*17,589 = 1.01*10^35 troy ounces of gold.
How many troy ounces of gold are there in a sphere whose radius is the distance from the Sun to Saturn (8.95*10^8 miles, says a reference)? The answer is
(4/3)*pi*(8.95*10^8 mi * 5280 ft/mi)^3 * 17,589 oz/ft^3 = 7.775*10^42 oz.
Now let's examine how much Price says these volumes of gold will cost.
In the first case (150 Earth-volumes of gold), the gold can be bought for 1 penny, compounded annually at 5%, for the number of years from Jesus's birth until 1774. Taking the year of Jesus's birth to be 4 B.C. (Are the lyrics of 'Jesus Christ Superstar' a good-enough historical source?), and remembering that there was no year Zero, the number of years is 1774-(-4)-1 = 1777 years. So the number of pence available in year 1777 is (1.05)^1777 = 4.502*10^37 pence. There are 12 pence per shilling and 20 shillings per pound sterling, so in British pounds this amount of money is 4.502*10^37 pence * (1 pound/240 pence) = 1.876*10^35 pounds. So, according to Price, 1.876*10^35 pounds of money will buy you 1.01*10^35 troy ounces of gold, which means that the price of gold (in 1777) is 1.876/1.01 = 1.857 pounds per troy ounce.
In the second case, the amount of money accumulated since Jesus's birth is (1.06)^(1772-(-4)-1) = (1.06)^1775 = 8.278*10^44 shillings * (1 pound/20 shillings) = 4.139*10^43 pounds. This amount of money will buy 7.775*10^42 oz of gold, for a price of 4.139/7.775 * 10^1 = 5.323 pounds per troy ounce.
So in one case Price says a troy ounce of gold costs 1.857 pounds, and in the other case he says it costs 5.323 pounds -- an almost 3-fold difference. (And are these prices historically accurate?) This discrepancy by Price is very suspicious. (Price has a little wiggle room with his wording "greater" rather than "equal to" or "about", but still.) Did one of us make a mistake in our arithmetic? (Somebody please check.) Am I the first person in 2006-1774 = 232 years to actually check Richard Price's calculations?
Mark Spahn (West Seneca, NY)
|
It may depend on what figures Price used for Earth's radius, Saturn's
orbit, and year of birth. Or even if he used the same figures for
both calculations. What were the accepted values in the 1770s.
For example, if he used Re as 3000 miles, Rs as 9.5E8, and year -1,
the two prices compute to 3.513 and 3.525. More reasonably, 3500 and
11e8 produce 2.21 and 2.27
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Mark Spahn
science forum addict
Joined: 07 Jul 2005
Posts: 62
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| Posted: Mon May 22, 2006 9:15 am Post subject:
Re: gold balls
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Barry,
I didn't consider the possibility that in 1772 and 1774 Richard Price used values for the radii of the Earth and of the orbit of Saturn that were different from the modern values of r = 3963 mi and R = 8.95E8 mi. Taking your hint, and letting Y be the number of years from the birth of Jesus until 1772, the price of gold (in pounds sterling per troy ounce) if the money derived from one penny at 5% compound interest for Y+2 years will buy 150 million Earth-size gold balls is
(1.05)^(Y+2) pence * (1/240) pound/pence
-------------------------------------------------------------------------------
150E6 * (4/3)pi * (r mi * 5280 ft/mi)^3 * 17589 troy ounces/ft^3
and the price of gold if the money derived from one shilling at 6% compound interest for Y years will buy a gold ball of the same radius as the radius R of Saturn's orbit is
(1.06)^Y shilling * (1/20) pound/shilling
----------------------------------------------------------------------.
(4/3)pi * (R mi x 5280 ft/mi)^3 * 17589 troy ounces/ft^3
Setting these two gold prices equal to each other, the relationship between R, r, and Y that I get (check my arithmetic!) is
R/r = cube root[1.6326E9*(1.06/1.05)^Y].
For Y=1772-(-4)-1 = 1775, this comes to R/r = 321,066,
compared with the modern value of R/r = 8.95E8/3963 = 225,839,
which is still a considerable discrepancy.
I do not know where to find the accepted values in the 1770's
for the radii of Earth and of Saturn's orbit.
-- Mark
"Barry Schwarz" <schwarzb@doezl.net> wrote in message news:6pv17294fgmh1erag3fl0d8fv25iaavrm1@4ax.com...
