The making of rockets in two parts, the first containing the making of rockets for the meanest capacity, the other to make rockets by a duplicate proposition, to 1000 pound weight or higher / experimentally and mathematically demonstrated, by Robert Anderson.
         Anderson, Robert, fl. 1668-1696.
      
       
         
           1696
        
      
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             The making of rockets in two parts, the first containing the making of rockets for the meanest capacity, the other to make rockets by a duplicate proposition, to 1000 pound weight or higher / experimentally and mathematically demonstrated, by Robert Anderson.
             Anderson, Robert, fl. 1668-1696.
          
           [17], 48 p. : ill.
           
             Printed for Robert Morden ...,
             London :
             1696.
          
           
             Reproduction of original in British Library.
          
        
      
    
     
       
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         eng
      
       
         
           Fireworks -- Early works to 1800.
        
      
    
     
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           The
           Making
           of
           ROCKETS
           .
        
         
           In
           Two
           Parts
           .
        
         
           The
           First
           Containing
           the
           Making
           of
           Rockets
           for
           the
           meanest
           Capacity
           .
        
         
           The
           other
           To
           make
           Rockets
           by
           a
           Duplicate
           Proposition
           ,
           to
           1000
           pound
           Weight
           or
           higher
           .
        
         
           Experimentally
           and
           Mathematically
           Demonstrated
           ,
           By
        
         
           ROBERT
           ANDERSON
           .
        
         
           LONDON
           :
           Printed
           for
           
             Robert
             Morden
          
           ,
           at
           the
           Atlas
           in
           Cornhil
           .
           1696.
           
        
      
       
         
         
         
           To
           the
           Right
           Honourable
           HENRY
           Earl
           of
           Romney
           .
        
         
           Vicount
           Sidney
           of
           Sheppy
           ,
           Baron
           of
           Milton
           ,
           Master
           General
           of
           his
           Majesty's
           Ordnance
           ,
           Constable
           of
           Dover
           Castle
           ,
           Lord
           Warden
           of
           the
           Cinque
           Ports
           ,
           and
           one
           of
           the
           Lords
           of
           his
           Majesty's
           most
           Honourable
           Privy
           Council
           .
        
         
           WELL
           knowing
           my
           most
           Noble
           Lord
           ,
           that
           these
           things
           will
           easily
           receive
           Perfection
           in
           your
           Hands
           ,
           which
           for
           many
           Reasons
           are
           beyond
           my
           reach
           .
        
         
           This
           Treatise
           (
           if
           it
           may
           deserve
           that
           name
           )
           is
           the
           least
           in
           
           Bulk
           ,
           and
           seemingly
           relating
           to
           the
           sleightest
           Subject
           I
           have
           met
           withal
           in
           Pyrotechnia
           .
           But
           in
           the
           many
           Volumns
           great
           and
           small
           that
           I
           have
           read
           relating
           to
           these
           Matters
           in
           our
           own
           and
           other
           Languages
           ;
           I
           do
           not
           find
           the
           least
           Pretence
           or
           Thought
           of
           doing
           that
           which
           here
           is
           undertaken
           ,
           
             viz.
             To
             raise
             so
             great
             a
             heap
             of
             Fire
             ,
             and
             to
             confirm
             the
             Fact
             by
             the
             greatest
             Proofs
             that
             can
             be
             had
             or
             wish'd
             for
             ,
             which
             are
             Experiments
             and
             Demonstrations
             Mathematical
             .
          
           Yet
           this
           alone
           is
           not
           the
           matter
           aim'd
           at
           ,
           the
           Problem
           is
           universal
           ,
           and
           applicable
           to
           the
           Fortifications
           of
           all
           sorts
           of
           Guns
           and
           other
           Engines
           with
           their
           Carriages
           ,
           &c.
           and
           is
           
             to
             increase
             or
             decrease
             the
             strength
             of
             Materials
             according
             to
             the
             Effects
             and
             Services
             required
             .
          
           But
           the
           greatest
           Skill
           in
           this
           Undertaking
           being
           
           to
           adjust
           the
           Instrument
           and
           Means
           in
           a
           due
           and
           proper
           Proportion
           to
           the
           Effect
           sought
           for
           ;
           I
           do
           with
           all
           Humility
           and
           profound
           Respect
           make
           offer
           of
           this
           small
           Essay
           .
        
         
           It
           is
           your
           Lordships
           great
           Abilities
           and
           Merit
           ,
           that
           has
           enabled
           you
           to
           tread
           the
           intricate
           and
           painful
           steps
           of
           Greatness
           ;
           and
           by
           the
           well
           discharging
           so
           many
           Eminent
           Employments
           ,
           to
           add
           ,
           (
           if
           any
           thing
           can
           be
           added
           )
           to
           the
           Great
           Name
           of
           your
           Renowned
           Ancestors
           .
           An
           ardent
           Zeal
           for
           the
           Welfare
           and
           Honour
           of
           your
           Country
           ,
           has
           always
           been
           the
           inbred
           Vertue
           of
           your
           Family
           ,
           and
           which
           is
           brought
           to
           its
           Perfection
           in
           your self
           .
        
         
           The
           Name
           of
           
             Master
             General
          
           of
           the
           Ordnance
           ,
           lays
           Claim
           to
           all
           my
           (
           more
           than
           25
           Years
           )
           Experience
           
           and
           Studies
           about
           the
           Art
           of
           Shooting
           in
           all
           sorts
           of
           Great
           Artillery
           amounts
           to
           :
           But
           the
           adding
           something
           (
           according
           to
           my
           poor
           Sphere
           and
           Capacity
           )
           to
           the
           Defence
           ,
           Safety
           and
           Reputation
           of
           my
           Native
           Country
           ,
           has
           at
           all
           times
           so
           intirely
           govern'd
           me
           ,
           that
           upon
           this
           account
           also
           ,
           and
           indeed
           chiefly
           ,
           I
           am
           emboldned
           to
           lay
           this
           mean
           Attempt
           of
           mine
           before
           your
           Lordship
           ;
           trusting
           that
           it
           may
           at
           some
           time
           or
           other
           undergo
           a
           Trial
           ,
           and
           by
           your
           Lordships
           Favour
           receive
           a
           meet
           Incouragement
           ,
           and
           procure
           your
           Lordships
           Pardon
           ,
           &c.
           to
        
         
           
             My
             Lord
             ,
          
           
             Your
             Lordships
             most
             Obedient
             ,
             Humble
             Servant
             ,
             
               Robert
               Anderson
            
             .
          
        
      
       
         
         
           TO
           THE
           Young
           PYROBOLISTES
           .
        
         
           ROckets
           are
           the
           most
           Artificial
           piece
           of
           Fire-work
           yet
           used
           amongst
           the
           Pyrobolistes
           ,
           and
           hath
           been
           more
           used
           of
           late
           Years
           than
           formerly
           ,
           and
           that
           the
           Young
           Artists
           may
           not
           spend
           their
           Time
           and
           Money
           unnecessarily
           ,
           I
           have
           given
           easie
           ,
           plain
           ,
           and
           ready
           Rules
           for
           making
           of
           Rockets
           to
           two
           Inches
           and
           half
           Diameter
           ,
           which
           is
           sufficient
           for
           all
           private
           Occasion
           ,
           viz.
           Of
           the
           Mould
           of
           a
           Rocket
           .
           Of
           the
           Rouler
           and
           Case
           .
           Of
           the
           Compositions
           .
           Of
           the
           Receipts
           of
           Rockets
           .
           Of
           the
           Driver
           .
           Of
           the
           Boring
           of
           the
           Rocket
           .
           Of
           the
           Stars
           and
           other
           Matter
           to
           be
           put
           in
           the
           Head
           of
           a
           Rocket
           .
           To
           Head
           a
           Rocket
           .
           Of
           the
           Sticking
           of
           a
           Rocket
           .
           And
           lastly
           ,
           to
           Fire
           the
           Rocket
           .
           And
           some
           Observations
           about
           the
           management
           
           of
           a
           Rocket
           in
           general
           ;
           all
           which
           I
           hope
           will
           prove
           casie
           and
           beneficial
           to
           the
           Ingenious
           ,
           and
           those
           that
           are
           willing
           to
           Learn
           :
           and
           what
           you
           do
           ,
           endeavour
           to
           do
           it
           well
           ,
           and
           do
           not
           be
           Conceited
           ;
           which
           if
           so
           ,
           I
           have
           my
           ends
           .
           And
           from
           these
           little
           beginnings
           greater
           Matters
           may
           be
           obtained
           ,
           and
           you
           may
           become
           serviceable
           to
           your
           Country
           ;
           in
           which
           be
           sure
           to
           be
           Careful
           ,
           Honest
           and
           Faithful
           .
        
      
       
         
         
           TO
           THE
           Other
           PYROBOLISTES
           .
        
         
           ABout
           fifteen
           Years
           since
           I
           considered
           of
           a
           method
           to
           increase
           or
           decrease
           the
           strength
           of
           the
           Metal
           of
           Guns
           ,
           which
           is
           this
           that
           I
           intend
           to
           discourse
           of
           .
           And
           at
           the
           Close
           of
           a
           small
           Treatise
           to
           hit
           a
           Mark
           published
           in
           the
           Year
           1691.
           
           I
           proposed
           that
           Problem
           in
           Print
           ;
           since
           that
           time
           there
           has
           been
           more
           than
           Ordinary
           occasion
           for
           it
           ,
           by
           Reason
           of
           the
           new
           Casting
           of
           the
           Mortar-pieces
           .
           About
           two
           Years
           since
           I
           put
           that
           Problem
           into
           a
           method
           ,
           and
           made
           a
           Draught
           of
           the
           whole
           matter
           to
           increase
           or
           decrease
           the
           strength
           of
           the
           Metal
           of
           a
           Gun
           in
           any
           possible
           Proportion
           assigned
           .
           But
           when
           I
           saw
           the
           Mortar-pieces
           brought
           from
           Sea
           broke
           ,
           it
           was
           thought
           to
           be
           a
           good
           time
           to
           shew
           it
           ,
           
           which
           was
           done
           ,
           and
           the
           whole
           matter
           discoursed
           of
           at
           large
           ,
           but
           it
           signified
           00.
           
           But
           now
           I
           apply
           that
           Problem
           to
           the
           making
           of
           Rockets
           for
           the
           young
           Artist
           ,
           as
           you
           see
           in
           its
           proper
           place
           .
           And
           it
           is
           manifest
           that
           the
           young
           Rocket-makers
           of
           this
           City
           are
           very
           Careful
           and
           Artificial
           in
           their
           Rockets
           of
           
             8d
             .
             12d
          
           .
           or
           18d
           .
           value
           ,
           otherwise
           they
           may
           break
           and
           so
           lose
           their
           Labour
           and
           Discredit
           themselves
           .
           Seeing
           these
           Mathematical
           Rules
           are
           so
           applicable
           to
           the
           greatest
           nicety
           of
           the
           Rising
           of
           all
           sizes
           of
           Rockets
           ;
           is
           it
           not
           more
           valuable
           to
           be
           applied
           to
           those
           Chargeable
           Instruments
           of
           War
           ,
           viz.
           Guns
           of
           all
           sorts
           ,
           with
           their
           Carriages
           ,
           and
           all
           other
           their
           Furniture
           ?
        
         
           As
           to
           the
           Doctrine
           of
           shooting
           by
           the
           increase
           and
           decrease
           of
           Powder
           ,
           this
           way
           of
           making
           of
           Rockets
           proves
           it
           to
           be
           absurd
           ;
           for
           all
           Rocket
           makers
           to
           this
           time
           weaken
           the
           Composition
           of
           their
           Rockets
           ,
           as
           their
           Rockets
           are
           in
           greatness
           ,
           or
           having
           greater
           quantities
           of
           
           Composition
           ;
           and
           that
           by
           chance
           ,
           and
           without
           any
           Mathematical
           Demonstration
           .
        
         
           And
           also
           by
           Experience
           ,
           in
           Table
           June
           1.
           1691.
           and
           in
           the
           first
           Column
           Experiment
           4
           ,
           against
           that
           in
           Column
           2
           you
           will
           find
           4
           Ounces
           of
           Powder
           ,
           and
           in
           Column
           3
           ,
           3377.
           
