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Treasures of the Earth: Geophysical and Geochemical Prospecting

Written by Iver P. Cooper

Conventional prospecting depended on learning to "read the earth": spotting pegmatites in granite; recognizing sulfide stains in outcrops, or a limonite mass (gossan, "iron hat") covering an ore body; examining talus slopes for desirable minerals and then working uphill to find their source; understanding where gold and other heavy metal particles might accumulate in a stream; searching the Gulf Coast for low mounds associated with a sulfurous smell—like the famous Spindletop dome.

Geophysical prospecting takes advantage of the local differences in the earth's physical properties (magnetism, gravity, seismic response, resistivity, etc.) created by geologic structures and changes in rock types, to find anomalies that are suggestive of gas, oil or mineral deposits.

Geochemical prospecting looks for chemical gradients, tracing these trails back to their source.

Well logging is not conventionally considered a form of prospecting, but the examination of drilling records can be quite revealing of what lies below the earth's surface.

 

The Lure of the Lodestone: Magnetometry

In what strange regions 'neath the polar star

May the great hills of massy lodestone rise,

Virtue imparting to the ambient air

To draw the stubborn iron. . . .

—Guido Guinicelli (d. 1276) (Bauer 16).

Magnetic Anomalies

 

The basis for magnetic prospecting is that the earth's powerful magnetic field magnetizes certain crustal materials, causing them to generate their own magnetic fields. These fields constitute a local magnetic anomaly that is superimposed on the general magnetic field created by the Earth's core.

The amenability of a mineral to magnetization is called its susceptibility; the most magnetizable ones are magnetite ("lodestone," iron oxide), ilmenite (titanium-iron oxide), and pyrrhotite (iron sulfide). The susceptibilities of rocks are in turn dependent on that of their component minerals. Igneous rocks can have relatively high susceptibilities whereas that of sedimentary rocks is low.

Magnetic prospecting is typically used to (1) find magnetic minerals, (2) find non-magnetic minerals that are associated with magnetic minerals (e.g., pentlandite, an iron-nickel or iron-nickel-cobalt sulfide, is associated with pyrrhotite, and copper, nickel, lead and zinc sulfides are associated with magnetite), or (3) determine the depth to basement (igneous) rocks and thus the depth of a sedimentary basin (which could in turn contain oilfields).

The earth's average total magnetic field is 0.5 Oersteds (50,000 gammas or nanoteslas). There are large-scale geographic variations in magnetic field strength; in 1965, it varied from about 68,000 gammas on the Antarctic coast, to about 24,000 gammas in southern Brazil (Dobrin 486). (At one time, it was thought that these variations might be regular enough so that navigators could use them to determine longitude.) Of course, over a sufficiently limited area, the variation is smaller; within Sweden, for example, it was about 1500 gammas. Grantville literature includes maps showing worldwide variation in magnetic declination, dip (inclination), horizontal force, and vertical force for 1907. ( EB11/Magnetism, Terrestrial, Figs. 1-4 ).

If a magnetic ore body (30% magnetite) were a sphere of 100 foot radius, with its center at a depth of 200 feet, then it would create a magnetic anomaly with a vertical component of 9,450 gammas (Dobrin 502). The anomaly is proportional to the average susceptibility and to the cube of the radius, and inversely proportional to the cube of the depth, so the ability to find an ore body falls off drastically as the body is buried deeper underground, and large bodies are much easier to find than small ones. But a small body near the surface may direct attention away from a large, deep one.

As an example of a real-life magnetic anomaly, take Pea Ridge, Missouri. Airborne magnetometers (altitude, 1800 feet) detected an anomaly of 3200 gamma. The ore body (good for two million tons annually) was at a depth of 1250 feet, and about 3000 feet in diameter. (557).

