Did King George III pay too little for astronomers or too much for tea?

In the opening pages of his 1998 biography George III: A Personal History, Christopher Hibbert tosses a remarkable statement into a footnote just after describing the allowance of Frederick, Prince of Wales, at George III’s birth:

Because of the fluctuating rate of inflation and other reasons it is not really practicable to translate eighteen-century sums into present-day equivalents. Multiplying the figures in this book by about sixty should give a very rough guide for the years before 1793. For the years of war between 1793 and 1815 the reader should multiply by about thirty, and thereafter by about forty.

“Not really practical” is wonderful understatement: it’s barely possible to compare the prices of things today to those of a half-century ago, and the modern economy at least existed in cartoon back then. I could conceivably have been paid for programming computers back then, but it would be harder for me to get into the field. To go back 250 years — before electricity, mass markets, public education, mass production, general incorporation laws, and nearly every form of transportation not muscle or wind-powered — and try to compare prices is nonsense. We may as well ask how many haikus it would take to tell Homer’s Odyssey, or how many limericks Ovid’s Metamorphoses would be.

I don’t mean to pick on Hibbert, who is clear he knows there’s no real sense comparing money amounts across a quarter millennium. Yet most historians writing for a popular audience will include such an conversion factor, even as the majority of them admit it’s hard to compare prices then and prices now. So why do they do it?

One answer is that when we read that George III gave the astronomer William Herschel a pension of £200 a year, starting in 1782, we wonder: is that a lot of money? But whether a price is a lot of money depends on how much money one has, yes, and what the prices are on all the other things one might buy. A specialist in a particular era can get familiar enough with the prices of those other things so as to judge whether the King got his astronomers cheap. The normal lay reader will reject being stuffed full of the costs of astronomers, coffee, clothing, rent, roast beef, tea, and transportation to London in 1782 instead of getting a simple answer.

“Multiply this figure by about sixty”, a simple answer, also hides some powerful mathematical tools. We can accept that however the economy of today differs from that of 1782, one can’t pension an astronomer for just £200, and there’s little else we could expect to buy in London for the 1782 prices (with occasional surprises: Francis Sheppard’s London: A History mentions some West End leases with rights to renew in perpetuity, and renters still paying late 18th-century rates). The conversion factor is certainly greater than one. But there is obviously some upper bound, too; however much prices have risen, they’re not a hundred million billion trillion times greater than they were in 1782. There’s a correct conversion factor somewhere in that not quite tight range.

Could sixty be right after all? £200 times 60 gives us £12,000, which seems a bit low for astronomers, particularly as Herschel went on working. Wolfgang Schivelbush’s Tastes of Paradise says that in London in 1700 a pound of cheap tea cost 8 to 10 shillings; pretending to not notice this is outside the date range (it’s the nearest figure I could find) and using sixty anyway, that suggests £24 to £30 for the cost today. My check of Tesco’s web site (for PG Tips, loose tea, 500 grams) indicates I should be paying closer to about £3. It’s a bit more at my local supermarket (converting dollars to pounds), but it’s closer to £3 than £30.

This sixty is not looking very good, but it would be surprising if the costs of getting an astronomer and getting a pound of tea rose at the same rates for centuries. Considering all the other things there were to buy in 1782 and today, we’d expect sixty to be low for some and high for others. Is there any other number which could do better?

Would getting the price of astronomers right be worth it if we actually buy tea more often? Should we pay more attention to the cost of a house, or of beer soup, or the Encyclopædia Britannica instead?

It seems there must be some number to use as our conversion factor that best fits the challenge of converting a price from 1782 to one of today. Or to put the optimistic phrase on it, there must be a factor that makes the smallest error when used so. (I wonder whether “best fit” or “smallest error” is the optimistic phrasing.) Perhaps it is sixty, or something near sixty, that is as good as can be.

And if you’ve nodded slightly impatiently along with the idea that there is some number that best fits the challenge of converting 18th century to 21st century prices, and we may not know what it is exactly but we can put it within a range, then you’ve accepted much of what is needed to understand calculus, with a bonus of understanding differential equations and statistics, and some more esoterically-named fields like finite elements.

For all that, there’s still an astounding thing Hibbert did with this conversion factor.