           Again
           ,
           in
           Column
           .
           1
           ,
           against
           Experiment
           1
           in
           Column
           2
           ,
           you
           find
           ½
           an
           Ounce
           of
           Powder
           ,
           and
           against
           that
           in
           Column
           3
           ,
           you
           find
           213
           ;
           now
           because
           the
           Requisite
           of
           Powder
           are
           as
           8
           to
           1
           ,
           therefore
           I
           multiply
           213
           by
           8
           ,
           and
           it
           makes
           1704
           ,
           much
           short
           of
           3377
           ,
           which
           indeed
           should
           have
           been
           equal
           to
           the
           said
           3377.
           that
           is
           the
           Ranges
           upon
           the
           plain
           of
           the
           Horizon
           are
           not
           as
           the
           Requisites
           of
           Powder
           which
           projected
           those
           Ranges
           ;
           the
           like
           may
           be
           done
           in
           all
           the
           other
           Experiments
           .
           I.
           have
           made
           hundreds
           of
           Experiments
           in
           several
           sorts
           of
           Mortar-pieces
           ,
           and
           am
           ready
           to
           make
           as
           many
           more
           ,
           all
           which
           will
           manifestly
           confute
           the
           Doctrine
           of
           shooting
           by
           the
           increase
           and
           decrease
           
           of
           Powder
           ,
           and
           have
           often
           invited
           the
           first
           promoter
           of
           that
           Doctrine
           to
           see
           his
           Invention
           confuted
           ;
           and
           I
           do
           here
           invite
           all
           the
           Practitioners
           in
           that
           Science
           of
           shooting
           by
           the
           increase
           and
           decrease
           of
           Powder
           ,
           to
           come
           and
           see
           their
           Doctrine
           confuted
           .
           I
           do
           hear
           assert
           it
           is
           impossible
           ever
           to
           bring
           that
           way
           of
           shooting
           to
           be
           so
           exact
           and
           ready
           for
           use
           ,
           in
           all
           or
           any
           sorts
           of
           Guns
           ,
           as
           the
           common
           or
           usual
           way
           is
           ,
           by
           keeping
           the
           Requisites
           of
           Powder
           constant
           ,
           and
           elevating
           the
           Piece
           .
           In
           the
           Complicating
           of
           Rockets
           ,
           whose
           Diameters
           are
           at
           any
           great
           distance
           ;
           we
           make
           use
           of
           Experiments
           of
           shooting
           made
           upon
           another
           Occasion
           ,
           and
           those
           Experiments
           serves
           sufficiently
           well
           ;
           but
           if
           we
           were
           to
           do
           them
           justly
           according
           to
           Art
           ,
           there
           should
           be
           two
           even
           Chased
           Guns
           of
           the
           same
           Proportion
           as
           the
           Rockets
           are
           of
           ,
           that
           is
           the
           Diameter
           of
           the
           exposed
           Rocket
           2½
           Inch
           multiplied
           by
           6
           is
           15
           Inches
           ,
           and
           those
           should
           be
           the
           Diameter
           and
           length
           of
           one
           of
           the
           Guns
           :
           4
           Inches
           the
           Diameter
           of
           the
           other
           Rocket
           ,
           multiplied
           by
           6
           is
           24
           Inches
           ,
           which
           4
           Inches
           for
           
           the
           Diameter
           ,
           and
           24
           Inches
           for
           the
           length
           should
           be
           the
           other
           Gun
           ,
           or
           any
           two
           Guns
           in
           that
           Proportion
           .
           For
           the
           Requisite
           of
           Powder
           take
           the
           Cube
           of
           4
           ,
           which
           is
           64
           ,
           as
           also
           the
           Cube
           of
           2½
           ,
           which
           is
           15.625
           ,
           divide
           the
           greater
           Cube
           Number
           by
           the
           lesser
           ,
           and
           the
           Quotient
           is
           4
           ,
           sufficiently
           near
           ;
           so
           the
           Requisites
           of
           Powder
           of
           these
           two
           Pieces
           are
           as
           4
           to
           1
           ,
           then
           take
           any
           reasonable
           Requisite
           of
           Powder
           for
           the
           4
           Inch
           Gun
           ,
           then
           take
           the
           fourth
           part
           of
           that
           Requisite
           for
           the
           Requisite
           of
           Powder
           for
           the
           lesser
           Gun
           ,
           discharge
           them
           both
           at
           one
           degree
           of
           Elevation
           ,
           and
           note
           their
           Ranges
           .
           Their
           Bullets
           are
           to
           be
           of
           the
           same
           Metal
           ,
           and
           of
           the
           same
           likeness
           ,
           and
           both
           exactly
           fit
           .
           In
           a
           Mathematical
           sence
           these
           Ranges
           should
           be
           equal
           ;
           but
           by
           Combination
           the
           greater
           quantity
           of
           Powder
           aggitates
           more
           upon
           the
           great
           Bullet
           ,
           than
           the
           lesser
           Requisites
           doth
           aggitate
           upon
           the
           lesser
           Bullet
           ,
           and
           that
           causes
           those
           differences
           ,
           the
           like
           when
           two
           quantities
           of
           Powder
           aggitate
           upon
           one
           Bullet
           ;
           it
           is
           Experience
           only
           that
           
           determines
           the
           matter
           .
           Although
           strange
           things
           sometimes
           happens
           ;
           yet
           this
           we
           will
           Assert
           ,
           and
           endeavour
           to
           maintain
           that
           Mathematical
           Knowledg
           ,
           join'd
           with
           faithful
           Experiments
           ,
           will
           do
           greater
           matters
           than
           most
           Men
           commonly
           conceive
           .
        
         
           
             Rob.
             Anderson
             .
          
        
      
       
         
         
           Rocket
           Moulds
           are
           made
           by
           Mr.
           Cuggley
           just
           without
           Cripplegate
           .
        
         
           Taper
           Bits
           for
           Rockets
           ,
           are
           made
           by
           Mr.
           Goode
           just
           within
           Cripplegate
           .
        
         
           Rods
           for
           Rockets
           ,
           are
           made
           by
           Mr.
           Stateham
           in
           
             Token-House-Yard
             ,
             Lothbury
          
           .
           All
           three
           right
           good
           Workmen
           .
        
      
    
     
       
         
           
           
           
             PROPOSITION
             I.
             
          
           
             Of
             a
             Rocket-Mould
             .
          
           
             LEt
             E
             M
             R
             D
             D
             H
             L
             E
             be
             a
             Rocket-Mould
             ,
             A
             B
             the
             Diameter
             of
             it
             ,
             viz.
             one
             Inch
             and
             half
             ;
             Z
             K
             4
             Diameters
             ,
             that
             is
             6
             Inches
             the
             height
             to
             be
             filled
             with
             Composition
             ,
             B
             E
             half
             a
             Diameter
             an
             overplus
             ,
             Z
             C
             the
             height
             of
             the
             boring
             4
             Inches
             and
             ½
             ,
             or
             ¾
             of
             the
             height
             of
             the
             Mould
             ,
             G
             F
             the
             Orifice
             one
             third
             of
             the
             Diameter
             of
             the
             Rocket
             half
             an
             Inch
             ,
             
             
             Z
             Y
             one
             sixth
             of
             the
             Diameter
             of
             the
             Rocket
             a
             quarter
             of
             an
             Inch
             ,
             the
             thickness
             of
             the
             Case
             ,
             D
             Y
             Z
             G
             C
             F
             Z
             Y
             D
             the
             bottom
             of
             the
             Rocket-Mould
             with
             the
             Needle
             to
             be
             put
             in
             and
             taken
             out
             ;
             R
             H
             a
             Pin
             of
             Iron
             to
             fix
             the
             Mould
             and
             Bottom
             together
             .
          
        
         
           
             PROPOSITION
             .
             II.
             
          
           
             Of
             the
             Rowler
             and
             Case
             of
             a
             Rocket
             .
          
           
             MAke
             the
             Body
             of
             the
             Rowler
             nine
             Diameters
             in
             length
             ,
             and
             in
             Diameter
             two
             thirds
             of
             the
             Diameter
             of
             the
             Rocket
             ,
             and
             the
             Head
             of
             the
             Rowler
             of
             the
             Rocket
             the
             same
             Diameter
             ;
             let
             the
             Diameter
             of
             the
             Neck
             of
             the
             Rowler
             be
             a
             little
             less
             than
             one
             third
             of
             the
             Diameter
             of
             the
             Rocket
             ,
             because
             when
             opened
             with
             a
             Cone
             of
             Wood
             the
             Orifice
             of
             the
             Rocket
             may
             be
             just
             one
             third
             smooth
             and
             hard
             to
             endure
             the
             Fire
             .
             Then
             the
             thickness
             of
             the
             Case
             will
             be
             one
             sixth
             of
             the
             Diameter
             of
             the
             Rocket
             ,
             which
             being
             well
             Rowled
             and
             Choaked
             ,
             the
             Case
             may
             be
             finished
             .
          
        
         
           
           
             PROPOSITION
             III.
             
          
           
             Of
             the
             Composition
             for
             Rockets
             .
          
           
             THE
             Ingredients
             which
             Rockets
             are
             Composed
             of
             are
             Saltpetre
             ,
             Sulphur
             ,
             and
             Wood-Coal
             mealed
             ,
             and
             passed
             through
             a
             fine
             Sieve
             .
             First
             ,
             take
             the
             largest
             of
             Small-Coal
             made
             of
             Birch-Wood
             .
             Secondly
             ,
             chuse
             the
             Yellowest
             Roch
             Sulphur
             .
             Thirdly
             ,
             take
             Saltpetre
             put
             in
             a
             Brass
             Vessel
             ,
             to
             which
             put
             so
             much
             fair
             Water
             as
             will
             dissolve
             it
             ,
             put
             that
             Vessel
             upon
             the
             Fire
             ,
             when
             it
             boils
             scum
             it
             clean
             ;
             when
             the
             Water
             evaporates
             and
             consumes
             ,
             stir
             it
             with
             a
             Spatula
             of
             Wood
             to
             meal
             it
             ,
             what
             remains
             of
             the
             Saltpetre
             upon
             the
             Spatula
             ,
             and
             sides
             of
             the
             Vessel
             ,
             rub
             off
             with
             your
             Spatula
             of
             Wood
             ;
             then
             meal
             it
             ,
             and
             pass
             it
             through
             a
             fine
             Sieve
             .
             A
             second
             way
             to
             Clarifie
             Saltpetre
             ;
             take
             a
             Crucible
             ,
             set
             it
             in
             the
             Fire
             ,
             put
             Saltpetre
             thereunto
             ,
             increase
             the
             Fire
             till
             the
             Saltpetre
             be
             Reduced
             to
             a
             liquid
             quality
             like
             Water
             ;
             when
             it
             boils
             take
             mealed
             Sulphur
             upon
             a
             Spatula
             of
             Iron
             ,
             and
             put
             it
             into
             the
             boiling
             Saltpetre
             ;
             so
             often
             repeated
             ,
             the
             Flegmy
             quality
             of
             
             the
             Saltpetre
             will
             be
             burnt
             away
             ,
             and
             the
             flame
             will
             remain
             as
             white
             as
             the
             Body
             of
             the
             Sun.
             Then
             pour
             it
             into
             some
             very
             smooth
             Vessel
             ,
             which
             being
             cooled
             ,
             you
             may
             reduce
             it
             into
             meal
             .
             These
             ways
             I
             have
             done
             for
             my
             Recreation
             ;
             but
             I
             usually
             take
             the
             cleanest
             Saltpetre
             to
             be
             found
             in
             Drugsters
             Shops
             ,
             and
             it
             does
             as
             well
             .
          
        
         
           
             PROPOSITION
             IV.
             
          
           
             The
             Receipts
             for
             Rockets
             .
          
           
             FOR
             an
             Inch
             ,
             an
             Inch
             and
             half
             ,
             and
             two
             Inch
             Rocket
             ,
             and
             for
             a
             White
             Fire
             ,
             take
             2
             Drams
             of
             Antimony
             ,
             1
             Ounce
             of
             Sulphur
             2½
             Ounces
             of
             Coal-dust
             ,
             6
             Ounces
             of
             Saltpetre
             ,
             and
             8
             Ounces
             of
             powder
             dust
             ,
             [
             
               Casimer
               du
               Grand
               Art
               d'
               Artillerie
               ,
               Partie
               1.
               
               Livre
               3.
               pag.
            