There are pitfalls for the unwary in magnetic surveying. Magnetite has a much higher susceptibility than other minerals. Hence, in Wisconsin, Michigan and Minnesota, many anomalies were found that were associated with commercially worthless deposits in which small amounts of magnetite were mixed with nonferrous minerals. It therefore helps to confirm a magnetic anomaly with the gravimeter (557). On the other hand, the survey would probably overlook a rich deposit of hematite, because hematite is non-magnetic. (555)

Magnetic surveys for ore bodies are made on a fine grid, with stations separated by as little as 25 feet. In the twentieth century, the main problem in magnetic surveying was making sure that the stations were sufficiently far away from iron objects. That will be less of a problem in the 1632verse, where there's a paucity of railroad tracks, power lines, wire fencing, and automobiles. However, there will be more difficulty in transporting the equipment from station to station.

Generally speaking, the magnetic anomalies associated with the ore bodies that are shallow and rich enough to be of interest are also likely to be so big that they will stand out against the regional variation within a given magnetic survey area. (Dobrin 553). Hence, regional correction isn't necessary.

The basement structures of interest to petroleum geologists are much deeper and their rocks are less magnetic. Hence, they are likely to generate anomalies measured in tens or at most hundreds of gammas. (Dobrin 503). Hence, to "see" these anomalies, we would need to correct for more regional features. This is feasible in the early seventeenth century; the first major magnetic survey (of the Atlantic) was conducted by Halley in 1701. (These surveys gradually become outdated, as the intensities change, by as much as 120 gammas/year, in an irregular way.) Regional magnetic trends can be mapped at a grid spacing of say ten miles (521).

Since the features are at a larger scale, sedimentary basin-oriented magnetic surveys are usually conducted by air or ship, and if land instruments are used, the stations are typically a mile apart.

A magnetic survey can take days or weeks, so one also has to worry about more rapid changes in magnetism with time. Magnetic storms occur intermittently, as a result of solar activity, and can change the field strength by 1000 gammas (more in polar regions). Hence, surveys must shut down during magnetic storms. There is also a predictable daily variation with an amplitude of about 25 gammas.

Magnetometers

Now let's talk about how geomagnetism is measured. I will use the term "magnetometer" to refer to any device, however primitive, that can be used to quantify the magnetic field. Other than at the magnetic poles and equator, the magnetic field has both a vertical and a horizontal component. Some magnetometers only measure one component, whereas others measure the total field.

According to Dobrin (19), "The magnetic compass was first used in prospecting for iron ore as early as 1640." Actually, I wouldn't be surprised if this use predated the Ring of Fire (RoF). The ability of iron objects to deflect the needle (“deviation”) was known in the sixteenth century.

A traditional compass has a magnetic needle, but it's constrained to move only horizontally. That limits its utility in detecting large masses of magnetic minerals; if you were standing over the orebody, the needle might stay still, or it might spin around, but it certainly isn't going to point straight down.

If the compass were free to pivot vertically, it would dip, thereby orienting the needle with the local magnetic field. The needle would be vertical at the earth's magnetic poles and horizontal on the magnetic equator. The magnetic "dip" (inclination) was discovered by Georg Hartmann in 1544 and further studied by Robert Norman later in the sixteenth century. William Gilbert suggested that the dip could be used to determine latitude when the sky was obscured; Henry Hudson refuted this (and in the process sailed rather close to the north magnetic pole). (Ricker)

While dip-compasses were invented in the sixteenth century, mining historians suggest that they were not used for prospecting until the eighteenth or even the nineteenth century (Brough 309). I suspect that this is too pessimistic. That said, the "Swedish Mining Compass" and innumerable variants certainly became popular in the nineteenth century.

There are, of course, many possible variations in how the needle is suspended, and how its position is gauged. One form was the inclinometer, which only pivoted vertically. A regular compass would be used to find the magnetic meridian (magnetic north-south line) and then the inclinometer needle would be aligned with it.

Modern dip needle magnetometers have a practical sensitivity of 10 gamma and a maximum sensitivity, in temperature-controlled environments, of 1 gamma. (Morrison 3.5).

EBCD15 says that the simplest absolute magnetometer (Gauss 1832) was a permanent bar magnet suspended by a gold [silk?] fiber; you had to measure the period of oscillation of the magnet. The problems of timing oscillations are discussed below in the context of pendulum-type gravimeters.

