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value of 40.61 cm (15 pouces). (In his calculations Mariotte assumes that one lieue (league)
contains 2300 toises (fathoms); as 1 toise equals 6 pieds, the length of his league is about
4482.8 m, which is slightly different from Perrault's assumed length.) With this value, and
assuming that the Seine catchment upstream from Paris occupies roughly 60 286.27 km
2
(3000 square leagues), he figures that this catchment would receive roughly 24.479 km
3
(7.1415
×
10
11
ft
3
) of rain per year, on average. He estimates the average velocity of the
Seine at the Pont Rouge in Paris from float velocity observations of around 1.35 m s
−
1
(250 ft min
−
1
), which he reduces to 0.54 m s
−
1
to account for the effect of bottom and side
friction. With a cross-sectional area of the river of 211.04 m
2
(2000 ft
2
) this velocity yields
an average annual discharge of 3.6032 km
3
(1.0512
×
10
11
ft
3
); this is equivalent with about
6 cm of water over the whole catchment and is less than 1
/
6 of the annual rainfall. From
this result Mariotte deduces that, even when evaporation, the moistening of surface soils
and the replenishment of groundwater are taken into account, there is enough rainwater to
produce springs and rivers.
Lest his readers not be convinced and still feel that this result applies only to rivers and
not to fountains and springs, as Perrault had argued, Mariotte proceeds next (p. 34) to apply
the same analysis to the great spring at Montmartre. He estimates its catchment area as
113 963 m
2
(30 000 square toises) and assumes a rainfall of 48.726 cm (18 pouces), which
is equivalent to 55 529 m
3
per year or roughly 0.105 m
3
min
−
1
(107 pintes per minute; there
are 35 pintes in a cubic foot). He then explains what happens in the field.
Now, the terrain of this mountain is sandy to a depth of 0.65 to 1.0 m (2 to 3 feet), & the bottom is clay
soil; part of the water of the large rains first runs to the bottom of the mountain, part of the rest stays
in the sand near the surface, and the rest flows between the sand and the clay; so, if we assume that it
would be only the fourth part of the total, which is...105l/min (107 pintes per minute), that quarter
would be around 26 l/min, which that spring should yield, & that's pretty close to what it yields, when
it is running well.
Mariotte's work is without question one of the highlights in the history of hydrology.
His treatment is clear and sound enough that it would not be out of place in present-day
descriptions, like those reviewed in Chapter 11. His determination of the river discharge rate
is based on solid reasoning, and therefore his comparison between precipitation and river
flow is a marked improvement over Perrault's calculation a decade earlier. In addition, he
shows cogently by different examples that rain water does penetrate the soil in sufficiently
large quantities and to sufficiently large depths to be the only possible cause of springs.
In this connection, his description of the “little channels or conduits” through which the
water penetrates into saturated soil, should establish him as the originator of the concept
of macropores. He further supports his ideas on the origin of springs by a mass balance
comparison between rainfall and outflow rate from the spring at Montmartre. The reference
to Perrault's rainfall measurements shows that Mariotte was familiar with Perrault's topic;
actually, it would be surprising if he had not been, because he had been working so closely
with his brother Claude Perrault at the Academie. This probably also explains why he
merely presented his own views, dispassionately, without criticizing or even mentioning
Perrault's outlandish theory on the origin of springs.
14.4.3 Lingering doubts and slow acceptance of the Common Opinion...
It might be thought that, after the work of Mariotte had put the rainfall percolation theory
for rivers and springs on a sufficiently firm foundation, the issue had been settled once and
for all. On the other hand, while Mariotte's arguments were sound and indisputable, he had