On Sun, 21 May 2006 05:21:42 -0400, "Mark Spahn" <mspahn@localnet.com>
wrote:
| Quote: | In an article in the May 2006 Harper's magazine, Michael Hudson says in an article titled "The New Road to Serfdom: an illustrated guide to the coming real estate collapse" (page 43):
The eighteenth-century philospher Richard Price identified this miracle
of compound interest and observed, somewhat ruefully, that had he
been able to go back to the day Jesus was born and save a single penny
-- at 5 percent interest, compounded annually -- he would have earned
himself a solid gold sphere 150 million times bigger than Earth.
Actually, Price worded his statement a little more clearly (Does "150 million times bigger" refer to diameter, or volume?):
"Money bearing compound interest increases at first slowly. But, the rate of increase being continually accelerated, it becomes in some time so rapid, as to mock all the powers of the imagination. One penny, put out at our Saviour's birth to 5 per cent compound interest, would, before this time, have increased to a greater sum, than would be contained in a hundred and fifty millions of earths, all solid gold. But if put out to simple interest, it would, in the same time, have amounted to no more than seven shillings and four pence half-penny. [This was written in 1774.]
And in 1772 Price wrote:
"A shilling put out to 6% compound interest at our Saviour's birth" (presumably in the Temple of Jerusalem) "would... have increased to a greater sum than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn's orbit."
Okay. Let's check the price of gold in these two examples. Do we get a similar price in each case?
A few preliminaries...
The price of gold is normally stated as a price per troy ounce.
How many troy ounces are there in a cubic foot of gold?
foot = 30.48 cm, specific gravity of gold = 19.32, so ft^3 = (30.48 cm)^3 = 28,317 cm^3.
A cubic centimeter of water weighs 1 gram, and the specific gravity of gold means that a cubic centimeter of gold weighs 19.32 times an equal volume of water; that is, a cubic centimeter of gold weighs 19.32 g. So a cubic foot of gold weighs 28,317*19.32 = 547,084 g = 547 kg = about 1200 pounds (avoirdupois, not sterling).
A troy ounce = 31.1034768 g, so a cubic foot of gold weighs 547,084/31.1 = 17,589 troy ounces.
The formula for the volume of a sphere is (4/3)*pi*R^3, the radius of the Earth is 3,960 miles, and there are 5,280 feet in a mile, so the volume of the Earth in cubic feet is
(4/3)*pi*(3960 mi * 5280 ft/mi)^3 = 3.83*10^22 ft^3.
The volume of 150 million such Earths is 150 million times this, or
5.745*10^30 ft^3, and since each cubic foot of gold weighs 17,589 troy ounces, 150 million Earth-size gold balls amounts to 5.745*10^30*17,589 = 1.01*10^35 troy ounces of gold.
How many troy ounces of gold are there in a sphere whose radius is the distance from the Sun to Saturn (8.95*10^8 miles, says a reference)? The answer is
(4/3)*pi*(8.95*10^8 mi * 5280 ft/mi)^3 * 17,589 oz/ft^3 = 7.775*10^42 oz.
Now let's examine how much Price says these volumes of gold will cost.
In the first case (150 Earth-volumes of gold), the gold can be bought for 1 penny, compounded annually at 5%, for the number of years from Jesus's birth until 1774. Taking the year of Jesus's birth to be 4 B.C. (Are the lyrics of 'Jesus Christ Superstar' a good-enough historical source?), and remembering that there was no year Zero, the number of years is 1774-(-4)-1 = 1777 years. So the number of pence available in the year 1774 is (1.05)^1777 = 4.502*10^37 pence. There are 12 pence per shilling and 20 shillings per pound sterling, so in British pounds this amount of money is 4.502*10^37 pence * (1 pound/240 pence) = 1.876*10^35 pounds. So, according to Price, 1.876*10^35 pounds of money will buy you 1.01*10^35 troy ounces of gold, which means that the price of gold (in 1774) is 1.876/1.01 = 1.857 pounds per troy ounce.
In the second case, the amount of money accumulated since Jesus's birth is (1.06)^(1772-(-4)-1) = (1.06)^1775 = 8.278*10^44 shillings * (1 pound/20 shillings) = 4.139*10^43 pounds. This amount of money will buy 7.775*10^42 oz of gold, for a price of 4.139/7.775 * 10^1 = 5.323 pounds per troy ounce.
