what is the linear value of one knot at the equator?
The knot (/nɒt/) is a unit of speed equal to one nautical mile (1.852 km) per hour, approximately 1.15078 mph. The ISO Standard symbol for the knot is kn. ... The knot is a non-SI (International Standard) unit that is "accepted for use with the SI".[This is from Google] !!.
GOOD JOB!! Mr. BB. You sourced your quote, though Google isn’t the source. The quote is from: https://en.wikipedia.org/wiki/Knot_(unit)
So . . . no banana for you.
Also, your post is knot really an answer to his question. From the context, his question should be read as “what is the linear value of one nautical mile at the equator?”
Johannes von Gumpach makes the same error, using “knot” when he means “nautical mile” on page 253 of his book The True Figure and Dimensions of the Earth (1862)
I use a quote from Gumpach’s book to partly answer the question
The explanation however will appear as simple, when as it is remembered that the nautical mile is an angular, rather than a linear measure, being one of 360x60=21,600 parts of the Earth's equatorial circumference whatever be the true linear value of that circumference. Hence considered as a linear measure it has as yet no definite value and its correctness depends absolutely on the correct linear measurement of an equatorial degree. If therefore the circumference of the Earth is taken too great by 166 or 167 miles, the nautical mile being one of its equal parts, and the subdivisions of the nautical mile or knots of the log-line__by which the distance sailed by a vessel is actually measured—are likewise taken too great; and consequently, the linear distance sailed by a vessel when reduced to angular distance, is reduced by means of too great a unit of measure; whence the number of nautical miles sailed both by computation and by the log-line, falls short of the true number.
This book is in the public domain. Here’s a link for a high-quality PDF image copy of an original book in the NY Public Library archive collection. The next time I’m there, I may “check it out.”
Everyone should read this book—for both its highly erudite presentation of science and mathematics, and Gumpach’s elaborate and convoluted writing style. This book is a collection of wordy sentences, full of appositives, presented in nuanced, painful, pedantic detail. It’s a reasonable substitute for self-flagellation.
My favorite part is his criticism of Sir Issac Newton. I’m sure the Royal Astronomical Society received him with open arms and great fanfare.
Origin of the Knot
As GA points out, Mr. Gumpach's tome, while illustrative, does not quite cover all the bases. For instance....sailing an equatorial path is always tricky.......crossing the Dateline insures problems because one never knows whether he/she is measuring speed in current terms - or in yesterday's terms. What might appear to be great speed yesterday might only appear to be a cipher, today.
Furthermore, historically......."knots" were measured somewhat erratically. The once-accepted method was accomplished by the "chip log." Of course, finding logs at sea was sometimes as difficult as finding logs in Mathematics. So....if the ship carried livestock for provision of meat and/or dairy, the "cow chip" was sometimes an adequate substitute. In the "Horse Latitudes," the whole cow was sometimes thrown overboard. Lacking that, Mr. Newton himself was often shanghaied in port and thrown overboard later. (Not for any particular measurement purposes, but for the fact that few personages - if any - can abide a windbag scientist.)
So....the present dilemma remains.....the "knot" is an unspecified quantity. In fact, it is the inspiration for the term "naught" meaning "nothingness" or "nonexistence" or "insignificant." Therefore, I urge that we forget about chasing the quixotic and focus on the more attainable. For instance, the search for the Yeti immediately comes to mind.
I apologize if some of the facts I have laid out are errrant. However, mostly I told the truth....mostly........
Your Humble Servant and WebCalc Historian,
Sir CPhill, Esq