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Henry Halbot, you wrote:
"Although again probably past the prime era of the method, it reinforces my 
often stated opinion that, given more time, innovation, and practice, it 
would have been significantly perfected in its accuracy and consistency. "

Well, the methods described in that article were not new, and I don't think 
they represent any approach to perfection. In fact, I see rather the 
opposite: advancing decadence.

I read this article some three or four years ago, and if I remember correctly, 
someone wrote a follow-up letter to the MNRAS pointing out that this was a 
known method for rating chronometers --known for decades. Indeed, a decade 
earlier, one T.N. Were related his experiences rating his chronometer by 
lunars and even then he referred to lunars in that decade as "too much 
neglected". The interesting change in the time elapsed between those two 
articles is that Were's results were published in the "Nautical Magazine" 
while Toynbee's results were relegated to the MNRAS --"Monthly Notices of the 
Royal Astronomical Society". I say "relegated" because the Nautical Magazine 
was a publication aimed at practicing navigators while the Monthly Notices 
were targeted to astronomers. The method had gone obsolescent, and its 
remaining advocates were primarily rediscovering aspects that were relatively 
common knowledge in the heyday of lunars.

By the way, I remember three or four follow-up letters to the MNRAS regarding 
Toynbee's article, so at least the astronomers enjoyed it!

And you wrote:
"We are also not advised as to whether or not the Captain had access to the 
newly calculated Lunar Tables which came out about the time of the published 
observations - I know only that the American Almanac first contained the new 
tables in 1855, but that does not necessarily mean that they might not have 
been available elsewhere before that date."

I consider it highly unlikely that he had any updated tables. But be advised 
that there are two separate improvements here. The improvement which was made 
in the American Ephemeris (and which somewhat surprised the Europeans) was 
due to a very simple revision. They took the established model of the Moon's 
motion, which had been in use since the early 19th century, reduced more 
recent observations, and re-generated the basic tables (for a modern analogy, 
they effectively re-calculated the "coefficients of the time series" used in 
the algorithms for calculating the hourly positions of the Moon). This had 
not been done in Britain in decades so the errors in the predicted positions 
were slowly building up. If lunars had mattered to any significant degree to 
British shipping at this point, they easily could have done the same thing. 

If you examine the first American Ephemeris and compare the lunar distance 
tables with the standard British Nautical Almanac for the same year, the 
American tables are moderately more accurate. The average errors are 
something like 30% smaller. When I compared these a few years ago, I found 
that one could get even better results, surprisingly, by averaging the 
British and American predictions. 

Just a few years after the first release of the American Ephemeris, the models 
of the Moon's motion were significantly improved, and these improvements were 
rolled out in later years in the various almanacs in Europe and the US. But 
it was too little, too late. By 1860, there were very few practitioners of 
lunars at sea.

I've posted it before, but for reference, here is T.N. Were writing about his 
experience with lunars in 1842:
"CHRONOMETERS AND LUNARS.

[After a preamble offering some revised positions for islands and points in the Indies...]

I would now beg to offer some remarks relative to chronometers, and the 
fearful consequences that may arise if we place too much confidence in them, 
which from their beautiful and improved construction we are now too apt to 
do, and neglect those observations of the Heavenly bodies (which can only be 
of use by their being in constant practice) when you may have confidence in 
them. 

On my outward voyage, I had a beautiful watch of Murray's, which differed only 
nine seconds, in my run from Portsmouth to the Great Ladrone (on the coast of 
China). I placed great reliance on this watch during my homeward voyage, 
after leaving the coast of Java, and as soon as the moon came in distance I 
obtained a few sets of sights which gave the watch a considerable error, 
nearly three minutes. At this time I imagined my distances must have been 
incorrect, but the day previous to getting on the L'Agulhas bank, and in a 
run of about thirty days from Java Head, I was fortunate enough to get the 
mean of some thirty or forty distances, and I was much astonished that they 
gave the watch an error of ninety miles to the westward. I also carefully 
observed the sun's semi-diameter, and this corresponding with the Nautical 
Almanac, gave me confidence in my sights, and shook my confidence in the 
chronometers. It also fortunately placed me on my guard, and as on rounding 
the land, I was in a position to make Cape L'Agulhas at daylight I did not 
bear away. I was running nine knots at the time, with a strong S.S.W. wind, 
and did not see the Cape until 2 P.M., having run since daylight about 80 
miles departure, which made the lunar sights as near correct as I could take 
the bearings of the land, at about four leagues distance in hazy weather. Had 
I been by chronometer, near the longitude of the Cape in the evening, I 
certainly should have borne away before morning, and had I done so, the 
melancholy fate of the ship which I commanded would, I fear, have been 
similar to the Arniston, Northumberland, and various others. 

How to account for this error in the watch has quite bewildered me, excepting 
it arose from magnetic attraction, as from some cause or carelessness a brace 
of pistols was placed close to the watches, which I had removed, directly I 
found the watches had altered their rates. The chronometer has since remained 
stationary, and retains the same rate as when I was off the Cape. 

On my passage towards England, after rounding the Cape, I took every 
opportunity of obtaining lunar distances ; and two days before I reached St. 
Helena, I spoke a ship which had also seen Cape L'Agulhas, and we differed 
seventy miles in our longitude. This startled me. But when I found my brother 
mariner had not taken any lunar sights, and having confidence in my 
instrument, I steered boldly for the island, and made it ahead about an hour 
before daylight. 

I was at St. Helena two days. Each day I got the Greenwich time from the 
observatory, and in taking the mean of my lunars about 100 distances, I was 
much pleased to find we only differed one second from each other. 

I would from these circumstances caution mariners, not to be too confident in 
their chronometers, and to lose no opportunity of obtaining lunar 
observations when practicable, and which I fear is now too much neglected, 
and which unless they are constantly practised can be of little avail, and 
can give no confidence to the observer. I have generally rated my 
chronometers by lunars, and have hitherto been fortunately correct in doing 
so, as they seldom retain the rate given by their constructors, and having 
two sextants, one of which being Troughton's, which as an instrument of 
confidence for navigation, is worth to me all the chronometers that were ever 
constructed. 

I have once before made some small contribution to your work, and am a 
subscriber from its commencement, and many an agreeable hour, I spend at sea 
in conning over its pages. Should yon think this worth inserting, or any part 
of it in your publication, I beg you will do so. 

I have the honour, &c., 
T. N. WERE, 
Commander of the Ship City of Derry. "

-FER




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