The Scottish Satterthwaites

The Quaker records I look at are on Ancestry (a subscription site).
If you go into the card catalogue you can search for Quaker records - the collection you want is England and Wales Quaker records up to 1837. 1837 was when civil registration began and all the nonconformist organisations were invited to surrender their records. The Quakers did continue keeping records after this - for example Ancestry has latter Quaker records which Liverpool and Manchester meetings kept.

The Quakers records did change over time. By the time of John's birth they recorded a birth note.
If you put in John Satterthwaite born 1795 you should find

RG6/0935 QM Lancashire
On the twenty sixth day of the eighth month 1795
was born at the Lorn Furnace Airgileshire, North Britain
unto John Satterthwaite and Alice his wife
a son named John
witnesses
Mary MacDougall, Midwife
Elin McIntyre ?
Peggy McDougall
Ann Light????

Why was the record in Lancashire and not Scottish records?
John and Alice Satterthwaite at that time were the only Quakers in the Scottish highlands.
Where abouts in Scotland were they?
Near Oban
Why does it say North Britain?
Thats what they called Scotland at that time.
.....................................................................................
Looking for a quaker marriage between a John Satterthwaite and Alice, there is only one.
Then looking for children of John and Alice. They may have had 8 children.

RG6/0153 MM Swarthmore
John Satterthwaite son of John Satterthwaite of Tockhow in the parish of Hawkshead yeoman and Martha his wife.
And Alice Park daughter of Edward Park of Skelwith in the parish of Hawkshead yeoman and Agnes his wife.
Married on the Fifteenth day of the fourth month called April 1786 at Colthouse Meeting House.
Witnesses relations
John Satterthwaite
Martha Satterthwaite
Edward Park
Michael Satterthwaite

RG6/1079 MM Swarthmoor
-On the first day of the fifth month called May 1787
was born at Lorn Furness, Argile, North Britain
unto John Satterthwaite and his wife Alice a son
named Dodgson John Satterthwaite
no witnesses - I have found no other reference to him.
-On the seventh Day of the first month called January 1789
was born at Lorn Furness in Argyllshire, North Breton
unto John Satterthwaite and Alice his wife a daughter
named Agnes
no witnesses
-On the fifth day of the eleventh month called November 1790
was born at Ulverstone
unto John Satterthwaite Butcher and Alice his wife a daughter
named Mary not sure about this one
witnesses
Rich. Jackson
Mary Dodgson 
-On the Thirteenth day of the seventh month called July 1793
was born at Lorn Furnace in the Parish of Macarne, County of Airgile
unto John Satterthwaite and Alice his wife a daughter
named Alice
witnesses
Malcolm McLaurin, surgeon
Margaret Ashburner
Sarah Harriman?
-On the twenty-sixth day of the eighth month 1795
was born at Lorn Furnace, Airgileshire, North Britain
unto John Satterthwaite and Alice his wife a son
named John
witnesses
Mary McDougall, Midwife
Elin McIntyre?
Peggy Macdougll
Ann Light?
RG6/0934 QM Lancashire
-On the fifteenth day of the twelfth month 1797
was born at Lorn Furnace in the parish of Macarn
unto John Satterthwaite and Alice his wife a son
named Edward
witnesses
Malcolm McLaurine, surgeon
Sarah Harriman?
Nanncy? McIntyre
Ann Lightburn ??
RG6/1007 QM Lancashire
-On the twenty-fifth day of the Fifth month 1800
was born at Lorn Furnace, Argyllshire
unto John Satterthwaite and Alice his wife a son
named William
witnesses
Cicely? McLauran Midwife
Sarah Harriman
Ann Lightbourn?
-On the first day of the sixt month 1803
was born at Bowsteadyeats, Ulverstone
unto John Satterthwaite and Alice his wife a son
named Daniel
witnesses
M Redhead, surgeon
Marey Dodgson
(all the above are in the form of birth notes)
RG6/0875 MM Swarthmore from a table of births
Born twenty-eighth day of first month 1806 at Bowsteadyeats
Michael son of John Satterthwaite of Bowsteadyeats yeoman

From RG6/0875 for the birth of John in 1795 his father John is described as a Steward.

So to recap
John Satterthwaite married Alice Park in 1786 at Colthouse
children possibly Dodgson John born 1787
                            Agnes born 1789
                            Mary born 1790 ?
                            Alice born 1793
                            John born 1795
                            Edward born 1797
                            William born 1800
                            Daniel born 1803
Between 1800 and 1803 the family moved from Lorn Furnace in Scotland to Ulverstone area, where they had a farm called Bowsteadyeats.

google Colthouse meeting house for lots of beautiful photos
google Bowstead yeats
on discovery.nationalarchives.gov.uk is reference to conveyances for a messuage at Bowstead Yeats : families of keen of Dublin, Pirt of Bowstead Yeats; Colton of Egton, Dickinson of Ulverston, Ormandy of Mansriggs, Satterthwaite of Lorn Furnace, co. Argyll, Satterthwaite of Ulverson, Hodgson and Travers of Ulverstone, Machell of Pennybridge. These records are at Lancashire record office in Preston. I don't have any experience of looking at these kinds of records. But it does prove a link between Bowstead Yeats and Lorn Furnace.