In the Schmidt vertical balance, the magnet was balanced on a knife edge, near but not at the center of mass, in such a manner that it would be turned clockwise (say) by gravity and counterclockwise by geomagnetism. The magnet was oriented perpendicular to the local "magnetic meridian" so the horizontal component of the magnetic field would not affect it. A mirror was attached to the top of the magnet, and a light beam reflected off the mirror to illuminate a graduated scale. It had a sensitivity of ten gamma. (Dobrin 505ff). All that Grantville literature says about this device is that it’s a relative magnetometer that “uses a horizontally balanced bar magnet equipped with mirror and knife edges.” (EBCD15).

The earth inductor, invented by Charles Delzenne in 1847, works on a completely different principle. A circular coil is mounted so that it can be rapidly rotated around an axis lying along a diameter of the coil. This axis in turn is mounted in a frame, which is itself mounted on pivots. If the axis isn't parallel to the local magnetic field, the field produces an alternating current in the coil, which in turn can be detected by a galvanometer. The frame would first be positioned horizontally (to measure the vertical component of the magnetic field with the galvanometer) and then vertically (to measure the horizontal component). (Kenyon) I do not believe that there is any description of the earth inductor in Grantville literature, but it’s conceivable that one of the resident electrical engineers is familiar with it. And it could certainly be re-invented.

Like the earth inductor, the aviator’s magnetic inductor compass senses the earth’s magnetic field by induction. The movement of an airplane causes the turning of a paddlewheel or windmill, which rotates the armature of a generator. The geomagnetic field induces a current in the armature coil, which can be sensed with a galvanometer. There was a controller (roughly equivalent to Delzenne’s frame) that could be rotated to indicate the desired heading, so that there would be no current if the plane were on course. The inductor compass was popular in the Twenties and Thirties but has long been obsolete. Still, Jesse Wood may know something about it.

The flux gate magnetometer was developed in World War II (for detecting submarines), the nuclear magnetic resonance (proton precession) magnetometer in 1954, and the optically-pumped magnetometer in the Sixties. The first two instruments have sensitivities of about one gamma (Morrison 3.5). They are briefly described by EB15 and McGHEST/Magnetometer.

While the encyclopedias don't provide much information about magnetometers that would be practical in the early post-RoF period, they aren't the only relevant Grantville literature.

The Scientific American Amateur Scientist column covered "how to make a sensitive magnetometer" in February 1968. Imagine my surprise when this turned about to be a differential (gradient measuring) proton procession magnetometer. "The magnetometer featured sensor coils wound on small bottles of distilled water and an audio amplifier employing germanium transistors and a hand-wound tuned transformer filter." (Fountain). We certainly aren't going to be mass producing these 'Wadsworth" magnetometers, but we probably have enough up-time transistors around to build a few of them. Or perhaps their integrated circuit equivalents.

Shipborne and Airborne Magnetometry

Magnetic surveys can be conducted from ships or aircraft, if the magetometer is towed so as to distance it from the metal of the vehicle, and you can calculate the position at which each reading was taken (Dobrin 523ff).

Putting a magnetometer in the air makes it possible to survey a large area quickly. However, you need a more sensitive instrument, because the intensity falls off with the cube of the effective depth (altitude plus depth from surface). Over the Dayton ore body in Nevada, the vertical anomaly was over 30,000 gamma and at an altitude of 500 feet, the total anomaly was about 3,000. (560).

Magnetometry in the 1632verse

I expect that dip-compasses will be used for iron ore prospecting in the USE and Sweden by 1633-1635. Don’t sneer at these simple devices; they were used in iron ore exploration until about 1950 (Kennedy, Surface Mining 57). And airships will come in very handy for magnetic surveys of the wilds of Norway, Sweden, Finland and Russia—if the magnetometer is sensitive enough for aerial use.

Newton's Apple: Gravimetry

Gravitational Anomalies

Now let's talk about gravity. If the earth were isolated in space, perfectly spherical, and of uniform density—that is, chunks of equal volume had the same mass—then the force of gravity you felt would be constant wherever you walked.

In fact, and fortunately, none of those conditions apply. We feel the gravitational force of the sun and moon as well as the earth—that's why tides exist. Also, the earth isn't perfectly spherical, and it isn't uniform. So even the earth's gravitational force isn't constant.

