1Regulator 6. of thoſe parts high; of which it ran before but 5. let
6 be found in the row of heights, and let the number 11. ſtand
ing under the ſame be taken and added to the number 25.
that is placed under the number 9. in the Additions, and 5. in
the heights, and you ſhall have 36; which is the quantity of the
water that runneth with the height of the River, when it is high
6 of thoſe parts, whereof it was before but 5.
6 be found in the row of heights, and let the number 11. ſtand
ing under the ſame be taken and added to the number 25.
that is placed under the number 9. in the Additions, and 5. in
the heights, and you ſhall have 36; which is the quantity of the
water that runneth with the height of the River, when it is high
6 of thoſe parts, whereof it was before but 5.
3. But if it ſhould be deſired, to know how much water it is
requiſite to add to make the River riſe ſo, as that it may run in
height 8. of thoſe parts of which before it ran but 5; one
ought to take the ſum of the number of the Series of Additions
ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39.
and this ſhall be the ſumme that muſt be added to 25: So that
to make the River to run 8. of thoſe parts in height, of which it
before did run 5, it will be neceſſary to add 39. of thoſe parts,
of which the River before was 25.
requiſite to add to make the River riſe ſo, as that it may run in
height 8. of thoſe parts of which before it ran but 5; one
ought to take the ſum of the number of the Series of Additions
ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39.
and this ſhall be the ſumme that muſt be added to 25: So that
to make the River to run 8. of thoſe parts in height, of which it
before did run 5, it will be neceſſary to add 39. of thoſe parts,
of which the River before was 25.
4. Likewiſe the ſame Table giveth the quantity of water
that runneth from time to time through a River, that increaſeth
by the addition of new water to the ſame in one of its heights, the
quantity of its water be known. As for example: If we knew that
the River in one minute of an hour diſchargeth 2500. of thoſe mea
ſures of water, and runneth in height 5. parts in the Regulator, and
afterwards ſhould ſee that it runneth 8 Palms high, finding in the
row of quantity the number placed under 8. which is 64. we would
ſay that the River heightned, carrieth of water 64. of thoſe parts
whereof it carried before but 25; and becauſe before it carried
2500. meaſures, by the Golden Rule we will ſay, that the River
carrieth 6400. of thoſe meaſures, of which before it carried 2500.
that runneth from time to time through a River, that increaſeth
by the addition of new water to the ſame in one of its heights, the
quantity of its water be known. As for example: If we knew that
the River in one minute of an hour diſchargeth 2500. of thoſe mea
ſures of water, and runneth in height 5. parts in the Regulator, and
afterwards ſhould ſee that it runneth 8 Palms high, finding in the
row of quantity the number placed under 8. which is 64. we would
ſay that the River heightned, carrieth of water 64. of thoſe parts
whereof it carried before but 25; and becauſe before it carried
2500. meaſures, by the Golden Rule we will ſay, that the River
carrieth 6400. of thoſe meaſures, of which before it carried 2500.
In this progreſs of Nature, is one thing really curious, and that
at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro
ceeding ordinately in the diverſions and additions, with additi
ons and diverſions ſo unequal, the abatings do notwithſtanding
alwaies prove equal, and ſo do the riſings: And who would ever
think that a River in height, v. g. 10. Palms, running and carry
ing an hundred meaſures in a minute of an hour, is to abate but
one Palm, onely by the diverſion of 19. of thoſe meaſures; and
then again, that the buiſineſs cometh to that paſs, that it abateth
likewiſe a Palm by the diverſion of three onely of thoſe meaſures,
nay, by the diverſion of but one meaſure? and yet it is moſt
certain: And this truth meets with ſo manifeſt proofs in experi
ence, that it is very admirable! And for the full ſatisfaction of
thoſe, who not being able to comprehend ſubtil demonſtrati
ons, desire to be clearly inform'd by the matters of fact, and to
ſee with their bobily eyes, and touch with their hands, what their
underſtanding and reaſon cannot reach unto: I will hear add
another very eaſie way to reduce all to an experiment, the
at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro
ceeding ordinately in the diverſions and additions, with additi
ons and diverſions ſo unequal, the abatings do notwithſtanding
alwaies prove equal, and ſo do the riſings: And who would ever
think that a River in height, v. g. 10. Palms, running and carry
ing an hundred meaſures in a minute of an hour, is to abate but
one Palm, onely by the diverſion of 19. of thoſe meaſures; and
then again, that the buiſineſs cometh to that paſs, that it abateth
likewiſe a Palm by the diverſion of three onely of thoſe meaſures,
nay, by the diverſion of but one meaſure? and yet it is moſt
certain: And this truth meets with ſo manifeſt proofs in experi
ence, that it is very admirable! And for the full ſatisfaction of
thoſe, who not being able to comprehend ſubtil demonſtrati
ons, desire to be clearly inform'd by the matters of fact, and to
ſee with their bobily eyes, and touch with their hands, what their
underſtanding and reaſon cannot reach unto: I will hear add
another very eaſie way to reduce all to an experiment, the
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