             145.
             ]
             Fill
             4
             Diameters
             and
             Bore
             2½
             .
             For
             an
             Inch
             and
             half
             ,
             and
             two
             Inch
             ,
             and
             two
             Inch
             and
             half
             Rocket
             ,
             and
             a
             Yellow
             Fire
             ,
             take
             1
             Ounce
             of
             Sulphur
             ,
             1
             Ounce
             of
             Coal-dust
             ,
             4
             Ounces
             of
             Saltpetre
             ;
             or
             take
             1
             Ounce
             of
             Sulphur
             ,
             1½
             Ounce
             of
             Coal-dust
             ,
             and
             4
             Ounces
             of
             Saltpetre
             .
             [
             
               Casimer
               du
               Grand
               Art
               d'
               Artillerie
               ,
               Partie
               1.
               
               Livre
               2.
               pag.
            
             99.
             ]
             Fill
             4
             Diameters
             ,
             and
             bore
             3
             ,
             or
             a
             little
             
             more
             .
             And
             
               Daniel
               Elrich
               Der
               grossen
               Kunst
               Artillerie
               Zweiter
               ,
               Thei
               l
               .
               pag.
               54.
               at
               .
            
             19.
             
             Advises
             to
             take
             1
             Ounce
             of
             Sulphur
             ,
             one
             Ounce
             of
             Coal
             dust
             ,
             4
             Ounces
             of
             Saltpetre
             .
             Again
             ,
             take
             1
             Ounce
             of
             Sulphur
             ,
             2
             Ounces
             of
             Coal
             ,
             and
             6
             Ounces
             of
             Saltpetre
             ;
             also
             take
             1
             Ounce
             of
             Sulphur
             2½
             of
             Coal
             ,
             and
             6
             of
             Saltpetre
             .
             
               Johann
               .
               Sigmund
               .
               Buchner
               in
               Theoria
               praxis
               Artilleria
               Andere
               Thei
               l
               ,
               pag.
            
             28.
             
             Weigh
             the
             Ingredients
             single
             ,
             put
             them
             into
             a
             wooden
             Bowl
             ,
             mix
             them
             very
             well
             together
             ,
             and
             pass
             them
             through
             the
             Sieve
             ,
             then
             your
             Composition
             is
             fit
             for
             use
             .
             In
             filling
             Rockets
             of
             one
             or
             two
             Inches
             Diameter
             ;
             let
             them
             be
             filled
             at
             6
             ,
             8
             ,
             or
             10
             times
             Charging
             ,
             and
             to
             every
             Charge
             10
             ,
             12
             ,
             or
             14
             blows
             with
             a
             Mallet
             ,
             and
             betwixt
             every
             three
             blows
             turn
             the
             Driver
             a
             little
             in
             your
             Hand
             ,
             so
             the
             Composition
             about
             the
             Needle
             will
             be
             preserved
             .
          
           
             Some
             of
             our
             Rocket-Makers
             cry
             up
             the
             Compositions
             of
             Woolverman
             and
             Nelson
             ,
             as
             though
             there
             was
             no
             Composition
             to
             be
             found
             like
             theirs
             ,
             and
             they
             are
             thus
             :
             that
             falsly
             called
             Woolverman's
             is
             1
             of
             Sulphur
             ,
             1
             of
             Coal
             ,
             and
             4
             of
             Saltpetre
             :
             and
             that
             of
             Nelson
             ,
             1
             of
             Sulphur
             ,
             1½
             of
             Coal
             ,
             and
             4
             of
             Saltpetre
             ,
             as
             they
             stand
             in
             the
             Remains
             of
             
             Mr.
             
               Francis
               Deane
            
             ,
             sometime
             Gunner
             of
             the
             Tower.
             These
             Compositions
             are
             Old
             and
             Common
             ,
             as
             you
             see
             ,
             they
             are
             Good
             ,
             Strong
             ,
             and
             dull
             Compositions
             ,
             and
             easily
             mannaged
             .
             Those
             Compositions
             where
             Powder
             is
             judiciously
             mixed
             are
             more
             lively
             ,
             and
             so
             more
             difficult
             to
             mannage
             .
          
        
         
           
           
             PROPOSITION
             V.
             
          
           
             Of
             the
             Driver
             of
             a
             Rocket
             .
          
           
             LEt
             y
             A
             F
             G
             H
             E
             B
             y
             be
             the
             Driver
             of
             the
             Rocket
             ,
             A
             F
             E
             B
             a
             piece
             of
             a
             Gun
             Barrel
             ,
             F
             G
             H
             E
             O
             L
             a
             piece
             of
             Box
             or
             hard
             Wood
             ,
             R
             L
             O
             q
             a
             hole
             for
             the
             Needle
             to
             pass
             through
             ,
             A
             C
             D
             B
             y
             a
             piece
             of
             Box
             to
             drive
             upon
             ;
             this
             we
             call
             a
             hollow
             Driver
             ,
             it
             dispatches
             business
             quickly
             ,
             and
             does
             right
             well
             .
             Or
             you
             may
             fasten
             a
             piece
             of
             Brass
             in
             the
             end
             of
             your
             Iron
             Driver
             with
             a
             hole
             in
             it
             to
             receive
             the
             Needle
             .
          
           
             If
             any
             will
             use
             a
             solid
             Driver
             ,
             let
             them
             have
             the
             bottom
             of
             the
             Mould
             as
             D
             y
             Z
             Z
             Z
             y
             D
             with
             a
             hole
             passing
             through
             the
             bottom
             ,
             as
             Z
             R
             ,
             for
             a
             strait
             Piercer
             to
             pass
             through
             
             
             which
             bottom
             will
             be
             a
             Guide
             to
             the
             Piercer
             to
             be
             just
             in
             the
             middle
             of
             the
             Rocket
             ,
             make
             a
             mark
             in
             your
             Piercer
             to
             be
             a
             guide
             to
             bore
             always
             an
             equal
             depth
             ,
             then
             take
             your
             Rocket
             out
             of
             the
             Mould
             ,
             open
             the
             hole
             with
             a
             Taper
             bit
             ,
             and
             your
             Work
             is
             done
             ,
             thus
             you
             may
             do
             for
             all
             sizes
             of
             Rockets
             .
          
        
         
           
             PROPOSITION
             VI.
             
          
           
             Of
             the
             Boring
             of
             a
             Rocket
             .
          
           
             MAke
             the
             Diameter
             of
             your
             Borer
             one
             third
             of
             the
             Diameter
             of
             your
             Rocket
             ,
             not
             for
             any
             necessity
             ,
             but
             for
             conformity
             to
             the
             other
             parts
             of
             the
             Rocket
             ;
             from
             that
             Diameter
             let
             it
             be
             exactly
             Taper
             to
             a
             point
             .
             Further
             ,
             there
             being
             an
             entrance
             made
             by
             the
             Needle
             ,
             it
             is
             very
             easie
             to
             bore
             the
             Rocket
             very
             exactly
             ,
             by
             holding
             the
             Rocket
             in
             the
             Left
             Hand
             ,
             and
             the
             Borer
             in
             the
             Right
             ,
             moving
             the
             Rocket
             in
             the
             Left
             Hand
             ,
             keeping
             the
             Borer
             fast
             in
             the
             Right
             Hand
             .
          
           
             If
             you
             make
             the
             Diameter
             of
             the
             Needle
             one
             third
             of
             the
             Diameter
             of
             the
             Rocket
             ,
             and
             so
             Taper
             ,
             you
             need
             no
             
             Borer
             ;
             here
             you
             shall
             find
             the
             Rocket
             will
             rise
             swifter
             than
             when
             bored
             ,
             the
             Composition
             lying
             looser
             about
             the
             Needle
             than
             if
             it
             were
             bored
             ,
             takes
             fire
             easier
             ,
             and
             this
             is
             most
             necessary
             in
             large
             Rockets
             ,
             viz.
             of
             3
             ,
             4
             ,
             or
             6
             Inches
             Diameter
             ;
             for
             such
             will
             hang
             too
             long
             time
             upon
             the
             Nails
             before
             they
             rise
             .
             Those
             Rockets
             whose
             Compositions
             are
             Composed
             of
             mealed
             Powder
             ,
             Saltpetre
             ,
             Coal
             and
             Sulphur
             ,
             fill
             four
             Diameters
             ,
             bore
             two
             and
             half
             .
             Those
             Composed
             of
             Saltpetre
             ,
             Coal
             ,
             and
             Sulphur
             fill
             four
             Diameters
             ,
             bore
             three
             or
             a
             little
             more
             .
          
           
             This
             will
             hold
             in
             Rockets
             of
             1
             Inch
             ,
             1½
             and
             2
             Inches
             ,
             but
             in
             larger
             Rockets
             there
             must
             be
             less
             solidity
             to
             the
             hollow
             Cone
             of
             Fire
             .
             I
             used
             for
             many
             years
             to
             drive
             my
             Rockets
             solid
             ,
             and
             to
             bore
             them
             after
             ,
             but
             that
             way
             did
             no
             better
             than
             these
             I
             now
             use
             and
             deliver
             ;
             but
             this
             is
             most
             certain
             that
             any
             one
             may
             drive
             and
             bore
             3
             Rockets
             with
             those
             hollow
             Drivers
             which
             I
             now
             use
             ,
             whilst
             one
             many
             finish
             the
             driving
             and
             boring
             of
             one
             Rocket
             with
             a
             solid
             Driver
             ;
             when
             the
             Rocket
             is
             near
             filled
             ,
             use
             a
             shorter
             Driver
             with
             a
             smaller
             hole
             .
          
        
         
           
           
             PROPOSITION
             VII
             .
          
           
             Of
             Stars
             for
             Rockets
             .
          
           
             1
             ,
             1
             ,
             2
             ,
             2.
             
             Sulphur
             .
          
           
             2
             ,
             3
             ,
             3
             ,
             2.
             
             Antimony
             .
          
           
             4
             ,
             6
             ,
             8
             ,
             6.
             
             Saltpetre
             .
          
           
             Meal
             these
             Ingredients
             fine
             ,
             pass
             them
             through
             a
             Sieve
             ,
             mix
             them
             with
             Water
             in
             which
             some
             Glue
             ,
             or
             Gum
             Araback
             ,
             or
             Gum
             Dragon
             hath
             been
             dissolved
             ,
             make
             them
             of
             the
             bigness
             of
             a
             Hazle
             Nut
             ,
             or
             small
             Wallnut
             ;
             roul
             them
             in
             meal
             Powder
             ,
             when
             dryed
             they
             are
             fit
             for
             use
             .
          
           
             Rockets
             are
             headed
             with
             small
             Serpents
             ,
             their
             Orifices
             washed
             with
             mealed
             Powder
             and
             Brandy
             Wine
             ,
             to
             take
             Fire
             .
          
           
             
             
               Of
               Rain
               and
               Hail
               .
            
             
               TAke
               any
               of
               those
               Receipts
               for
               Stars
               ,
               viz.
               1
               Sulphur
               ,
               2
               Antimony
               ,
               and
               4
               Saltpetre
               ;
               if
               you
               moisten
               that
               Composition
               with
               Oil
               of
               Petre
               only
               made
               well
               into
               Paste
               ,
               formed
               into
               little
               Globes
               ,
               rowled
               into
               mealed
               Powder
               ;
               such
               Stars
               will
               have
               Red
               Colour
               :
               the
               same
               Composition
               moistned
               with
               Linseed
               Oil
               will
               have
               a
               Red
               mixed
               with
               White
               :
               the
               same
               Composition
               mixed
               with
               Oil
               of
               Petre
               and
               Linseed
               Oil
               mixed
               together
               ,
               will
               make
               an
               Amethist
               Fi●e
               .
               All
               these
               will
               require
               a
               long
               time
               a
               drying
               ,
               the
               best
               time
               is
               to
               make
               them
               in
               the
               Summer
               .
            
             
               The
               same
               Composition
               mixed
               with
               Gum
               Araback
               Water
               ,
               and
               Colophone
               ,
               gives
               a
               Red
               Yellowish
               Fire
               .
               The
               former
               Composition
               moistned
               with
               Brandy
               and
               Oil
               of
               Petre
               ,
               or
               Linseed
               Oil
               ,
               mixed
               together
               ,
               requires
               less
               drying
               Powder
               of
               Glass
               ,
               Powder
               made
               of
               Sawdust
               mixed
               with
               the
               former
               Composition
               gives
               different
               Fire
               ;
               Coal
               dust
               instead
               of
               Antimony
               ,
               all
               which
               you
               may
               govern
               by
               your
               own
               Reason
               .
               Take
               the
               Old
               Proverb
               ,
               
                 So
                 many
                 Men
                 ,
                 so
                 many
                 Minds
                 .
              
