Edmond Halley's Contributions to Hydrogeology
David Deming
Abstract
The nature of the hydrologic cycle is one of the oldest and most important questions in geology (Deming 2005, 2014, 2018). The mystery was how the water balance between oceanic, terrestrial, and atmospheric waters was maintained. As Edmond Halley (Figure 1) himself noted, over the course of recorded human history “the sea has not sensibly decreased by the loss in vapor; nor yet abounded by the immense quantity of fresh water it receives continually from the rivers” (Halley 1691, 469). There had to be some return flow of sea water to the land, but how this occurred was debated for hundreds of years. The first person to unequivocally assert that all stream flow was sourced in precipitation and infiltration was the potter, Bernard Palissy (c. 1510–1590). In his book, Admirable Discourses, Palissy concluded that “all fountains proceed only from springs produced by rain” (Palissy 1957, 55). But Palissy's arguments were not widely accepted. Systematic and quantitative hydrologic studies were not conducted until the latter decades of the 17th century. In De l'origine des fontaines (1674) Pierre Perrault (1611–1680) published the first quantitative estimates of precipitation in a drainage basin and showed it was sufficient to account for all stream flow (Perrault 1674). However, Perrault did not fully understand the process of infiltration. Perrault's experiment was repeated and refined by his colleague in the French Academy of Sciences, Edme Mariotte (c. 1620–1684). In Traité du mouvement des eaux et des autres corps fluides, Mariotte (1686) conceded that infiltration was not universal and uniform, but anticipated the modern theory of macropores by arguing “that in uncultivated land, and in woods, there are several little canals, which are very near the surface of the earth, into which the rainwater enters; and that those canals are continued to a great depth” (Mariotte 1718, 16–17). It is certain that the work of Perrault and Mariotte was read and contemplated by members of the Royal Society in England (Dooge 1974). Both Perrault's De l'origine des fontaines (1674) and Mariotte's Traité du mouvement des eaux et des autres corps fluides (1686) were reviewed in the Royal Society's Philosophical Transactions almost immediately following their publication. Among the Fellows of the Royal Society interested in hydrological problems was Edmond Halley (1656–1743). “The magic of numbers has earned for Pierre Perrault, Edme Mariotte, and Edmond Halley the title of founding fathers of the science of hydrology” (Parizek 1963, 4). Edmond Halley was a man of such prodigious and varied accomplishments that his biography is difficult to write (Figure 2). “His output of papers was phenomenal, his unpublished work prodigious, and his range of interests surprising even for the seventeenth century” (Ronan 1969, 140). Halley was born on October 29, 1656, while the Scientific Revolution was still in progress. His birth date is certain, as John Aubrey (1626–1697) informs us that he obtained the date “from Mr. Halley himself” (Aubrey 1898, 282). Halley's father was a soapmaker with no intellectual pedigree, but an industrious individual who had become prosperous through frugality and prudent investments. The father determined that his son should have a first-class education and the youth was initially schooled at home by a hired tutor. When Edmond was old enough he was enrolled at St. Paul's school, an eminent private school for boys established in AD 1509. At St. Paul's, it was said that Halley “excelled in every branch of classical learning, but was particularly taken notice of for the extraordinary advances he made at the same time in mathematics” (Anonymous 1757, 2494). Although this assertion may strike the reader as hagiographical, it is entirely consistent with Halley's later achievements. At age 17 Halley entered Queen's College at Oxford. At Oxford Halley studied Latin, Greek, and Hebrew, and acquired “so much knowledge in geometry as to make a complete dial” (Wood 1820, 536). But Halley's chief preoccupation was astronomy. He brought to Oxford an extraordinary collection of astronomical instruments that had been purchased by his father “who spared no expense to encourage his son's genius” (Anonymous 1757, 2494). These were no amateur instruments. Halley had a telescope some 24 feet in length and a sextant 2 feet in diameter (Ronan 1969, 8). In Catalogus Stellarum Australium, Halley (1679) recorded that his youthful study of astronomy “was so intense that I read through and found out in a short time every hidden fact in that science” (Ronan 1969, 7). In time, Halley's interests expanded beyond astronomy to encompass an enormous range of subjects (Biswas 1970). These included meteorology, geophysics, mathematics, oceanography, and hydrology. Nor was his research and writing limited to the sciences. Halley published a paper on the history of the city of Palmyra (Halley 1695) and attempted to