So in one case Price says a troy ounce of gold costs 1.857 pounds, and in the other case he says it costs 5.323 pounds -- an almost 3-fold difference. (And are these prices historically accurate?) This discrepancy by Price is very suspicious. (Price has a little wiggle room with his wording "greater" rather than "equal to" or "about", but still.) Did one of us make a mistake in our arithmetic? (Somebody please check.) Am I the first person in 2006-1774 = 232 years to actually check Richard Price's calculations?
Mark Spahn (West Seneca, NY)
|
It may depend on what figures Price used for Earth's radius, Saturn's
orbit, and year of birth. Or even if he used the same figures for
both calculations. What were the accepted values in the 1770s.
For example, if he used Re as 3000 miles, Rs as 9.5E8, and year -1,
the two prices compute to 3.513 and 3.525. More reasonably, 3500 and
11e8 produce 2.21 and 2.27
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Peter Webb
science forum Guru Wannabe
Joined: 05 May 2005
Posts: 192
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| Posted: Tue May 23, 2006 12:57 am Post subject:
Re: gold balls
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The earth-Sun distance was first determined in 1770 or 1771, as a result of the observation of the 1769 transit of venus. This provided the earth-Sun distance to within about 2.5%; using Newton's laws (or even Keplers laws, which had been known for years) this allows the orbital distance of Saturn to be calculated to within 2.5%. The example of Saturn's orbit was probably used as an example by Richard Price because the size of the solar system had just been determined accurately for the first time. An error of 2.5% on orbital distance is an error of 7.5% in volume of the sphere of the same radius.
http://www.vt-2004.org/Background/Infol2/EIS-F3.html
BTW, the 1769 transit is probably why I speak English and not French or Dutch - Captain Cook discovered the east coast of Australia on his expedition to observe the transit from Tahiti. Without this, it is unlikely that the English would have been the first to colonise Australia.
Regards
Peter Webb
"Mark Spahn" <mspahn@localnet.com> wrote in message news:127309u80ocg4d5@corp.supernews.com...
Barry,
I didn't consider the possibility that in 1772 and 1774 Richard Price used values for the radii of the Earth and of the orbit of Saturn that were different from the modern values of r = 3963 mi and R = 8.95E8 mi. Taking your hint, and letting Y be the number of years from the birth of Jesus until 1772, the price of gold (in pounds sterling per troy ounce) if the money derived from one penny at 5% compound interest for Y+2 years will buy 150 million Earth-size gold balls is
(1.05)^(Y+2) pence * (1/240) pound/pence
-------------------------------------------------------------------------------
150E6 * (4/3)pi * (r mi * 5280 ft/mi)^3 * 17589 troy ounces/ft^3
and the price of gold if the money derived from one shilling at 6% compound interest for Y years will buy a gold ball of the same radius as the radius R of Saturn's orbit is
(1.06)^Y shilling * (1/20) pound/shilling
----------------------------------------------------------------------.
(4/3)pi * (R mi x 5280 ft/mi)^3 * 17589 troy ounces/ft^3
Setting these two gold prices equal to each other, the relationship between R, r, and Y that I get (check my arithmetic!) is
R/r = cube root[1.6326E9*(1.06/1.05)^Y].
For Y=1772-(-4)-1 = 1775, this comes to R/r = 321,066,
compared with the modern value of R/r = 8.95E8/3963 = 225,839,
which is still a considerable discrepancy.
I do not know where to find the accepted values in the 1770's
for the radii of Earth and of Saturn's orbit.
-- Mark
"Barry Schwarz" <schwarzb@doezl.net> wrote in message news:6pv17294fgmh1erag3fl0d8fv25iaavrm1@4ax.com...
On Sun, 21 May 2006 05:21:42 -0400, "Mark Spahn" <mspahn@localnet.com>
wrote:
| Quote: | In an article in the May 2006 Harper's magazine, Michael Hudson says in an article titled "The New Road to Serfdom: an illustrated guide to the coming real estate collapse" (page 43):
The eighteenth-century philospher Richard Price identified this miracle
of compound interest and observed, somewhat ruefully, that had he
been able to go back to the day Jesus was born and save a single penny
-- at 5 percent interest, compounded annually -- he would have earned
himself a solid gold sphere 150 million times bigger than Earth.