The earth's force of gravity is the aggregate result of the individual pulls of every drop of water, every grain of sand, and every chip of rock on the planet. Each individual pull is proportional to the density of the "bit" (assuming all bits are equal in volume) and the distance between the observer and that bit, and inversely proportional to the cube of the distance between the observer's center of gravity and that of the planet. (For a sphere of uniform density, these "pulls" add up so that the aggregate effect is inversely proportional to the square of the distance between the centers.)

So if the Assiti were suddenly to replace a sphere of rock, some distance beneath your feet, with a sphere of water, there would be a reduction in the local force of gravity, because water isn't as dense as rock (usually) and the "pull" from that sphere would be reduced. This is a negative gravitational anomaly. And if the Assiti instead replaced the sphere of rock with a sphere of solid lead, the density and thus the "pull" would be increased, and we would have a positive gravitational anomaly. The difference in density that creates the anomaly is called the density contrast.

As we walk away from the point that lies directly above this Assiti sphere, the anomaly becomes smaller (less positive or less negative) and eventually becomes undetectable.

Now, here are the two key points that make this of interest to people who want to find oil. First, oil is often trapped above or alongside a geological structure called a salt dome, essentially a big vertical mass of salt extruded upward like geological toothpaste. Secondly, salt is usually less dense than the surrounding rock.

If we can detect these small changes in local gravity that are the result of density contrast, then we can find salt domes.

So, we have two questions to answer before we can design an appropriate instrument. First, how small are the anomalies associated with salt domes (or other geologic structures that we want to find)? Second, how do they compare in magnitude to the average force of gravity and to the other conditions that can affect local gravity?

In the geophysical prospecting business, gravitational force is measured in galileos (Gals). On this scale, the average gravitational force at the earth's surface is 980 Gals. A milliGal is one-thousandth of a Gal; a microGal, one-millionth.

The average density of rock salt is 2.22; sedimentary rock, 2.50; igneous (2.7); and metamorphic rock, 2.74. So, on average, there is a density contrast of 0.28 between salt and sedimentary rock, creating a negative gravitational anomaly.

For a sphere in a homogeneous country rock, the peak gravitational anomaly (milligals) is 8.53 * density contrast * radius (kilofeet)³ /depth (kilofeet)². The shape of the gravitational anomaly profile (the falloff as you move away from directly above the center of the sphere) indicates the depth of the sphere.

A vertical cylinder is a better model of a salt dome (or a volcanic plug), but the formula is more complex; 12.77 * density contrast * (length of the cylinder + diagonal distance from surface point above axis of cylinder to perimeter of top face - diagonal distance to perimeter of bottom face). Thus, a cylinder of salt with a constant density contrast of 0.2, running from 2,000 feet to 14,000 feet, with a radius of 4,000 feet, would create an anomaly of 4.88 milligals. If the contrast were 0.3, it would be 7.32 milligals, and if the cylinder also ran from 1,000 to 13,000 feet, it would be 9.66. On the other hand, if the contrast were 0.2 and the cylinder ran from 8,000 to 14,000 feet, it would be 0.98.

Given knowledge of Newton’s law, potential theory, and calculus, all of which are in Grantville literature, the mathematicians of NTL Europe should be able to calculate the anomaly profiles that would be created by various density contrast geometries.

The peak negative anomaly associated with the deep seated Lovell Lake salt dome (Jefferson County, Texas) was about one milliGal (Dobrin2d, 400). The one over Minden Dome, Louisiana was about 5.5 milligals. (Dobrin 470).

You can have a salt dome present and not detect it by gravity methods because of lack of density contrast. The density range of salt (2.1-2.6) overlaps with that of sandstone, 1.61-2.76; shale, 1.77-3.20; limestone, 1.93-2.90 (Seigel). Or the dome could be obscured because the reduced gravitational force from the salt is compensated for by increased gravitational force from the cap rock (cap rocks are usually anhydrite, 2.93; calcite, 2.65; or gypsum, 2.35).Or you could see a density contrast, but find that salt isn't involved. Hence, a favorable gravity survey was usually followed by (more expensive but more informative) seismic studies.