reconstruct the time and place at which Julius Caesar first landed in Britain (Halley 1686). Halley (1693) also authored a short paper that became the foundation of the science of social statistics and the basis of the life insurance business, An Estimate of the Degrees of Mortality of Mankind. Halley's thoughts and experiments on the hydrologic cycle were published in two issues of the Transactions of the Royal Society in 1687 and 1691 (Halley 1687, 1691). Publication dates for these manuscripts are uncertain. It is difficult to ascertain exact dates for composition and publication of Transactions manuscripts for the latter half of the 1680s. These were years of political tumult and social unrest in Britain that culminated in the Glorious Revolution of 1688 (Deming 2012, 243–247). Manuscripts were evidently collected for some time and published in a numbered issue of the Transactions. A number of issues were then bound together in a volume with an assigned date that could differ by a few years from the actual date of publication. Halley's first hydrological paper, An Estimate of the Quantity of Vapour Raised Out of the Sea by the Warmth of the Sun, described an experiment designed to estimate the magnitude of water evaporated from the Earth's oceans. As Halley explained, “in what proportion these vapours [water] rise, which are the sources not only of rains, but also of springs and fountains has not, that I know of, been well examined” (Halley 1687, 366). Halley placed a thermometer in a pan of water and heated it by holding it over a bed of coals. We are not informed of the temperature reached or maintained. Halley only stated “we brought the water to the same degree of heat which is observed to be that of the air in our hottest summers” (Halley 1687, 367). Weighing the pan before and after evaporation, Halley found that water “exhales the thickness of 60 parts of an inch in two hours from its whole surface… which quantity, will be found abundantly sufficient to serve for all the rains, springs and dews” (Halley 1687, 367–368). This estimate had to be regarded as a minimum because evaporation could also be caused by “the winds, whereby the surface of the water is licked up sometimes faster than it exhales by the heat of the sun” (Halley 1687, 368). Halley proceeded to apply the results of his experiment to explain why flow from the Atlantic Ocean to the Mediterranean Sea through the Straights of Gibraltar was always influent. Extrapolating from his crude experiment with the pan of water warmed by burning coals, Halley estimated the amount of water vapor evaporated from the surface of the Mediterranean Sea on a summer day to be 5280 million tons (Halley 1687, 368). To estimate river flow into the Mediterranean, Halley began by working with a convenient stream that he could measure directly: the Thames River. Halley estimated flow through the Thames at the Kingston Bridge, the first sensible point above tidal influences, by multiplying the flow rate by the cross-sectional area of the river basin. This was a crude method, because even at that time it was known that the flow rate in a river was not constant but varied throughout the basin. In Traité du mouvement des eaux et des autres corps fluides, Edme Mariotte (1686) noted that flow near the base and sides of a stream is not so fast as the middle surface (Deming 2018). Halley estimated flow through the Thames to be about 19 million m3 per day, about three times the modern estimate. He then assumed that nine major rivers flowing into the Mediterranean each contributed 10 times the flow of the Thames in England. Why 10 times as much? Because, Halley explained, “not that any of them is so great in reality, but to comprehend with them all the small rivulets that fall into the sea, which otherwise I know not how to allow for” (Halley 1687, 369). Halley concluded that cumulative river flow into the Mediterranean Sea was “little more than one-third of what is proved to be raised in vapour out of the Mediterranean in 12 hours time” (Halley 1687, 369). Thus the Mediterranean necessarily had to be constantly recharged by an influx from the Atlantic Ocean. Although Halley's estimates and methods were crude by modern standards, his approach was quantitative and experimental, a contrast to the unbridled sort of theoretical speculations that often characterized the natural philosophy of the preceding centuries. In Halley's (1691) second hydrological paper, An Account of the Circulation of the Watry Vapours of the Sea, and of the Cause of Springs, he attempted to complete his description of the hydrologic cycle by explaining the fate of water evaporated from the ocean. According to the ancient Greek theory of the four elements, the evaporation of water was regarded as the transformation of the element of water into the element of air. The ancients had no way of discerning that air was not a homogeneous substance. In the latter half of the 17th century, the science of chemistry was still in a nascent