            
          
        
         
           
           
             PROPOSITION
             VIII
             .
          
           
             To
             Head
             a
             Rocket
             .
          
           
             TUrn
             a
             piece
             of
             Wood
             just
             so
             big
             as
             your
             Rocket
             is
             ,
             with
             a
             Cone
             at
             one
             end
             thereof
             ,
             paste
             a
             piece
             of
             strong
             Paper
             about
             the
             Wood
             ,
             then
             paste
             another
             piece
             of
             Paper
             about
             the
             Cone
             ,
             and
             paste
             both
             Papers
             together
             ;
             then
             put
             your
             Stars
             into
             this
             Paper
             Vessel
             ,
             with
             some
             Rocket
             Composition
             to
             break
             the
             Vessel
             ,
             then
             put
             a
             little
             Paste
             a
             little
             within
             the
             sides
             of
             this
             Paper
             Vessel
             ,
             then
             draw
             it
             upon
             your
             Rocket
             ,
             and
             paste
             it
             to
             the
             Rocket
             ,
             so
             your
             Work
             is
             done
             .
          
        
         
           
             PROPOSITION
             IX
             .
          
           
             Of
             the
             Sticking
             of
             Rockets
             .
          
           
             THE
             Stick
             of
             a
             Rocket
             ought
             to
             be
             seven
             times
             the
             length
             of
             the
             Rocket
             or
             more
             ,
             viz.
             a
             Rocket
             of
             an
             Inch
             and
             half
             ,
             six
             Diameters
             thereof
             ,
             the
             length
             of
             the
             Rocket
             ,
             is
             nine
             Inches
             ,
             seven
             
             times
             nine
             is
             sixty
             three
             Inches
             ,
             that
             is
             five
             Foot
             three
             Inches
             .
             The
             breadth
             of
             the
             Stick
             at
             the
             Head
             ,
             three
             quarters
             of
             an
             Inch
             or
             less
             ,
             the
             thickness
             half
             an
             Inch
             or
             less
             ,
             the
             small
             end
             of
             the
             Stick
             three
             eighths
             of
             an
             Inch
             and
             square
             ,
             and
             to
             be
             made
             of
             light
             Deal
             ;
             such
             a
             Stick
             will
             do
             very
             well
             ,
             and
             may
             be
             counted
             Custom
             without
             Demonstration
             .
             In
             the
             Winter
             1695.
             there
             were
             two
             sets
             of
             Fire
             works
             ,
             in
             the
             first
             of
             which
             the
             Wind
             was
             Northward
             ,
             and
             the
             Rockets
             in
             their
             rising
             worked
             into
             the
             Wind.
             In
             the
             second
             the
             Wind
             was
             Westward
             ,
             and
             had
             the
             same
             effect
             as
             the
             first
             ;
             the
             Reason
             was
             because
             the
             Stick
             was
             to
             heavy
             at
             the
             upper
             end
             ,
             and
             too
             light
             at
             the
             lower
             ;
             and
             so
             the
             Center
             of
             Gravity
             of
             the
             Rocket
             and
             Stick
             was
             too
             near
             the
             Rocket
             :
             when
             indeed
             the
             Center
             of
             Gravity
             should
             be
             in
             the
             middle
             ,
             betwixt
             the
             lower
             end
             of
             the
             Stick
             and
             upper
             end
             of
             the
             Rocket
             ;
             and
             to
             do
             which
             the
             bigger
             end
             of
             the
             Stick
             ought
             to
             be
             downward
             ;
             by
             this
             means
             a
             lighter
             Stick
             would
             serve
             ,
             and
             if
             the
             Wind
             did
             drive
             the
             Rocket
             ,
             the
             Rocket
             would
             move
             less
             ,
             and
             yet
             perpendicular
             to
             the
             Horizon
             .
             Nature
             it self
             has
             taught
             us
             the
             same
             ;
             for
             all
             Birds
             ,
             especially
             Birds
             of
             a
             swift
             flight
             ,
             spread
             their
             Tails
             for
             their
             Guide
             .
             Sticks
             of
             Rockets
             ought
             to
             be
             one
             
             to
             another
             as
             the
             length
             and
             Diameters
             of
             the
             respective
             Rockets
             ;
             that
             is
             ,
             as
             the
             Diametre
             1½
             Inch
             is
             to
             the
             thickness
             of
             its
             Stick
             ,
             so
             is
             4
             Inches
             the
             Diameter
             of
             a
             4
             Inch
             Rocket
             to
             the
             thickness
             of
             its
             respective
             Stick
             .
             As
             the
             length
             of
             one
             Rocket
             is
             to
             its
             Stick
             ;
             so
             is
             the
             length
             of
             any
             other
             Rocket
             to
             its
             Stick
             :
             and
             as
             the
             weight
             of
             one
             Rocket
             is
             to
             the
             weight
             of
             its
             Stick
             ;
             so
             is
             the
             weight
             of
             any
             other
             Rocket
             to
             the
             weight
             of
             its
             respective
             Stick
             .
          
        
         
           
             PROPOSITION
             X.
             
          
           
             To
             fire
             the
             Rocket
             .
          
           
             PLace
             the
             Rocket
             perpendicular
             to
             the
             Horizon
             by
             four
             Nails
             ,
             make
             a
             port-fire
             ,
             about
             half
             an
             Inch
             in
             Diameter
             ,
             with
             single
             Paper
             ,
             viz.
             1
             Sulphur
             ,
             2
             Saw-dust
             sifted
             fine
             ,
             or
             rather
             Logwood
             beaten
             and
             sifted
             fine
             ,
             4
             of
             mealed
             Powder
             ,
             and
             8
             of
             Saltpetre
             ;
             or
             make
             the
             port-fire
             with
             Rocket
             Composition
             :
             fire
             the
             port-fire
             ,
             move
             it
             gently
             towards
             the
             Orifice
             of
             the
             Rocket
             till
             it
             takes
             fire
             .
          
           
             
             
               Observations
               concerning
               Rockets
               .
            
             
               (
               1.
               )
               IF
               a
               Rocket
               be
               driven
               not
               hard
               enough
               it
               either
               consumes
               or
               breaks
               ;
               if
               just
               hard
               enough
               it
               rises
               well
               ;
               if
               two
               hard
               it
               turns
               a
               loft
               ,
               and
               breaks
               not
               at
               the
               just
               turn
               .
            
             
               (
               2.
               )
               If
               a
               Rocket
               be
               bored
               not
               deep
               enough
               it
               will
               not
               rise
               well
               ;
               if
               just
               deep
               enough
               it
               rises
               well
               ;
               if
               too
               deep
               it
               often
               breaks
               .
            
             
               (
               3.
               )
               If
               a
               Rocket
               be
               bored
               with
               too
               great
               a
               Borer
               it
               will
               not
               rise
               well
               ;
               if
               with
               a
               fit
               Borer
               it
               rises
               well
               ;
               if
               with
               too
               small
               a
               Borer
               it
               breaks
               ,
               or
               rises
               not
               well
               .
            
             
               (
               4.
               )
               If
               the
               Composition
               be
               too
               moist
               it
               will
               not
               rise
               well
               ;
               if
               too
               dry
               it
               rises
               too
               fast
               or
               breaks
               .
            
             
               (
               5.
               )
               If
               a
               Rocket
               be
               made
               ,
               and
               kept
               in
               too
               dry
               or
               too
               moist
               a
               place
               ,
               it
               will
               have
               the
               same
               effect
               as
               at
               the
               (
               4.
               )
            
             
             
               (
               6.
               )
               The
               Velocity
               of
               a
               Rocket
               is
               caused
               by
               the
               boring
               ,
               or
               in
               the
               hollow
               Cone
               ;
               the
               time
               of
               its
               flight
               is
               in
               the
               solid
               part
               above
               the
               boring
               ,
               which
               solid
               part
               ought
               to
               be
               less
               in
               a
               great
               Rocket
               than
               in
               a
               little
               one
               .
               From
               these
               Observations
               a
               Youth
               may
               take
               any
               Composition
               (
               in
               Reason
               )
               and
               make
               a
               good
               Rocket
               .
            
          
        
         
           
             PROPOSITION
             XI
             .
          
           
             The
             weight
             of
             the
             Mallets
             for
             Rockets
             .
          
           
             THE
             weight
             of
             the
             Mallets
             which
             Rockets
             are
             driven
             with
             ,
             ought
             to
             be
             as
             the
             Cube
             of
             the
             Respective
             Diameters
             of
             their
             bores
             ,
             viz.
             If
             the
             weight
             of
             the
             Mallet
             for
             an
             Inch
             Rocket
             be
             twelve
             Ounces
             ,
             the
             weight
             of
             the
             Mallet
             for
             an
             Inch
             and
             half
             Rocket
             ought
             to
             be
             two
             Pounds
             and
             half
             ,
             and
             for
             a
             two
             Inch
             Rocket
             six
             Pounds
             ,
             &c.
             
          
        
         
           
           
             PROPOSITION
             XII
             .
          
           
             How
             Rockets
             are
             estimated
             .
          
           
             ROckets
             are
             estimated
             either
             by
             Measure
             or
             by
             Weight
             ;
             if
             by
             Measure
             ,
             then
             by
             the
             Common
             Standard
             by
             Inches
             or
             by
             Feet
             ;
             if
             by
             Weight
             ,
             then
             they
             are
             estimated
             by
             Cast
             Iron
             ,
             that
             is
             ,
             by
             the
             Gunners
             Rule
             ,
             viz.
             An
             Inch
             Rocket
             weigheth
             two
             Ounces
             and
             a
             quater
             :
             an
             Inch
             and
             half
             Rocket
             weigheth
             half
             a
             Pound
             :
             a
             two
             Inch
             Rocket
             weigheth
             a
             little
             above
             a
             Pound
             :
             a
             three
             Inch
             Rocket
             weigheth
             almost
             four
             Pounds
             :
             a
             four
             Inch
             Rocket
             weigheth
             nine
             Pounds
             :
             an
             eight
             Inch
             Rocket
             weigheth
             seventy
             two
             Pounds
             ,
             which
             may
             be
             called
             a
             Rocket
             Royal.
             
          
        
         
           
           
             PROPOSITION
             XIII
             .
          
           
             Of
             the
             cause
             of
             the
             Rockets
             rising
             .
          
           
             
             LET
             A
             C
             B
             be
             the
             hollow
             Cone
             for
             the
             the
             Fire
             ,
             A
             y
             C
             Z
             B
             the
             Superficies
             of
             that
             Cone
             ,
             all
             the
             Lines
             O
             Z
             at
             right
             Angles
             with
             B
             C
             ,
             and
             all
             the
             Lines
             O
             y
             at
             Right
             Angle
             with
             A
             C
             ;
             now
             all
             the
             Angles
             Z
             O
             y
             being
             towards
             R
             ,
             whether
             the
             Angles
             Z
             O
             y
             are
             Obtuse
             or
             Acute
             ,
             but
             the
             more
             acuter
             the
             better
             .
             The
             Rays
             of
             fire
             Z
             O
             and
             y
             O
             issuing
             from
             the
             sides
             of
             the
             Cone
             B
             C
             and
             A
             C
             ,
             and
             continually
             agitating
             with
             greater
             force
             one
             upon
             another
             at
             O
             ,
             forcing
             the
             whole
             Cone
             B
             C
             A
             upward
             from
             the
             point
             R
             ;
             (
             and
             the
             wider
             the
             bore
             is
             (
             in
             Reason
             )
             the
             Rocket
             will
             rise
             with
             the
             greater
             velocity
             ;
             if
             the
             Composition
             and
             deepness
             of
             boring
             be
             sutable
             .
             )
             By
             the
             Rays
             Z
             X
             ,
             
             and
             y
             Z
             of
             fire
             ,
             crossing
             ,
             each
             other
             at
             the
             Center
             of
             the
             Cone
             R
             ,
             and
             the
             point
             R
             ,
             as
             it
             were
             ,
             remains
             fixt
             ;
             and
             here
             the
             similitude
             of
             Guns
             and
             Rockets
             appears
             plainly
             ,
             a
             Gun
             remains
             fixt
             upon
             the
             Center
             of
             Motion
             of
             the
             Trunnions
             ,
             and
             projects
             its
             burden
             forth
             ;
             but
             a
             Rocket
             flys
             from
             its
             burden
             ,
             leaving
             it
             at
             R
             ,
             as
             it
             were
             fixt
             .
          
