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Curious old navy math techniques.
#1
Greetings,  gentlemen.  I found a  couple  of interesting  old  books  which,  considering  lockdowns  and  general inability to  cross   a street  without  damn mask,  may  help  to develop  not  very  useful  skills.  But  a  lot  of  people  have  used them  for  sure. One  of them  Mathematics for  navigators  by  Delwyn  Hyatt.  Yes, 1944. Of  course  it  is  kind  of  obsolete. But please  consider  the  fact it  was taught during  WWII to officers  who would  serve  in  the  real situations,  not in a  front of  a  simulator.  In  many  cases  its  methods  are kinda "not  straight  forward" to  say least.  But  some are  really  good.  For  instance,  Adding  and  subtracting  figures  from  left  to  right,  they  way  we write  them. I  tried  it  and  after  several  attempts  found  out  that  it is much  faster  than  traditional  ones. Also,  havesine  and other  formulas  presented  in  quite  different,  again,  not  easy  for  me to  understand,  wording  and  form.  Anyway,  real  navy  folks  really  used  it.  So,  as  a  due respect tio  their  work,  let's  try  to  understand their  daily  routines  doing  it.  Not  easy,  my  opinion.

Another one, Navigation and NAutical  Astronomy,  by  Dutton,  1943.  Again, thyere  are  a lot  of  info,  which  probably  none  of  us  would ever  use,  but  there are  also a  lot  of proves  and  explanations,  which  we  take  for granted  without  even  thinking  where did  it  come  from.  Moder editions  of  Dutton   don't  have  some  of  it.  I  consider  it  as of  a  hystorical   value.

I  am  always  fascinated  by  the  old methods  of  navigation, when Energizer'  Bunny  wasn't  even  conceived  yet.  No  batteries,  cloudy  skies,  rolling  horizon  and wet  and  misery  all  around.  And  they  did  it. Years ago  we  were taught  to  use sliding  rules.  It  gives  you  anything,  up  to  3  decimal.  Recently  saw  it  in  the  antique  shop  for  $271.  And  only  then  I  realized  how  ancient am  I.

Thank  you.

Respectfully,
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#2
Nice to hear about the publications, shipmate. Something I'd be very interested in investigating.

Just because their math techniques seem antiquated doesnt mean they were wrong. Just last night I was working on a small boat design. I used a slide rule to perform every calculation and had lots of fun, but there was a certain problem with which i had trouble. So instead of continuing with decimals in that problem I tried using a fraction technique (improper fractions) learned from an old naval architecture book I've been reading and the problem worked out ok. Using fractions the old fashioned way uncomplicated the math in this instance and allowed me a better look at what was going on. As a kid in school I was taught to avoid improper fractions and I have my whole life. Now I resent those educators for narrowing my mind.

My new moto: THERE IS NOTHING IMPROPER ABOUT IMPROPER FRACTIONS

That slide rule you saw in the antique store was well overpriced. Go to garage and yard sales and you can find them for a small fraction of the shop price. Sometimes you can get them for free. Of course there are rare slide rules out there for which a collector might pay a high price, but normally slide rules are cheap. Keep looking, slide rules are not rare. There are warehouses still full of them. I just bought a perfect 10 inch engineering slide rule for $14.

My question is, are the books you mentioned available as pdf downloads?

Cheers.
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#3
Thanks  for  the  response. Yes,  I  know,  that  that  price  for  that  particular  slide ruler  meant  it  belonged  to  Captain James Cook  or  Professor E. Fermi.  At  least.  One  of  the  best  are  the  ones  that  were  manufactured  in  Germany,  before  WWII. They  were  kind  of  slightly  yellowish  in  color  because  real  ivory  was  used.  Precision  and qualiity-  not  matched.  But  for  a  regular  calcs  any  slide  ruler  would  work. By  the  way,  in  Chech Republic  they  made  it with a real  big  magnifying  glass  making  calculations very  handy.  Regrading  fractions.  Yes,  I  also  had  my  time  with  educators regarding  that  issue. Found  it later  that there  iis  no  problem  in  working  with  that  kind  of  fractions  whatsoever.  
Regarding books.  Math  for  navigators I  bought  on  Amazon,  about  $ 10.00 Plus  shipping  and  handling.  Dutton  1944,  and  I'm  not  kidding,  was  left  on  the top of  the  garbage  can.  So  it  was a really  free  lunch.  Maybe  later,  if  you  want,  I'll  try  to  scan  TAble  of  Content, and let  me know  what  section  you  and other  gentlemen  would  like  to  get, so  I'll  try  to  scan  it. Book is  only 106  pages  long,  and  kind  of  half-size.

MAybe  pdf  is  available. Just  don't  know.
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#4
Good on you.

Dutton is a big name in marine circles. To accept one of his books left on the garbage was smart - as long as the book doesnt smell too bad...

The other book sounds familiar but I just can't remember if I read it. Reading the contents page might serve to remind me.

BTW... Sometimes you can find slide rule accuracy to 4 or more digits. Some accurate slide rules were made in 20 inch lengths, a few even longer - more accuracy comes with slide rule length, but its not convenient to carry a 20 inch slide rule in a brief case.

Thanks for your post. I like to write stories here but it's like I'm talking to myself most of the time. Years ago there were more folks here on this site. According to the number of views there are plenty of people who visit the posts, but very few actually say anything.

