What exactly does this notation in an old letter mean?

Question

This is from a letter sent around 1859:

I think the curly braces are just to be treated like parentheses, so that part is fine (if that's not the case, do tell), but I struggle to understand what that dot represents. From context I would assume that it's actually a decimal point, but when it's mixed with the degree symbol in that manner inside the braces it almost looks more like a multiplication symbol (but that doesn't really make sense in the other expressions, like "1 dot 00", since in that case that term would just be 0). So, how exactly should I be reading this? Does "585° dot 26" actually mean 585.26°?

Answer 1

The translation that Tyma Gaidash links to in the comments explains what these terms mean: they are the orbital positions of Venus, Earth, Jupiter, and Saturn at time $t$ years. So the value for a given planet is $360^\circ/P_\text{orb}$, where $P_\text{orb}$ is its orbital period in earth years.

The Royal Astronomical Society of Canada's Calgary Centre has this web page which gives the orbital periods of the planets in years to a very high precision (strangely, it gives the orbital period of Earth as $1.0000007$ years, which perhaps somebody can explain in the comments):

$$\begin{array}{c|c|c|} & P_\text{orb} & 360^\circ/P_\text{orb} \\ \hline \text{Venus} & 0.61517237 & 585.2018^\circ \\ \hline \text{Jupiter} & 11.8663142 & 30.3380^\circ \\ \hline \text{Saturn} & 29.47305083 & 12.2145^\circ \\ \hline \end{array}$$

This clearly shows that "585° dot 26" should be interpreted as $585.26^\circ$, and similarly for Jupiter and Saturn. The third column matches your quoted figures to better than one part in $2000$; if we interpreted the last two digits as arcminutes, the match would be no better than one part in $80$.

Updated to add: The Calgary Centre's Larry McNish was kind enough to reply to my query about that $1.0000007$:

It was the result of applying Kepler's third law to the published JPL values for the planetary orbits as they were back in 2009.

I've attached the spreadsheet (which had a JPL value of the semi-major axis for the Earth's orbit as 1.00000018 a.u.)

Either because I used too many digits of precision in the answer or because it was measured as sidereal years.

365.256622 / 1.0000007 = 365.25636632054357561949706635205 which is very close to the number of days in a sidereal year https://en.wikipedia.org/wiki/Earth%27s_orbit 365.256363004 days[13]

Answer 2

It's a smaller form of the unit( ° ) known as minutes, 1°= `60 or 60 minutes, there's also another unit known as seconds, 60 seconds (`` 60 ) = 1 minute.

Just to clarify, it isn't related to the unit of time.

Answer 3

This is a decimal place as the $3.73$ excludes arcminutes.