        
      
       
         
         
         
           PART
           II.
           TO
           OUR
           PYROBOLISTES
           .
        
         
           A
           duplicate
           Proposition
           .
        
         
           HAving
           one
           Rocket
           well
           proved
           in
           all
           its
           Parts
           ,
           viz.
           a
           three
           Inch
           Rocket
           .
           Then
           ,
        
         
           To
           decrease
           the
           Velocity
           of
           the
           Composition
           of
           the
           aforesaid
           Rocket
           ,
           to
           make
           it
           fit
           for
           a
           4
           Inch
           4½
           and
           5
           Inch
           Rocket
           .
        
         
           And
           to
           increase
           the
           Velocity
           of
           the
           aforesaid
           Composition
           ,
           to
           adapt
           it
           to
           a
           2
           Inch
           1½
           and
           1
           Inch
           Rocket
           ,
           keeping
           the
           same
           kind
           of
           Boring
           .
        
         
           Secondly
           ,
           From
           the
           exposed
           Rocket
           of
           3
           Inches
           ,
           to
           increase
           the
           Diameter
           of
           the
           Orifice
           of
           the
           Rockets
           of
           4
           :
           4½
           and
           5
           
           Inches
           Diameter
           ;
           and
           to
           decrease
           the
           Diameter
           of
           the
           Orifice
           of
           the
           Rockets
           of
           2
           :
           1½
           and
           1
           Inch
           Diameter
           ,
           to
           adapt
           them
           to
           the
           exposed
           Rocket
           ,
           keeping
           the
           Composition
           of
           the
           same
           Velocity
           .
        
         
           
             From
             Experimental
             and
             Mathematical
             Demonstration
             .
          
           
             The
             Resolution
             of
             this
             Problem
             will
             manifestly
             shew
             ,
             the
             invalidity
             of
             the
             Doctrine
             of
             Shooting
             by
             the
             increase
             and
             decrease
             of
             Powder
             ;
             and
             that
             weak
             and
             narrow
             Scantling
             it
             pinfolds
             in
             ,
             
               too
               mean
               for
               this
               lofty
               Engine
               .
            
             It
             also
             tells
             the
             Gun-Founder
             how
             to
             give
             his
             Guns
             their
             due
             Fortification
             ;
             otherwise
             they
             may
             become
             useless
             Instruments
             of
             War.
             It
             teacheth
             our
             Pyrobolistes
             to
             direct
             their
             Work
             so
             that
             it
             may
             rise
             well
             ,
             and
             not
             break
             nor
             fall
             .
             It
             teacheth
             Artificers
             to
             increase
             and
             decrease
             the
             force
             or
             strength
             of
             their
             Materials
             in
             any
             possible
             Proportion
             assigned
             .
          
           
             This
             Proposition
             was
             publickly
             proposed
             three
             Months
             before
             the
             publication
             of
             this
             Book
             ,
             but
             no
             Resolution
             given
             by
             any
             .
          
        
         
           
           
             PROPOSITION
             XIV
             .
          
           
             The
             Complication
             of
             Rockets
             in
             Relation
             to
             their
             Borers
             .
          
           
             FRom
             a
             2
             Inch
             and
             half
             Rocket
             ,
             we
             Complicate
             other
             Rockets
             ,
             viz.
             a
             four
             Inch
             Rocket
             thus
             ,
             we
             take
             the
             Cube
             of
             4
             ,
             which
             is
             64
             ,
             also
             we
             take
             the
             Cube
             of
             2½
             ,
             which
             is
             15.625
             ,
             with
             which
             we
             divide
             64
             ,
             the
             Quotient
             is
             4
             ▪
             and
             so
             many
             times
             the
             lesser
             Rocket
             is
             contained
             in
             the
             greater
             ,
             that
             is
             as
             4
             is
             to
             1.
             
             Then
             I
             look
             into
             the
             Tables
             of
             Ranges
             for
             the
             year
             1691.
             
             Iune
             1
             ,
             and
             in
             the
             second
             Column
             I
             find
             the
             requisite
             of
             Powder
             1
             and
             4
             ,
             and
             against
             the
             4
             in
             the
             third
             Column
             I
             find
             the
             Range
             3377
             ;
             and
             in
             the
             third
             Column
             against
             1
             I
             find
             the
             Range
             652
             ,
             which
             I
             multiply
             by
             4
             ,
             the
             Ratio
             of
             the
             Rockets
             ,
             and
             it
             is
             2608
             :
             Now
             if
             this
             last
             Number
             had
             been
             equal
             to
             3377
             ,
             the
             Range
             with
             the
             Quadruple
             of
             Powder
             ,
             it
             would
             have
             confirmed
             the
             shooting
             by
             the
             increase
             and
             decrease
             of
             
             Powder
             ;
             but
             as
             it
             is
             short
             ,
             it
             is
             a
             visible
             Demonstration
             of
             the
             error
             of
             that
             Doctrine
             :
             and
             if
             the
             Doctrine
             of
             shooting
             by
             the
             increase
             and
             decrease
             of
             Powder
             were
             true
             ,
             there
             would
             be
             no
             need
             for
             our
             Pyrobolistes
             to
             give
             different
             Velocities
             of
             Compositions
             to
             different
             sizes
             of
             Rockets
             ,
             but
             one
             Composition
             would
             have
             served
             all
             sizes
             ;
             which
             every
             Youth
             knows
             the
             Contrary
             .
          
           
           
             In
             the
             Parabola
             A
             H
             Z
             let
             A
             G
             be
             2608
             ,
             and
             A
             H
             3377
             ;
             then
             G
             Z
             and
             H
             Z
             are
             the
             Velocities
             of
             the
             equal
             and
             unequal
             Ranges
             .
             
               Toricellius
               22.
               
               Prop.
               de
               motu
               projec
               .
               lib
               secund
               .
            
          
           
             Then
             as
             G
             Z
             the
             Velocity
             of
             the
             equal
             Range
             ;
             is
             to
             one
             third
             of
             the
             Diameter
             of
             the
             four
             Inch
             Rocket
             1.
             333
             ;
             so
             is
             H
             Z
             the
             Velocity
             of
             the
             unequal
             
             Range
             ,
             to
             a
             larger
             Diameter
             of
             the
             4
             Inch
             Rocket
             ,
             to
             keep
             the
             same
             Composition
             .
          
           
             Or
             as
             the
             equal
             Range
             2608
             ,
             is
             to
             the
             unequal
             Range
             3377
             ;
             so
             is
             the
             square
             of
             the
             Diameter
             of
             the
             Orifice
             of
             the
             4
             Inch
             Rocket
             ,
             to
             the
             square
             of
             the
             Diameter
             of
             the
             Orifice
             of
             the
             Rocket
             inlarged
             ,
             keeping
             the
             same
             Composition
             .
          
           
             Or
             as
             the
             equal
             Range
             2608
             ,
             is
             to
             the
             unequal
             Range
             3377
             ;
             so
             is
             the
             Area
             of
             the
             Orifice
             of
             the
             Rocket
             of
             4
             Diameter
             ,
             when
             taking
             ⅓
             of
             the
             Diameter
             ;
             to
             the
             Area
             of
             the
             Orifice
             of
             the
             same
             Rocket
             when
             enlarged
             ,
             to
             bare
             the
             Composition
             that
             would
             serve
             a
             Rocket
             of
             two
             Inches
             and
             a
             half
             ,
             taking
             ⅓
             of
             the
             Diameter
             of
             the
             Rocket
             for
             the
             Diameter
             of
             its
             Orifice
             .
          
           
             
               Example
               .
            
             
               
                 2608
                 The
                 equal
                 Range
                 3
                 .
                 4′6308
              
               
                 3377
                 The
                 unequal
                 Range
                 3.028531
              
               
                 The
                 square
                 of
                 1.333
                 ,
                 &c.
                 the
                 Diam
                 .
                 of
                 the
                 equal
                 Oriffice
                 .249660
              
               
                 Take
                 the
                 half
                 .361883
              
               
                 The
                 Diam
                 .
                 of
                 the
                 new
                 Orifice
                 1.516
                 one
                 Inch
                 and
                 half
                 .180941
              
            
          
           
             
             
               Take
               another
               Example
               .
            
             
               August
               24.
               1691.
               
               I
               look
               in
               Column
               2
               ,
               and
               find
               the
               Requisites
               of
               Powder
               half
               an
               Ounce
               ,
               and
               2
               Ounces
               ,
               and
               against
               those
               Requisites
               in
               Column
               3
               I
               find
               1482
               the
               unequal
               Range
               ,
               and
               236
               the
               equal
               Range
               ;
               which
               I
               multiply
               by
               4
               ,
               and
               it
               makes
               944.
               
            
             
               
                 944
                 The
                 equal
                 Range
                 2.974972
              
               
                 1482
                 The
                 unequal
                 Range
                 3.170848
              
               
                 The
                 Square
                 of
                 1.333
                 ,
                 &c.
                 the
                 equal
                 Orifice
                 .249660
              
               
                 .445536
              
               
                 The
                 Diameter
                 of
                 the
                 new
                 Orifice
                 1.67
                 .222768
              
            
             
               Here
               may
               be
               seen
               the
               concurrence
               of
               Experiments
               made
               upon
               another
               account
               ,
               not
               then
               thinking
               to
               apply
               it
               to
               the
               Complication
               of
               Rockets
               .
               I
               made
               2
               Rockets
               of
               4
               Inches
               Diameter
               ,
               and
               a
               Taper
               bit
               according
               to
               this
               method
               ,
               and
               bored
               three
               Diameters
               ,
               and
               left
               2
               Inch●s
               Solid
               ,
               and
               they
               rose
               well
               .
            
             
               An
               example
               of
               a
               Rocket
               of
               6
               Inches
               Diameter
               ,
               keeping
               the
               same
               Composition
               .
               Take
               the
               Cube
               of
               6
               ,
               which
               is
               216
               ,
               
               divide
               that
               Cube
               by
               the
               Cube
               of
               4
               ,
               which
               is
               64
               ,
               the
               Quotient
               is
               3
               ,
               that
               is
               the
               Composition
               in
               the
               Rocket
               of
               4
               Inches
               ,
               is
               to
               the
               Composition
               in
               the
               Rocket
               of
               6
               Inches
               ,
               is
               as
               1
               to
               3
               ;
               then
               I
               look
               in
               the
               Table
               of
               Aug.
               24.
               and
               find
               in
               the
               second
               Column
               the
               Requisites
               of
               Powder
               half
               an
               Ounce
               ,
               and
               an
               Ounce
               and
               a
               half
               ;
               and
               against
               these
               Requisites
               in
               Column
               three
               800
               ,
               the
               unequal
               Range
               ,
               and
               236
               the
               equal
               Range
               ,
               which
               I
               multiply
               by
               3
               ,
               and
               it
               makes
               708
               :
               then
               as
               4
               is
               to
               6
               ,
               so
               is
               twelve
               half
               quarters
               of
               an
               Inch
               ,
               the
               Diameter
               of
               the
               new
               Orifice
               of
               the
               four
               Inch
               Rocket
               ,
               to
               eighteen
               half
               quarters
               of
               Inches
               ;
               that
               is
               2
               Inches
               and
               1
               quarter
               :
               or
               as
               4
               is
               to
               6
               ,
               so
               is
               1½
               ,
               that
               is
               3
               halfs
               ,
               to
               4½
               half
               Inches
               ,
               that
               is
               2¼
               .
               Then
               I
               had
               no
               such
               Ranges
               ,
               that
               their
               Requisites
               of
               Powder
               were
               in
               Proportion
               as
               the
               Cube
               of
               6
               is
               to
               the
               Cube
               of
               2½
               ;
               therefore
               was
               I
               forced
               to
               help
               my self
               by
               Proportion
               ,
               which
               is
               the
               same
               in
               Substance
               .
            
             
               
                 708
                 The
                 equal
                 Range
                 2.850033
              
               
                 800
                 The
                 unequal
                 Range
                 2.903089
              
               
                 The
                 Square
                 of
                 2¼
                 ,
                 or
                 18
                 half
                 quarters
                 2.510544
              
               
                 The
                 half
                 of
                 this
                 Logarithm
                 2.563600
              
               
                 Half
                 quarters
                 of
                 Inches
                 19.13
                 that
                 is
                 2.2
                 is
                 1.281800
              
            
          
           
             
             
               A
               second
               Example
               ,
               
                 April
                 21
                 ▪
                 1692.
                 