Are you from czechoslovakia? My family name immigrated from there 150 years ago on a sailing ship. I may be related somehow to president Benis.
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#5
Of course,  I  do  believe that  slide  ruler  can  be  customized  to any  size  of  inner  pocket  or a  briefcase.  Sir  Winston' technical  adviser  always  had  one  slide  ruler  in  his  pocket.  Just  in a  case. Once  they were  sitting  in  the empty  hall waiting for a meeting  to  start.  Sir  Winston  asked  his Science-technical  advisor:  Can  you  tell  me  how  much  whiskey  did  I  drink  in  my  lifetime?  His  technical  advisor  took  his  truthful   slide  ruler,  made  some  estimations and said: Well,  My  Lord,  it  would  fill this  room  up to  the  arm-chair  height."  Sir  Winston  took a look  at  the  arm-chair  then  raised  his  eye  to  the  celling  and  said:  Damn,  so  much  to  do  and  so  little  time  left."  Yes,  slide rulers  are  very  handy.  Not  sure 4 decimals  are  needle.  Most  engineering  calcs  I  did  during  my  career required two  decimals only.,  NAvig  trig  would  not  require  more.  Anyway,  plotting  anything less that a thickness of a  pencil  lead  or compass  needle  isn't not  practical  and  a little bit  ona  side of  early  paranoya.

Yes,  I  will  scan n  a  Table  of Content.  Will  be  sometimes  next week.  And  I  think  the  fact  other members  are  reading  the  posts is a  very good  sign. Unless it  is a very  specific  navig.  question/problem  they  just read  such  stuff  like  this  one  for  info  only. But  if  you  ask a specific  nav.  question-you  will  get very  qualified and  friendly responses. My  personal  experience.
NO,  I'm not  from  Czechoslovakia. Never been  over  there  but consider  its capital,  Prague  a heart  of  Europe. And  this  is  NOT  my  opinion.  It  is well-known  fact.  Cultural  and  historical for  sure.  I  don't  want  to  discuss  what  is  going  on  in  Europe  anyway,  just  waste  of  time  and space,   and Czech  republic is not  an  exception.  Too  obvious  and  very sad. One  of my favorite   authors  is  from  that  country.  And  of  course  my relatives-4th  generation  Americans  also  arrived  to these  shores  on a  steamer.  Boing flights were  overbooked.
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#6
Great reply,
but I can think of a circumstance in which 4 or more slide rule places might come in handy - such as if i should lend 347,250 and need to know my exact return at 3.72%. I'd want a slide rule accurate to 6 places, maybe 8... the ship often lent money or gave credit to sailors. The captain just took it from their wages.

Old nav or sailing books often had a chapter on ship's finances and the buying of overseas supplies and cargo. I suppose they did their important 6 digit figuring longhand. Even log tables might not account for every penny.

However, you are right in engineering terms. Why provide for 4 digit accuracy when the machinery is only capable of 3.

Great story about Winston... where in the world did you ever get that info... funny, yet a poignant truism.

I'm with you... I hardly give Europe any notice... I live in the Philippines.
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#7
Here is the closest thing I could find to the Hyatt book

http://www.survivorlibrary.com/library/t...n_1921.pdf
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#8
Thank  you.

You  are  right.,  i can't  imagine  anyone using  a caliper ,  even  micrometer,  to  get  more than  two decimal.  Yes,  one may  get  it  and  what? To boast  about  it  to a  first blonde  in a  Singles?  What  about  that  little  drum  ona  sextant?  There is  practicality in  everything, at  least  I see  it  this  way,  in  navig  that  preclude  us  of scientific  exorcises  Just  Because.  I  think  nobody  expressed  it  better  than  great  CAptain  Lecky  in  his  Wrinkles  in  Practical  NAvigation. When  he  conducted  some  experiments  ona  shore-there  was a  very  good  practical reason  why  did  he  do  it.

The  book  you  found  in  pdf  format is  much better  than  the  one  I have  written  about.  I  mean  by  content.  The  book  I  have  in  my  possession  is  oriented  on  students  who  like  math like a bride  likes a  pimples  on  her  face.  Not they were  hating  it. No  They  just  did not  know it. I  tried  to  follow  some  directions  and  i  have so  much  sympathy  for  those  miserables.  It  is  detailed,  kind  of  intuitive,  but  for  me  it  was difficult. Again,  just a  historical  one.  

Am  a  big  fan  of  Sir  Winston.  HAve  quite  a  lot  of  books written  by  him  and  a little  bit  about  him.  He  was  The Personality  in  the  best  meaning  of  this  word.  His career took  ups  and  downs  many  times. And  his  childhood  was  kind  of  specific.  But  nobody  can  deprive  him  ofm  his  personal  courage  and absolutely  fantastic determination. just  one  fact  .  He  flew  to  the  US  to  the  meeting  with  FDR duing  the  war in a  military  cargo  plane  and  his  personal doctor  was  next  to  him  because  of a real  possibility  of  cardiac  arest. In  Casablanka  he  almost  died from a  bout  of  pnemonia  and still was  able  to  conduct important  meeting.  Exceptional  man. Yes,  made  mistakes. And  who  didn't .  Anyway,  believe  it  or  not,  even  in  Soviet  Russia  when  asked  whom  they  considered the  greatest  person  of  20 century  Russians answered Churchill,  not  Uncle  Joe.  Tells a lot. 

Live  in  States.
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#9
Greetings,
As I've wrote, I will scan a few pages of the books just mentioned above. If anyone has any interest in more scanned pages-please, let me know. Again, it is kind of of historic interest.
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#10
If you have a chapter on how to use meridional parts that would be helpful. Or perhaps you could explain instead.

Thanks
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#11
In Bowditch and Dutton meridional parts explained in a very detailed manner
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#12
These  are scanned images  of  pages  from  the  old math  book.  Please,  see the  attachments. Thanks./


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