# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Errors in Cotter's book, updated**

**From:**George Huxtable

**Date:**2003 Jan 8, 10:47 +0000

Here's an updated list of some things I suspect are wrong in Charles H Cotter's otherwise-excellent book "A History of Nautical Astronomy". Jan Kalivoda has kindly helped by confirming some earlier diagnoses and adding others of his own. If any listmember has others to add, I would be pleased to receive them. I doubt if my list, below, is at all exhaustive: I have not deliberately searched out errors; these are just the ones I have stumbled across in my own reading. It might be useful to print out the list below and insert it into your copy of Cotter. The paging corresponds to my Hollis & Carter 1968 edition, the last page of its index being 387.. I think there was also a US edition: the paging was probably identical. I doubt if there were any later editions. Here goes- =========================== page 49. The third paragraph starts- "The civil day at sea commenced at midnight", which is correct. In the next paragraph Cotter states "The civil day commenced when the Mean Sun culminated at noon." which is contradictory, and wrong ========================== page 118, foot of. Cotter states "Augmentation = Moon's semidiameter x sine apparent altitude". This is wrong. It would be roughly true to state instead- Augmentation (in minutes) = Moon's semidiam. (in degrees) x sine apparent altitude but more accurate to say- Augmentation (in minutes) = Moon''s semidiam. (in minutes) x sine apparent altitude / 55. ========================== page 120, 2nd line, Cotter says- "... body Y, which has the same APPARENT place as body X". but fig 5 shows body Y at the same TRUE place as body X. ========================== page 210-212, Borda's method. Here I think Cotter has got into a real mess with his trig. The equation that precedes equation (Y) is given as - (sin D/2)^2 = sin{(M+S)/2 + theta} sin {(M+S)/2 - theta} Here, he has got the last term the wrong way round and it should be- (sin D/2)^2 = sin{(M+S)/2 + theta} sin {theta- (M+S)/2} so in consequence, in equation (Y), the second sine term in the product of two sines is also reversed. Similarly in the last equation on page 210, for log sin D/2, the last term in the sum should end up as log sin (theta- (M+S)/2), not log sin ((M+S)/2 - theta), as Cotter gives it. If you slavishly follow Cotter's steps, you will end up taking the log of a negative quantity, which is an impossibility. I think Cotter has realised there's something wrong, without being sure what it is, because on page 211 he states the rules in words for clearing the distance, and in rule 5 he says- "Find the sum of and difference between theta and phi". Because he hasn't defined here which way round to take that difference, the navigator will presume that he should subtract in such a direction as to give a positive answer. So that bit of "fudging" has got Cotter out of his problem. In fact the subtraction should ALWAYS be theta - phi, and NEVER as stated at the foot of 210, phi - theta. On line 3 of page 212, that's what he has written down in the calculation, theta - phi, just as it should be. ========================= There's an additional error in Rule 5, page 211, in that the last sentence should not read- "The result is the sine of half the true lunar distance, that is D/2.", but instead- "The result is the LOG sine of half the true lunar distance, that is D/2." ======================== page 226, Dunthorne's method. Dunthorne's is in fact a rigorous method of clearing the lunar distance, but Cotter has included it in his list of approximate methods ======================== page 237. For a navigator, it may be useful to know that alpha Aquilae is more familiar as Altair, alpha Arietis as Hamal, and alpha Pegasi as Markab. ========================= page 250. The four equations shown on this page all use the quantity s, but I cannot find any definition of s. I presume that s is half the perimeter of the PZX triangle, so- s = 1/2 (ZX + PZ + PX) In the third expression, for cos P/2, a quantity s with a subscript 2 appears. That little 2 appears to be a misprint should be erased. ======================== page 264. Cotter says, about finding the moment of noon by equal Sun altitudes- "By taking the equal-altitude sights shortly before and after noon the necessity for applying a correction for the change in the Sun's declination in the interval is obviated, since any such change will be trifling." I disagree with Cotter's analysis here. It seems to me that the correction necessary for a changing declination does not reduce as the interval chosen gets closer to noon. =========================== page 265. Re Hall's rule. Cotter introduces delta-d as the correction in seconds of time.. This ought to be delta-h and in the equation near the foot of the page, cos h should be cosec h. page 266. Similarly, in the equation at the top of this page cos h should be cosec h. ========================== page 354. Napier's rule. I suspect that the second expression, shown as- cos x = cos y cos z is wrong, and should be- cos y = cos x cos z ========================== It's rather disappointing that so many errors can be found in Cotter, and indicates some degree of carelessness in the checking and proofreading. But we can all get things wrong, as I have good reason to know... The prevalence of these detected errors leaves me suspecting that there may be many more, lurking as-yet unseen. They detract somewhat, but not a lot, from the value of Cotter's book, which remains by far the best source I know to treat the development of astronavigation, and is a wonderful goldmine of references. George Huxtable.