              
            
             
               I
               look
               in
               Column
               2
               ,
               and
               find
               the
               Requisites
               of
               Powder
               12
               Drams
               ,
               and
               36
               Drams
               ;
               and
               against
               these
               Requisites
               in
               the
               third
               Column
               I
               find
               1176
               the
               unequal
               Range
               ,
               and
               303
               the
               equal
               Range
               ,
               which
               I
               multiply
               by
               3
               ,
               and
               it
               makes
               909.
               
            
             
               
                 909
                 The
                 equal
                 Range
                 2.958564
              
               
                 1176
                 The
                 unequal
                 Range
                 3.070407
              
               
                 The
                 Square
                 of
                 18
                 half
                 quarters
                 2.510544
              
               
                 2.622387
              
               
                 20.47
                 ,
                 that
                 is
                 2
                 Inches
                 and
                 a
                 half
                 ,
                 and
                 47
                 /
                 100
                 1.311193
              
            
             
               Here
               may
               be
               seen
               one
               Example
               makes
               the
               Diameter
               a
               little
               more
               than
               two
               Inches
               and
               a
               half
               ,
               and
               in
               the
               other
               a
               little
               less
               ,
               therefore
               we
               make
               the
               Taper
               Bores
               just
               two
               Inches
               and
               a
               half
               for
               a
               6
               Inch
               Rocket
               .
               To
               work
               from
               a
               two
               Inch
               and
               a
               half
               Rocket
               to
               an
               Inch
               ,
               put
               the
               unequal
               Range
               in
               the
               first
               place
               ,
               and
               the
               Work
               is
               done
               .
               The
               Composition
               these
               4
               and
               6
               Inch
               Rockets
               were
               made
               of
               ,
               were
               1
               Sulphur
               ,
               1½
               Coal
               ,
               and
               4
               Saltpetre
               ;
               but
               I
               believe
               1
               Sulphur
               ,
               1
               Coal
               ,
               and
               4
               Salt-petre
               would
               do
               better
               ,
               there
               being
               no
               
               great
               danger
               of
               the
               Rocket
               breaking
               ,
               by
               Reason
               of
               the
               large
               Diameter
               of
               the
               Bore
               ,
               and
               Tapering
               to
               a
               point
               ;
               and
               by
               the
               same
               Reason
               ,
               a
               lesser
               solid
               Head
               is
               required
               ,
               that
               is
               about
               2
               Inches
               in
               a
               4
               Inch
               ,
               and
               1¼
               in
               a
               6
               or
               8
               Inch
               Rocket
               ,
               will
               suffice
               .
            
          
        
         
           
             PROPOSITION
             XV.
             
          
           
             The
             Complication
             of
             Rockets
             in
             Relation
             to
             their
             Composition
             ,
             with
             some
             Cautions
             and
             Limitations
             .
          
           
             TO
             decrease
             the
             Velocity
             of
             the
             Composition
             of
             1
             ,
             1½
             ,
             and
             4
             ,
             which
             served
             to
             a
             2½
             Inch
             Rocket
             ,
             to
             make
             it
             fit
             for
             a
             4
             Inch
             Rocket
             :
             remember
             the
             Ratio
             of
             the
             Rockets
             are
             as
             1
             to
             4.
             
             Look
             in
             the
             Table
             of
             Ranges
             ,
             and
             find
             the
             Requisites
             of
             Powder
             in
             the
             second
             Column
             ,
             as
             1
             to
             4
             ,
             and
             against
             them
             in
             the
             third
             Column
             the
             Ranges
             ,
             viz.
             3377
             and
             652
             ,
             then
             multiply
             the
             equal
             Range
             by
             4
             ,
             and
             it
             is
             2608
             ,
             (
             in
             fig.
             1.
             )
             In
             the
             Parabola
             Z
             A
             H
             ,
             let
             A
             H
             be
             equal
             to
             3377
             ,
             and
             A
             G
             equal
             to
             2608
             ;
             then
             H
             Z
             ,
             and
             G
             Z
             will
             be
             
             the
             Velocity
             of
             the
             Powder
             ,
             which
             projected
             those
             Ranges
             ,
             and
             we
             increase
             or
             decrease
             the
             Velocity
             of
             the
             Salpetre
             by
             the
             Ratio
             of
             G
             Z
             to
             H
             Z
             :
             then
             let
             A
             C
             in
             fig.
             2
             ,
             be
             equal
             to
             H
             Z
             in
             fig.
             1
             ,
             and
             A
             B
             in
             fig.
             2
             ,
             be
             equal
             to
             G
             Z
             in
             fig
             1
             ;
             then
             draw
             the
             Ordinate
             C
             H
             and
             B
             G
             in
             fig.
             2
             ,
             and
             by
             these
             two
             Lines
             ,
             viz.
             C
             H
             and
             B
             G
             we
             increase
             or
             decrease
             the
             Velocity
             of
             the
             Coal
             .
             Further
             ,
             let
             D
             F
             in
             fig.
             3
             ,
             be
             equal
             to
             C
             H
             in
             fig.
             2
             ;
             and
             D
             E
             in
             fig.
             3.
             be
             equal
             to
             B
             G
             in
             fig.
             2
             :
             draw
             the
             Ordinates
             F
             K
             and
             E
             I
             ,
             and
             by
             these
             3
             Lines
             we
             increase
             or
             decrease
             the
             Velocity
             of
             the
             Sulphur
             .
          
           
             Then
             if
             we
             take
             the
             Logarit●m
             of
             (
             0
             )
             (
             1
             )
             (
             ●
             )
             (
             4
             )
             (
             8
             )
             3377
             3.518531
             1.759265
             0.879632
             0.439816
          
           
             And
             is
             26●8
             3.416308
             1.708154
             0.854077
             0.427038
             that
             is
             ,
             the
             Ranges
             under
             (
             0
             )
             ,
             their
             Logarithm
             under
             (
             1
             )
             the
             half
             of
             the
             Log.
             under
             (
             2
             )
             ,
             the
             numbers
             answering
             those
             Logarithms
             are
             the
             Lines
             H
             Z
             and
             G
             Z
             in
             fig.
             1.
             
             The
             Logarithm
             under
             (
             4
             )
             is
             the
             fourth
             part
             of
             the
             Logarithm
             under
             (
             1
             )
             :
             The
             Numbers
             answering
             these
             Logarithms
             ,
             are
             the
             Lines
             C
             H
             ,
             and
             B
             G
             in
             
             fig.
             2.
             
             Further
             ,
             the
             Logarithm
             under
             (
             8
             )
             is
             the
             eighth
             part
             of
             the
             Logarithm
             under
             (
             1
             )
             ;
             the
             Numbers
             answering
             those
             Logarithms
             ,
             are
             the
             Ordinates
             F
             K
             and
             E
             I
             in
             the
             Parabola
             F
             D
             K.
             
          
           
             
               Or
               you
               may
               take
               the
               difference
               of
               the
               Logarithms
               under
               (
               1
               )
               viz.
               102223
            
             
               Half
               51111
            
             
               Quarter
               25555
            
             
               Eighth
               12777
            
          
           
             By
             Adding
             or
             Subtracting
             these
             Log.
             to
             or
             from
             the
             Logarithm
             of
             the
             Salt-petre
             ,
             Coal
             ,
             and
             Sulphur
             ,
             you
             have
             your
             desire
             ,
             viz.
             their
             Velocities
             either
             increased
             or
             decreased
             :
             or
             thus
             ,
             take
             the
             difference
             of
             the
             Logarithm
             of
             the
             two
             Ranges
             102223
             ,
             and
             Subtract
             it
             from
             the
             Logarithm
             of
             the
             Square
             of
             the
             Number
             of
             Drams
             ,
             Ounces
             ,
             or
             Pounds
             of
             Salt-petre
             ,
             or
             from
             the
             Logarithm
             of
             the
             fourth
             power
             of
             the
             Numbers
             of
             Drams
             ,
             Ounces
             ,
             or
             Pounds
             of
             Coal
             .
             And
             Lastly
             ,
             that
             difference
             being
             Subtracted
             from
             the
             Logarithms
             of
             the
             eighth
             power
             of
             the
             Number
             of
             the
             Drams
             ,
             Ounces
             ,
             or
             Pounds
             of
             Sulphur
             ,
             there
             will
             remain
             three
             Logarithms
             ,
             the
             first
             being
             divided
             by
             2
             ,
             the
             
             second
             by
             4
             ,
             and
             the
             third
             by
             8
             ;
             there
             will
             remain
             three
             Logarithms
             ,
             the
             Numbers
             answering
             to
             which
             ,
             will
             be
             the
             Number
             of
             Drams
             ,
             and
             Tenths
             of
             the
             Salt-petre
             ,
             Coal
             ,
             and
             Sulphur
             desired
             .
          
           
             
               To
               Weaken
               the
               Velocity
               of
               the
               Composition
               of
               1
               ,
               1½
               ,
               and
               4.
               
            
             
               3377
               The
               unequal
               Range
               3.518531
            
             
               2608
               The
               equal
               Range
               3.416308
            
             
               The
               Square
               of
               64
               Drams
               of
               Saltpetre
               3.612360
            
             
               Take
               the
               half
               3.510137
            
             
               Drams
               56.9
               nine
               Tenths
               of
               Saltpetre
               1.755068
            
          
           
             
               The
               fourth
               power
               of
               twenty
               four
               Drams
               of
               Coal
               5.520844
            
             
               The
               difference
               of
               the
               Logarithm
               of
               unequal
               ,
               and
               equal
               Ranges
               Subtract
               .102223
            
             
               Is
               the
               Logarithm
               of
               the
               fourth
               power
               ,
               which
               being
               divided
               by
               fourth
               5.418621
            
             
               22
               Drams
               63
               /
               100
               of
               Coal
               1.354655
            
             
               
               The
               eighth
               power
               of
               fix
               〈…〉
               Drams
               of
               Sulphur
               9632960
            
             
               The
               difference
               of
               the
               Logarithm
               .102223
               Subtract
               .102223
            
             
               Is
               the
               Logarithm
               of
               the
               eighth
               power
               which
               being
               divided
               by
               8
               9.530737
            
             
               15
               Drams
               54
               /
               100
               of
               Sulphur
               1.191342
            
          
           
             The
             Composition
             will
             be
             Sulphur
             15½
             ,
             Coal
             22½
             ,
             and
             Saltpetre
             57
             ;
             but
             if
             you
             quicken
             the
             Velocity
             ,
             the
             equal
             Range
             will
             be
             in
             the
             first
             place
             of
             the
             Proportion
             .
          
        
         
           
           
             PROPOSITION
             XVI
             .
          
           
             Tables
             of
             Ranges
             made
             with
             Mortar-pieces
             .
          
           
             JUne
             1.
             1691.
             
             On
             Wimbleton-Heath
             at
             15
             deg
             .
             of
             Elevation
             ,
             with
             a
             four
             Inch
             Mortar-piece
             ,
             and
             a
             turned
             Iron
             Ball.
             
          
           
             
               
                 
                   1
                
                 
                   2
                
                 
                   3
                
              
               
                 
                   Experiments
                   .
                
                 
                   Powder
                   .
                
                 
                   Chain
                   .
                
              
               
                 
                   1
                
                 
                   ½
                
                 
                   213
                
              
               
                 
                   2
                
                 
                   1
                
                 
                   652
                
              
               
                 
                   3
                
                 
                   2
                
                 
                   1640
                
              
               
                 
                   4
                
                 
                   4
                
                 
                   3377
                
              
            
          
           
           
             August
             24.
             1691
             
             :
             At
             15
             deg
             .
             of
             Elevation
             ,
             with
             a
             3½
             Inches
             Mortar-piece
             ,
             and
             a
             turn'd
             Iron
             Ball.
             
          
           
             
               
                 
                   1
                
                 
                   2
                
                 
                   3
                
                 
                   4
                
                 
                   5
                
              
               
                 
                    
                
                 
                   The
                   Chamber
                   of
                   this
                   Mortar-piece
                   a
                   Frustum
                   of
                   a
                   Cone
                   .
                
                 
                   The
                   Chamber
                   of
                   this
                   Mortar
                   piece
                   a
                   Frustum
                   of
                   a
                   Sphere
                   .
                
              
               
                 
                    
                
                 
                   Powder
                
                 
                   Chain
                   .
                