state of development (Deming 2016). But it is apparent from Halley's conclusions that he and others had moved beyond the ancient Greek theory of four elements and recognized that air could be a heterogeneous mixture of different gasses. Halley had adopted the atomic theory and he regarded water vapor as a substance distinct from air. After being heated, Halley (1691) postulated that atoms of water expanded and were “dispersed into and assimilated with the ambient air” (p. 469). Water vapors were then carried by wind into the interiors of the continents where they were “compelled by the stream of the air to mount up with it to the tops of the mountains, where the water presently precipitates” (Halley 1691, 471). Precipitation occurred because “the air is so cold and rarified [on mountain tops] as to retain but a small part of those vapours” (Halley 1691, 470–471). Halley sidestepped the difficult question of how infiltration occurred, and whether or not it was universal and uniform. Instead he postulated that water would gather in “caverns of the hills,” reminiscent of Aristotle's conception of air turning into water inside caves (Halley 1691, 471). “Breaking out by the sides of the hills,” the water thus collected “forms single springs” (Halley 1691, 471). These in turn combined to form “little rivulets or brooks,” and the smaller streams merged in a common valley to “become a river” (Halley 1691, 471). It was not obvious that this process would supply enough water to maintain flow in a major river. Addressing this difficulty, Halley argued that “one would hardly think the collection of water condensed out of vapor [to be sufficient], unless we consider how vast a trace of ground that river drains” (Halley 1691, 471). He then proposed “a rule, that the magnitude of a river… is proportionable to the length and height of the ridges from whence its fountains arise” (Halley 1691, 471). In this age of experimental philosophy, the savants of the Royal Society were anxious to distinguish their work from the idle speculations of natural philosophers. Isaac Newton used the word hypothesis to describe the unconstrained speculations that had characterized the natural philosophy of the past (Deming 2012, 224). Newton contrasted hypothesis with theory. For Newton, a theory was an explanation derived directly from observation or experimentation. Halley thus considered it essential to point out that “this theory of springs is not a bare hypothesis but founded upon experience” (Halley 1691, 471). The experience Halley referred to was his trip to the island of St. Helena. In 1676 Halley, then a youth of 20, made his first significant scientific contribution by mapping the stars of the southern hemisphere. On St. Helena, Halley found that his observations were continually hampered by condensation at high altitudes (Cook 1998, 73). This condensation, Halley noted, “was a great impediment to my celestial observations” (Halley 1691, 471). Halley recognized the role of terrestrial precipitation in the hydrologic cycle, but evidently believed that most contributions to stream flow occurred through overland flow. He doubted that infiltration and groundwater flow was sufficient to maintain the discharge from natural springs for long periods of time. Halley concluded that his hypothesis of condensation at high altitudes “is more reasonable than that of those who derive all springs from the rain-waters” (Halley 1691, 472). He argued that it was often the case that “no rain falls for a long space of time,” yet some springs “are perpetual and without diminution” (Halley 1691, 472). Among Halley's scientific contributions was a to what be a hydrological to estimate the age of the from the of the ocean. Halley was the first person to this In a published in the Royal Society's Philosophical Transactions in Halley first that and had human history to or years. But he argued a of the of described in it be well how those should be to be of natural they are as of time before the of the (Halley Halley then described a for the age of the He noted that the of without drainage through time. The streams that them carried in that The of the were an influx of from all the the oceans. Halley argued that of the could be made at different in time the rate of could be estimated and to time the of the It was for the of all from an observation of the of in their (Halley Halley conceded that the rate of in the was to be in a human time He concluded that his be of no to it very great of time to to our (Halley the of the century, Halley's for the age of the was by the John Instead of of the at different estimated the rate at which the was by the rate at which was being carried to the by the major He concluded that “a of between and of years had water condensed upon the 1898, we know that estimate was The modern estimate of the age of the is years estimate was in because the time of in the is not is from the by precipitation and of as well as in the The nature of these would have been in or