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Guyou's Two Methods
From: Dave Walden
Date: 2011 Jun 30, 10:23 -0700

GUYOU's two methods

Your DR is 74-52W, 38-12N. UTC is 081707 on 7 Jun 2011. You have corrected observations of 3 stars:

Alkaid 23-53.8
Altair 59-55.3
Hamal 16-8.7

You discover that your inspection tables, short tables, calculator, laptop, even your backup flat Bygrave are all missing. Luckily you've been following NAVLIST, and have nine pages of a Spherical Meridional Parts table that you just xeroxed at hand. What to do? Fortunately, you have memorized Guyou's method for calculating a "time sight line of position" using just the MP table.

First, Alkaid:

d Dec 49 15.5 49.258 +49° 15.5' 0.8597 +North
L Lat DR 38 12 38.200 +38° 12.' 0.6667 +North

Ho 23 53.8 23.897 +23° 53.8' 0.4171

Dec + Ho 73.155 +73° 9.3' Addition
Dec - Ho 25.362 +25° 21.7' Subtraction

MP (Lat)= 2483.5 MP table look up
MP [ 90 - (Dec + Ho) ]= 1025.6 MP table look up
MP [ 90 - (Dec - Ho) ]= 5127.8 MP table look up

MP(Lat)+MP[ 90 - (Dec + Ho) ]=A 3509.1 Addition
MP[ 90 - (Dec - Ho) ]-MP(Lat)=B 2644.3 Subtraction

MP(x)=A; => x= 50.369 +50° 22.2' MP table look up
MP(x)=B; => y= 40.275 +40° 16.5' MP table look up

MP (90-x) = 2593.8 MP table look up
MP (90-y) = 3448.8 MP table look up

DIFFERENCE D -855.0 Subtraction

MP(90-Z)=C/2; => 90-Z= 44.899 +44° 53.9' MP table look up
MP(90-Pe)=D/2; => 90-Pe= 7.107 +7° 6.4' MP table look up

Azimuth, Z= 45.101 Subtraction
Local Hour Angle, LHA, Pe= 97.107 Subtraction

IF Dec > Hc, switch Z and Pe Pe 97.107 +97° 6.4'
Z 45.101 +45° 6.1'
(If star West, Zn=360-Z) Zn 314.899 +314° 53.9'

Now use LHA and GHA to calc Long

GHA 172 9.7 172.162 +172° 9.7'

AP Long (=LHA-GHA) -75.055 -75° 3.3' -West
AP Lat 38 12 38.200 +38° 12.' +North

So, at your AP of 38-12N, 75-3.3 W, you plot your LOP perpendicular to Zn=315

Then, Hamal.

Luckily, just before you try and calculate a time sight LOP for Altair, a star almost due south, while looking in your drawer for a new pencil, you find your old (1911) copies of Guyou's Nouvelles Tables de Navigation, Vol 1 and 2. This will give a quicker solution for your last star, Altair.

To get local hour angle to the nearest 20', we use AP long=74deg 59.5min. For lat, nearest 20' gives, AP lat=39deg 20min.

GHA 81 19.5 81.325 +81° 19.5'
D Dec 8 54 8.900 +8° 54.' 0.1553 +North
L Lat AP 38 20 38.200 +38° 20.' 0.6690 +North
calc fm GHA& AP Long Pe 6.333 +6° 20.' 0.1105 +West
Long AP -74 59.5 -74.992 -74° 59.5' -1.3089 -West
Ho 59 55.3 59.922 +59° 55.3' 1.0458

H+D= 68.822 +68° 49.3' =4129.3'
H-D= 51.022 +51° 1.3' =3061.3'

Volume 1,Table Gauche(H'+D')/2 1100.8'
Volume 1,Table Droite(H'-D')/2 2675.2'

Sum=H' 3776.0 +63° 56.0'
Diff=D' -1574.4' -26° 14.4'

Volume 2, Ze 12.6
Volume 2, He 3783.6'= +63° 3.6'

Zn= 192.6

H'-He (deg long at this lat)= -0.125 -0° 7.5' In nm, 5.9

So, just one opening of Volume 1, and one opening of Volume 2. Pretty quick!

(Please let me know where I can get these Volumes!)

Attached are scans of excel versions of the tables and calculations, sample MP tables from Friocourt and Inman (My copy of Inman has a hand sewn canvas cover and notations on the fly of ships it has served. I got it cheap since the seller said it was pretty well used. I consider myself lucky to have it!), extracts from Goyou's Novelles Tables, a plot, and the ICE data used to generate the problem. Descriptions of Guyou's methods can be found through Google Books and other sources.

Note also that Guyou was quite a fellow. He made contributions to mathematics, cartography, naval architecture, astronomy, and the French Academy, as well as navigation. I'm sure our French friends can tell us more.

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