                 
                   Powder
                
                 
                   Chain
                   .
                
              
               
                 
                   1
                
                 
                   ½
                
                 
                   236
                
                 
                   ½
                
                 
                   144
                
              
               
                 
                   2
                
                 
                   1
                
                 
                   496
                
                 
                   1
                
                 
                   304
                
              
               
                 
                   3
                
                 
                   1½
                
                 
                   800
                
                 
                   1½
                
                 
                   1258
                
              
               
                 
                   4
                
                 
                   2
                
                 
                   1482
                
                 
                   2
                
                 
                   3394
                
              
            
          
           
           
             ●
             April
             21.
             162.
             
             At
             15
             deg
             .
             of
             Elevation
             ,
             with
             a
             3½
             Inch
             Mortar-piece
             ,
             and
             a
             turn'd
             Iron
             Ball.
             
          
           
             
               
                 
                   1
                
                 
                   2
                
                 
                   3
                
              
               
                 
                   Experiment
                   .
                
                 
                   Powder
                   .
                
                 
                   Chain
                   .
                
              
               
                 
                   1
                
                 
                   12
                
                 
                   303
                
              
               
                 
                   2
                
                 
                   24
                
                 
                   746
                
              
               
                 
                   3
                
                 
                   36
                
                 
                   1176
                
              
               
                 
                   4
                
                 
                   48
                
                 
                   1820
                
              
               
                 
                   5
                
                 
                   60
                
                 
                   2698
                
              
            
          
           
             Thus
             have
             I
             given
             plain
             and
             easie
             Rules
             to
             the
             Young
             Pyrobolistes
             for
             the
             making
             of
             small
             Rockets
             ;
             and
             also
             for
             the
             making
             of
             great
             Rockets
             ,
             to
             them
             of
             a
             greater
             Knowledge
             and
             Purse
             ,
             even
             such
             as
             was
             reputed
             impossible
             ;
             for
             a
             4
             Inch
             Rocket
             was
             given
             in
             by
             our
             ablest
             Pyrobolistes
             to
             be
             out
             of
             size
             ,
             and
             therefore
             impossible
             to
             rise
             .
             Now
             ,
             if
             that
             4
             Inch
             Rocket
             was
             thought
             so
             ,
             what
             will
             they
             say
             to
             them
             of
             6
             ,
             8
             ,
             10
             or
             12
             Inches
             Diameter
             ;
             for
             certainly
             this
             Rule
             takes
             in
             all
             sizes
             to
             500
             or
             1000
             weight
             ,
             or
             higher
             .
          
           
           
             
               
                 Necessary
                 Tables
                 for
                 Rockets
                 .
              
               
                 
                   Inches
                   and
                   half
                   Inches
                   .
                
                 
                   Pounds
                   of
                   Rockets
                   .
                   Ounces
                
                 
                   Ounces
                   of
                   Compos
                   .
                   for
                   Rockets
                   .
                
                 
                   Pounds
                   of
                   the
                   Mall
                   .
                   Ounces
                
              
               
                 
                   1
                
                 
                   2
                   3
                
                 
                   4
                
                 
                   5
                   6
                
              
               
                 
                   1
                
                 
                   02
                
                 
                   0●01
                
                 
                   12
                
              
               
                 
                   1½
                
                 
                   08
                
                 
                   0004
                
                 
                   0002
                   08
                
              
               
                 
                   2
                
                 
                   001
                   02
                
                 
                   0010
                
                 
                   0006
                   0●
                
              
               
                 
                   2½
                
                 
                   002
                   04
                
                 
                   0018
                
                 
                   0011
                   11
                
              
               
                 
                   3
                
                 
                   003
                   12
                
                 
                   0032
                
                 
                   0020
                   04
                
              
               
                 
                   3½
                
                 
                   006
                   00
                
                 
                   0051
                
                 
                   0032
                   04
                
              
               
                 
                   4
                
                 
                   009
                   00
                
                 
                   0076
                
                 
                   0048
                   00
                
              
               
                 
                   4½
                
                 
                   012
                   13
                
                 
                   0108
                
                 
                   0068
                   08
                
              
               
                 
                   5
                
                 
                   017
                   09
                
                 
                   0148
                
                 
                   0093
                   12
                
              
               
                 
                   5½
                
                 
                   023
                   06
                
                 
                   0197
                
                 
                   0120
                   12
                
              
               
                 
                   6
                
                 
                   030
                   06
                
                 
                   0256
                
                 
                   0162
                   00
                
              
               
                 
                   6½
                
                 
                   038
                   10
                
                 
                   0326
                
                 
                   0206
                   06
                
              
               
                 
                   7
                
                 
                   048
                   04
                
                 
                   0407
                
                 
                   0251
                   00
                
              
               
                 
                   7½
                
                 
                   059
                   05
                
                 
                   0500
                
                 
                   0316
                   06
                
              
               
                 
                   8
                
                 
                   072
                   00
                
                 
                   0607
                
                 
                   0384
                   00
                
              
               
                 
                   8½
                
                 
                   086
                   06
                
                 
                   0728
                
                 
                   0460
                   09
                
              
               
                 
                   9
                
                 
                   102
                   08
                
                 
                   0864
                
                 
                   0546
                   12
                
              
               
                 
                   9½
                
                 
                   120
                   09
                
                 
                   1016
                
                 
                   0643
                   00
                
              
               
                 
                   10
                
                 
                   140
                   10
                
                 
                   1285
                
                 
                   0748
                   04
                
              
               
                 
                   10½
                
                 
                   162
                   13
                
                 
                   1372
                
                 
                   0868
                   03
                
              
               
                 
                   11
                
                 
                   187
                   02
                
                 
                   1578
                
                 
                   0998
                   04
                
              
               
                 
                   11½
                
                 
                   213
                   14
                
                 
                   1805
                
                 
                   ●40
                   10
                
              
               
                 
                   12
                
                 
                   423
                   00
                
                 
                   2048
                
                 
                   1296
                   ●0
                
              
            
          
           
             
             
               The
               Use
               of
               these
               Necessary
               Tables
               .
            
             
               IN
               the
               first
               Column
               you
               have
               the
               Inches
               and
               half
               Inches
               ,
               to
               12
               Inches
               .
               In
               the
               second
               and
               third
               Columns
               you
               have
               the
               weight
               of
               Pounds
               and
               Ounces
               of
               the
               Rockets
               ,
               when
               six
               Diameters
               in
               length
               .
               In
               the
               fourth
               Column
               you
               have
               the
               Ounces
               of
               Composition
               to
               fill
               those
               Rockets
               4
               Diameters
               .
               In
               the
               fifth
               and
               sixth
               Columns
               you
               have
               the
               weight
               of
               the
               Mallets
               to
               drive
               those
               Rockets
               in
               Pounds
               and
               Ounces
               .
            
             
               An
               Example
               in
               the
               whole
               ,
               for
               a
               three
               Inch
               Rocket
               .
               I
               find
               3
               in
               the
               first
               Column
               under
               Inches
               and
               half
               Inches
               ;
               in
               the
               second
               and
               third
               Column
               ,
               under
               Pounds
               and
               Ounces
               of
               Rockets
               .
               I
               find
               three
               Pounds
               and
               12
               Ounces
               the
               weight
               of
               the
               Rocket
               when
               finished
               ,
               being
               6
               Diameters
               .
               In
               the
               fourth
               Column
               I
               find
               32
               Ounces
               of
               Composition
               to
               fill
               4
               Diameters
               .
               In
               the
               fifth
               and
               sixth
               Columns
               I
               find
               20
               Pounds
               4
               Ounces
               for
               the
               Mallet
               to
               drive
               that
               Rocket
               .
            
             
               When
               Rockets
               are
               of
               a
               great
               weight
               ,
               the
               Mallet
               will
               be
               too
               heavy
               to
               manage
               ,
               therefore
               do
               thus
               .
               The
               Mallet
               of
               a
               three
               Inch
               Rocket
               ,
               viz.
               20
               Pounds
               weight
               is
               
               of
               a
               good
               size
               ;
               and
               we
               will
               make
               an
               Example
               of
               a
               3
               Inch
               and
               7½
               Rockets
               ,
               and
               we
               will
               take
               it
               as
               useful
               that
               all
               Rockets
               to
               3
               Inches
               Diameter
               ,
               may
               be
               filled
               with
               eight
               Charges
               ,
               but
               further
               not
               ,
               then
               against
               7½
               in
               the
               first
               Column
               .
               In
               Colum
               4
               I
               find
               500
               Ounces
               of
               Composition
               for
               that
               Rocket
               ,
               which
               I
               divide
               by
               8
               ,
               and
               the
               Quotient
               will
               be
               62.5
               .
               In
               the
               Parabola
               A
               H
               Z
               ,
               let
               A
               H
               be
               the
               Number
               of
               Ounces
               5062
               5
               in
               the
               Mallet
               for
               the
               7½
               Rocket
               ,
               and
               A
               G
               the
               Number
               of
               Ounces
               324
               in
               the
               Mallet
               for
               a
               3
               Inch
               Rocket
               ;
               then
               the
               Ordinates
               H
               Z
               and
               G
               Z
               will
               be
               the
               Forces
               of
               those
               Mallets
               ;
               then
               as
               H
               Z
               is
               to
               G
               Z
               ,
               so
               is
               62.5
               to
               15.811
               ,
               that
               is
               15
               Ounces
               and
               ●●●1000
               shall
               be
               your
               Charge
               of
               Composition
               .
               Further
               ,
               divide
               62.5
               by
               15.811
               ,
               the
               Quotient
               will
               be
               3.2●22
               /
               10000
               the
               Number
               of
               Charges
               in
               the
               eight
               part
               of
               the
               Composition
               ;
               then
               multiply
               39529
               by
               8
               ,
               there
               will
               be
               31.
               
               ●●31000
               Charges
               in
               that
               Rocket
               .
               Lastly
               ,
               give
               about
               eighteen
               blows
               to
               every
               Charge
               ,
               with
               that
               Mallet
               for
               the
               3
               Inch
               Rocket
               ,
               so
               your
               Work
               will
               be
               done
               ,
               by
               two
               Men
               ,
               in
               two
               hours
               .
            
             
               
               
                 324
                 2.510545
              
               
                 62.5
                 Squared
                 3.591760
              
               
                 5062.5
                 Sub.
                 6.102305
              
               
                 3.704364
              
               
                 ½
                 2.397941
              
               
                 15.811
                 is
                 Sub.
                 1.198970
              
               
                 62.5
                 is
                 from
                 1.795880
              
               
                 3.9529
                 Rest
                 0.596910
              
               
                 8.
                 
                 Log.
                 0.903090
              
               
                 31.623
                 Sum
                 of
                 2
                 Logarithm
                 1.500000
              
               
                 15811
                 Add
                 1.198970
              
               
                 500.
                 the
                 Sum
                 of
                 Logarithm
                 2.698970
              
            
             
               Iune
               26.
               1696.
               
               Then
               was
               fired
               a
               4
               and
               6
               Inch
               Rocket
               ,
               Mr.
               Ayres
               Junior
               fired
               them
               both
               off
               a
               hand
               ,
               Mr.
               Dandridge
               ,
               Mr.
               Rodway
               ,
               my self
               ,
               and
               several
               other
               being
               present
               :
               the
               6
               Inch
               Rocket
               had
               3
               Inches
               solid
               Head
               ,
               that
               is
               about
               the
               double
               of
               what
               it
               ought
               to
               have
               had
               ,
               the
               Reason
               of
               that
               was
               to
               hold
               Fire
               ;
               it
               moved
               off
               the
               Nails
               at
               about
               78
               deg
               .
               of
               Elevation
               ,
               and
               the
               Horizontal
               Range
               was
               just
               15
               Chains
               ,
               that
               is
               330
               Yards
               ,
               by
               which
               we
               may
               find
               the
               Altitude
               of
               that
               Parabola
               it
               moved
               in
               ,
               and
               the
               greatest
               Range
               ,
               and
               Consequently
               the
               greatest
               Perpendicular
               Altitude
               it
               could
               have
               reached
               .
            
             
             
               In
               the
               Parabola
               A
               B
               C
               ,
               Let
               A
               C
               be
               equal
               to
               330
               Yards
               ,
               A
               D
               equal
               to
               165
               the
               Angle
               D
               A
               E
               78
               degrees
               ,
               then
               in
               the
               right
               Angled
               Triangle
               E
               D
               A.
               