Actually, Price worded his statement a little more clearly (Does "150 million times bigger" refer to diameter, or volume?):
"Money bearing compound interest increases at first slowly. But, the rate of increase being continually accelerated, it becomes in some time so rapid, as to mock all the powers of the imagination. One penny, put out at our Saviour's birth to 5 per cent compound interest, would, before this time, have increased to a greater sum, than would be contained in a hundred and fifty millions of earths, all solid gold. But if put out to simple interest, it would, in the same time, have amounted to no more than seven shillings and four pence half-penny. [This was written in 1774.]
And in 1772 Price wrote:
"A shilling put out to 6% compound interest at our Saviour's birth" (presumably in the Temple of Jerusalem) "would... have increased to a greater sum than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn's orbit."
Okay. Let's check the price of gold in these two examples. Do we get a similar price in each case?
A few preliminaries...
The price of gold is normally stated as a price per troy ounce.
How many troy ounces are there in a cubic foot of gold?
foot = 30.48 cm, specific gravity of gold = 19.32, so ft^3 = (30.48 cm)^3 = 28,317 cm^3.
A cubic centimeter of water weighs 1 gram, and the specific gravity of gold means that a cubic centimeter of gold weighs 19.32 times an equal volume of water; that is, a cubic centimeter of gold weighs 19.32 g. So a cubic foot of gold weighs 28,317*19.32 = 547,084 g = 547 kg = about 1200 pounds (avoirdupois, not sterling).
A troy ounce = 31.1034768 g, so a cubic foot of gold weighs 547,084/31.1 = 17,589 troy ounces.
The formula for the volume of a sphere is (4/3)*pi*R^3, the radius of the Earth is 3,960 miles, and there are 5,280 feet in a mile, so the volume of the Earth in cubic feet is
(4/3)*pi*(3960 mi * 5280 ft/mi)^3 = 3.83*10^22 ft^3.
The volume of 150 million such Earths is 150 million times this, or
5.745*10^30 ft^3, and since each cubic foot of gold weighs 17,589 troy ounces, 150 million Earth-size gold balls amounts to 5.745*10^30*17,589 = 1.01*10^35 troy ounces of gold.
How many troy ounces of gold are there in a sphere whose radius is the distance from the Sun to Saturn (8.95*10^8 miles, says a reference)? The answer is
(4/3)*pi*(8.95*10^8 mi * 5280 ft/mi)^3 * 17,589 oz/ft^3 = 7.775*10^42 oz.
Now let's examine how much Price says these volumes of gold will cost.
In the first case (150 Earth-volumes of gold), the gold can be bought for 1 penny, compounded annually at 5%, for the number of years from Jesus's birth until 1774. Taking the year of Jesus's birth to be 4 B.C. (Are the lyrics of 'Jesus Christ Superstar' a good-enough historical source?), and remembering that there was no year Zero, the number of years is 1774-(-4)-1 = 1777 years. So the number of pence available in the year 1774 is (1.05)^1777 = 4.502*10^37 pence. There are 12 pence per shilling and 20 shillings per pound sterling, so in British pounds this amount of money is 4.502*10^37 pence * (1 pound/240 pence) = 1.876*10^35 pounds. So, according to Price, 1.876*10^35 pounds of money will buy you 1.01*10^35 troy ounces of gold, which means that the price of gold (in 1774) is 1.876/1.01 = 1.857 pounds per troy ounce.
In the second case, the amount of money accumulated since Jesus's birth is (1.06)^(1772-(-4)-1) = (1.06)^1775 = 8.278*10^44 shillings * (1 pound/20 shillings) = 4.139*10^43 pounds. This amount of money will buy 7.775*10^42 oz of gold, for a price of 4.139/7.775 * 10^1 = 5.323 pounds per troy ounce.
So in one case Price says a troy ounce of gold costs 1.857 pounds, and in the other case he says it costs 5.323 pounds -- an almost 3-fold difference. (And are these prices historically accurate?) This discrepancy by Price is very suspicious. (Price has a little wiggle room with his wording "greater" rather than "equal to" or "about", but still.) Did one of us make a mistake in our arithmetic? (Somebody please check.) Am I the first person in 2006-1774 = 232 years to actually check Richard Price's calculations?
Mark Spahn (West Seneca, NY)
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It may depend on what figures Price used for Earth's radius, Saturn's
orbit, and year of birth. Or even if he used the same figures for
both calculations. What were the accepted values in the 1770s.
For example, if he used Re as 3000 miles, Rs as 9.5E8, and year -1,
the two prices compute to 3.513 and 3.525. More reasonably, 3500 and
11e8 produce 2.21 and 2.27
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