Halley's time. Halley's range of interests and contributions to the were and He was most noted as an When he from St. in Oxford to Halley the degree of of and he was a of the Royal The publication of Catalogus Stellarum (1679) Halley's as an and of the first Halley was most for his work on Halley's in the was by no an than Isaac of the of in to In Halley published what was his most important work in (Halley The work was into and published the same as A of the of Halley's with a short history of from through the work of Isaac The of this work is a “the astronomical elements of the in a of all the that have been (Halley 7). This short the elements of 24 in Halley's “the of a prodigious of (Halley Halley explained, have considered the of as they in very and make their after long periods of time” (Halley Halley's was by what was almost an in Halley the that the of and were more than the of the same are which make that the which observed in the was the same with that which and notice of and described in the and which I have return and observed in the (Halley Halley then the I to that it will return in the (Halley Although Halley's to be it was the of an because Halley had to account for in the caused by and (Ronan 1969, Halley's was the of a and It was also a of of universal and a of the and in celestial Halley may be the of the science of He on the of the Earth's (Halley and made two through the and Atlantic to in the Earth's In Halley published the results of his studies in the form of a the in throughout the and Atlantic A and the of the in the and Halley's was the first of an being a of Halley's has been as “one of the most important in the history of (Cook 1998, A Halley also published of by the Greek who and the These included De the of a and De of an De only in and Halley no Halley and the by himself the arguments and made by Perrault, Mariotte, Halley, and the old that the hydrologic cycle was by through the from the sea to the for some time. Among those who the was natural and of the Royal first published in the (Deming to that the of the were and designed by Among those by was the of two of natural believed that terrestrial waters were sourced in the sea because some springs at the same no with in springs have their from the sea, and not from and I from the of which always the same quantity of the of a known to in the of which to have to groundwater flow to the The immediately the noted, or feet than the and the above of no very To explain flow from the sea to the land, The difficult question of how water became fresh was The theory was also adopted by the In An to a of and described the work of Mariotte and Halley in some yet their conclusions (Figure the ancient of the and the arguing by that the for the same as the the or the the and of a Sea all the parts and of the in a and through those and of the it out of the sides of the and its even to its return into the sea conceded that Halley's theory of condensation at high altitudes be in some it would not work in England. experience that in at there is no such also made to Mariotte's that all stream flow in be the of how it to that some very of such as we have in the of have but others more in very rivers” The of and springs was also by as to the theory precipitation and infiltration. how it to that one is so so and a so they proceed from rain or any The of the theory of how make arguments by that to be The history of science is a history of and a to the of human Halley's (1691) paper on the of the modern reader may be to read the assertion that there may “a certain sort of may be to that of A is “a or a human It is an ancient in natural philosophy, reminiscent of Aristotle's of natural In De that a of natural and Thus moved while the element of to Halley from two years of natural He and the ancient of the and the He that we may allow the of the their ridges being placed through the of the serve as it were for to fresh water for the of man and (Halley 1691, An was an used by and for Thus the streams by condensation on mountain ridges were so of the to be the more to the (Halley 1691, Halley's is a that even at the very height of the Scientific the most with one in the with that we to be such as the of noted that which would strike us as the way of at the the for of all the intellectual which the human has and in the the one which to to have been the most in and the most in the of its is the one to the of and in Newton and all was it was Edmond Halley who was in Newton to write and Newton at in of Halley was to that Newton had the in the history of explaining the of the in the Newton had in how an of directly to three of (Deming 2012, by Halley, Newton for When the was Halley to his that the Royal Society had no to for its publication. Halley the expense of publication out of his it not for Halley's and have the scientific proposed that “the history of what man has in this is at the history of the great who have Although the has out of a of the of Halley and Newton make it difficult to