            
             
               
               
                 Radius
                 90
                 10.000000
              
               
                 Tangent
                 78
                 10.672525
              
               
                 A
                 D
                 165
                 2.217484
              
               
                 D
                 E
                 776.22
                 2.889989
              
               
                 D
                 B
                 388.11
              
               
                 As
                 the
                 Sine
                 of
                 the
                 double
                 of
                 the
                 Elevation
                 407
                 2.609594
              
               
                 Is
                 to
                 Radius
                 1000
                 3.000000
              
               
                 So
                 is
                 the
                 Horizontal
                 distance
                 at
                 78
                 deg
                 .
                 330
                 2.518514
              
               
                 To
                 the
                 greatest
                 Range
                 in
                 the
                 Parabola
                 810.8
                 2.908920
              
               
                 Half
                 of
                 the
                 greatest
                 Range
                 is
                 the
                 Perpend
                 ▪
                 hight
                 desired
                 405.4
              
            
             
               So
               then
               the
               greatest
               height
               of
               that
               6
               Inches
               Rocket
               in
               its
               flight
               was
               three
               hundred
               eighty
               and
               eight
               Yards
               ,
               had
               it
               been
               put
               Perpendicular
               ,
               its
               height
               would
               have
               been
               four
               hundred
               and
               five
               Yards
               .
            
             
               The
               flight
               of
               Rockets
               does
               sufficiently
               well
               agree
               with
               that
               of
               the
               Parabola
               at
               each
               end
               of
               the
               Quadrant
               ;
               but
               towards
               45
               degrees
               it
               differs
               more
               .
            
             
               A
               Rocket
               of
               an
               Inch
               and
               half
               Diameter
               ,
               filled
               5
               Diameters
               ,
               and
               bored
               two
               and
               a
               half
               ,
               and
               a
               little
               more
               ,
               with
               this
               Composition
               ,
               viz.
               8
               Powder-dust
               ,
               6
               Salt-petre
               ,
               2½
               Coal
               ,
               and
               1
               Sulphur
               ,
               and
               layed
               to
               30
               degrees
               of
               Elevation
               ;
               Ranged
               the
               Rocket
               880
               Yards
               ,
               that
               is
               half
               a
               Mile
               .
            
          
        
         
           
           
             To
             make
             Rockets
             to
             Swim
             upon
             the
             Water
             ,
             Dive
             into
             the
             Water
             ,
             and
             keep
             above
             the
             Water
             .
          
           
             
               An
               Example
               of
               an
               Inch
               Rocket
               .
            
             
               MAke
               the
               Case
               12
               Diameters
               ,
               which
               will
               be
               in
               this
               Example
               12
               Inches
               ,
               fill
               it
               with
               two
               Compositions
               ,
               viz
               a
               Weaker
               and
               a
               Stronger
               ;
               fill
               2
               Inches
               with
               the
               Weaker
               Compsition
               ,
               then
               1½
               with
               the
               Strong
               ,
               then
               2
               with
               the
               Weak
               ,
               1½
               with
               the
               Strong
               .
               Lastly
               ,
               2
               Inches
               with
               the
               Weak
               ,
               then
               there
               will
               remain
               3
               Inches
               for
               Corn
               Powder
               ,
               for
               the
               Report
               .
            
             
               The
               Weak
               Composition
               to
               Swim
               above
               Water
               ;
               take
               3
               of
               meal
               Powder
               ,
               1
               of
               Coal
               .
            
             
               The
               Strong
               Composition
               to
               Dive
               under
               the
               Water
               ,
               and
               leap
               above
               the
               Water
               ;
               take
               8
               of
               mealed
               Powder
               ,
               1
               of
               Saltpetre
               ,
               and
               1
               of
               Coal
               .
            
          
           
             
             
               To
               divide
               the
               Driver
               .
            
             
               FRom
               the
               lower
               end
               of
               your
               Driver
               set
               off
               3
               Inches
               ,
               then
               2
               Inches
               ,
               then
               1
               ●
               ,
               then
               2
               Inches
               ,
               then
               1½
               ▪
               Lastly
               ,
               2
               Inches
               ;
               make
               the
               Rockets
               of
               a
               just
               length
               ,
               and
               so
               you
               may
               see
               the
               Divisions
               of
               the
               Driver
               appear
               above
               the
               Case
               as
               you
               fill
               .
            
          
           
             
               The
               Use.
               
            
             
               FIre
               the
               Rocket
               in
               your
               Hand
               with
               with
               your
               Port-fire
               ,
               through
               it
               into
               a
               deep
               Water
               ,
               (
               otherwise
               it
               will
               stick
               in
               the
               Mud
               )
               it
               will
               Swim
               a
               little
               while
               ;
               but
               when
               the
               Strong
               Composition
               takes
               fire
               it
               will
               Dive
               ,
               and
               when
               the
               Strong
               Composition
               is
               spent
               it
               will
               jump
               up
               ,
               &c.
               
               The
               Weak
               Composition
               being
               the
               last
               ,
               the
               Rocket
               for
               some
               time
               will
               Swim
               upon
               the
               Water
               ,
               and
               then
               give
               a
               Report
               .
               This
               Rocket
               is
               all
               Solid
               .
            
          
           
             
               To
               make
               a
               Rocket
               Charger
               .
            
             
               LET
               the
               length
               of
               the
               Charger
               E
               G
               ,
               be
               one
               Diameter
               and
               half
               ,
               the
               breadth
               of
               the
               Charger
               H
               Z
               ,
               one
               Diameter
               and
               one
               third
               ,
               the
               length
               of
               the
               
               Neck
               of
               the
               Charger
               that
               slippeth
               upon
               the
               Handle
               B
               C
               ,
               two
               Diameters
               ;
               the
               breadth
               of
               that
               Ferril
               A
               B
               ,
               one
               third
               of
               the
               Diameter
               of
               the
               Rocket
               :
               betwixt
               eight
               or
               nine
               of
               these
               Charges
               will
               fill
               a
               Rocket
               4
               Diameters
               .
            
             
             
               You
               may
               cut
               the
               Charger
               A
               B
               C
               D
               H
               G
               Z
               A
               in
               Paper
               ,
               then
               it
               may
               be
               made
               in
               Copper
               ,
               Close
               A
               to
               D
               ,
               and
               B
               to
               C
               ,
               Sodder
               both
               ends
               together
               ;
               bring
               H
               G
               Z
               into
               more
               than
               half
               a
               round
               ,
               and
               A
               B
               and
               C
               D
               in
               a
               round
               ,
               put
               it
               then
               upon
               a
               Handle
               ,
               then
               it
               is
               fit
               for
               use
               .
            
          
           
             
             
               To
               make
               good
               Coal
               for
               Rockets
               .
            
             
               TAke
               pieces
               of
               a
               light
               dry
               Deal
               Board
               about
               12
               Inches
               in
               length
               ,
               and
               about
               the
               thickness
               of
               2
               Fingers
               or
               less
               ;
               put
               them
               into
               an
               Oven
               ,
               put
               fire
               to
               the
               Wood
               ;
               when
               they
               are
               burned
               enough
               take
               them
               out
               ,
               and
               put
               them
               into
               an
               Iron
               ,
               Brass
               ,
               or
               Eathern
               Pot
               ,
               close
               it
               well
               with
               a
               Cover
               ,
               that
               it
               takes
               no
               Air
               ,
               the
               Fire
               being
               extinguished
               ,
               beat
               it
               and
               pass
               it
               through
               a
               fine
               Sieve
               ,
               then
               it
               is
               fit
               for
               use
               .
               If
               the
               Wood
               be
               not
               well
               burnt
               ,
               put
               it
               into
               the
               Oven
               again
               ,
               and
               so
               repeat
               your
               Work
               :
               such
               Coal
               will
               make
               a
               Rocket
               fly
               very
               lively
               ,
               if
               not
               with
               two
               much
               Life
               .
            
          
           
             
               Compositions
               for
               Reports
               .
            
             
               
                 
                   
                      
                  
                   
                     A
                  
                   
                     B
                  
                   
                     C
                  
                   
                     D
                  
                
                 
                   
                     〈…〉
                     Saltpetre
                  
                   
                     9.
                     
                  
                   
                     4.
                     
                  
                   
                     3.
                     
                  
                   
                     2.
                     
                  
                
                 
                   
                     Salt
                     of
                     Tartar
                  
                   
                     3.
                     
                  
                   
                     3.
                     
                  
                   
                     2.
                     
                  
                   
                     1.
                     
                  
                
                 
                   
                     Sulphur
                  
                   
                     1.
                     
                  
                   
                     2.
                     
                  
                   
                     1.
                     
                  
                   
                     1.
                     
                  
                
              
            
             
               Take
               Sulphur
               1
               ,
               Tartar
               3
               ,
               and
               Salt-petre
               9
               ,
               grind
               these
               well
               together
               ,
               and
               dry
               them
               .
               A
               few
               Grains
               of
               this
               Powder
               being
               fired
               ,
               will
               give
               as
               great
               a
               Clap
               as
               a
               Musket
               when
               it
               is
               discharged
               .
               Dr.
               
                 French
                 ,
                 pag.
              
               171.
               
               Take
               any
               of
               these
               Ingredients
               
               under
               A
               B
               C
               or
               D
               ,
               mix
               them
               well
               together
               ,
               put
               a
               little
               quantity
               of
               that
               mixture
               into
               a
               Fire-Pan
               ,
               set
               it
               upon
               the
               Fire
               ,
               and
               in
               a
               little
               time
               it
               will
               give
               a
               great
               Report
               .
            
          
           
             
               A
               further
               use
               of
               the
               Tables
               .
            
             
               WHat
               is
               done
               in
               the
               14
               and
               15
               Propositions
               ,
               by
               taking
               the
               Cubes
               of
               the
               Diameter
               of
               the
               Bores
               of
               the
               Rockets
               ,
               may
               be
               done
               by
               the
               Tables
               in
               2
               and
               3
               ,
               or
               Tab
               4.
               
               Thus
               ,
               look
               in
               the
               first
               Column
               for
               the
               Diameters
               of
               the
               Rockets
               ,
               viz.
               2½
               and
               4
               ,
               and
               against
               them
               ,
               in
               Column
               2
               and
               3
               ,
               I
               find
               2
               Pounds
               and
               4
               Ounces
               ,
               and
               9
               Pounds
               ,
               divide
               the
               greater
               Number
               by
               the
               lesser
               ,
               the
               Quotient
               will
               be
               4
               ,
               near
               enough
               ,
               so
               the
               Ratio
               of
               these
               two
               Rockets
               are
               as
               4
               to
               1
               ,
               and
               this
               is
               by
               the
               weight
               of
               the
               Rockets
               .
            
             
               In
               the
               other
               Example
               I
               find
               4
               and
               6
               in
               the
               first
               Column
               ,
               and
               against
               them
               〈…〉
               Column
               4
               ,
               I
               find
               76
               and
               256
               Ounces
               of
               Composition
               for
               these
               two
               Rockets
               ;
               then
               divide
               the
               greater
               by
               the
               lesser
               ,
               the
               Quotient
               will
               be
               3
               and
               more
               ,
               which
               is
               the
               same
               thing
               as
               if
               you
               made
               use
               of
               the
               Cubes
               of
               their
               Diameters
               ;
               for
               indeed
               these
               Tables
               are
               made
               by
               the
               Cubes
               of
               the
               respective
               Diameters
               .
            
          
        
      
       
         
         
           A
           Conclusion
           .
        
         
           IF
           any
           one
           presumes
           to
           say
           they
           have
           Resolved
           the
           14.
           
           Proposition
           before
           the
           Publication
           of
           this
           ,
           they
           might
           have
           been
           so
           kind
           as
           to
           put
           it
           into
           Practice
           for
           the
           Defence
           of
           the
           Nation
           .
           If
           any
           say
           they
           can
           do
           it
           ,
           I
           desire
           them
           so
           to
           do
           ,
           
             That
             I
             may
             see
             my
             desires
             accomplished
             ,
          
           viz.
           Great
           Guns
           and
           their
           Carriages
           truly
           fortified
           and
           neatly
           made
           ,
           
             which
             would
             be
             great
             satisfaction
          
           ;
           however
           this
           may
           shew
           to
           the
           next
           Age
           what
           has
           been
           offered
           to
           this
           .
        
         
           
             Iuly
             25.
             1696.
             
          
        
         
           FINIS
           .