We can also detect the positive gravitational anomaly associated with a large ore body. The metallic minerals include manganite (4.32), chromite (4.36), ilmenite (4.67), magnetite (5.12), malachite (4.0) , pyrite (4.6), pyrrhotite (4.65), cassiterite (6.92) and wolframite (7.32). For example, the Mobrun copper-zinc-silver-gold ore body was essentially pyrite in igneous rock. Its peak anomaly was about 1.6 milligals. The Pyramid lead-zinc ore body in Canada peaked at 0.8 milligals, and a Russian chromite deposit at 1.2. (Seigel).

Grantville literature (EB15CD) warns that different structures can produce the same anomalies. For example, a large sphere with a small density and a small sphere with a big density contrast, centered at the same depth, could have the same anomaly profiles.

From the foregoing, it seems that we want to be able to detect anomalies in the 1-10 milliGal range. Moreover, if we want to map the structure, not merely detect the peak, we would probably want sensitivity on the order of 0.1 milligals. So that means that we need to be able to subtract out, not only the average force of gravity, but also any large-scale variations with a magnitude larger than perhaps 0.01 milligals.

EB15CD may scare some would-be prospectors away from gravimetry; it says that for petroleum and mineral prospecting, the necessary accuracy is approaching the microGal (0.001 milligal) level. (Modern petroleum surveys use gravimeters with an accuracy of about 0.005 milligals (Seidel).)

Because the earth bulges at the equator, putting the surface further away, the force is less there (978 Gals) than at the poles (983 Gals). (This includes a slight correction for the centrifugal force caused by the Earth's rotation, which the gravimeters can't distinguish from the gravitational force.) The variation is highly nonlinear, but at 45 degrees, it’s 980.6, and within a few degrees of that value, the change in gravity with latitude is about 90 milligals per degree (Author’s calculation).

The terrain effect is more complicated. If you are on the summit of a mountain, you are moved further from the center of the earth, reducing gravity by about 0.3 milliGals per meter elevation above "sea level" (the "free air" effect), but the additional mass of the mountain is pulling on you, increasing gravity by about 0.1 milliGal per meter if the mountain had average crustal density (2.67)(Bouguer effect), for a net elevation effect of 0.2 milligals/meter.

The accuracy of the elevation data for the "station" limits the achievable accuracy in measuring local gravity. The surveyors in Grantville will be familiar with methods of determining elevation. An elevation difference may be measured trigonometrically, or estimated from the air pressure difference sensed by a barometer. With the anomalies of interest being on the order 1-10 milligals at peak, we clearly must be able to measure elevation with an accuracy of a meter or two. That’s not too difficult on the Hanoverian plain but more problematic in the Carpathians.

The formulae for the latitude, free air and Bouguer effects are in Grantville literature (EB15CD).

You are affected, of course, not only by the land beneath your feet but also, to a lesser extent, by hills and valleys nearby. Even a two foot “bump” would, if less than 55 feet away, require a correction of 2 microgals; which would have to be taken into account in a high-precision (using gravimeters of ~ 1-10 microGal sensitivity) survey. The total effect, outside mountain regions, is not likely to exceed 1 milliGal (Wu), but that's still a lot if you are trying to detect a peak anomaly of 1-10 milligals. Hence, it’s a good idea to locate the stations as much as possible on flat terrain, even if that means departing from a mathematically perfect grid arrangement.

In 1939, Hammer developed complex terrain correction zone charts and tables that provided accuracy to 0.1 milligals; for example, a 30' hill at 50 feet from the station, or a 4300' peak that was 12 miles away, each would warrant an adjustment of 0.1 milligals. (Dobrin 420ff). These tables didn’t pass through RoF but can certainly be prepared by an appropriately programmed computer; based on knowledge of physics and calculus that Grantville can pass on. The real problem is that to apply these corrections, you need a detailed, accurate topographic survey.

If you are trying to detect a small-scale feature like a salt dome, then you need to subtract out regional trends caused by deep-seated structural features. For example, as you approach the Gulf of Mexico from inland, there is a decrease in regional gravity of about 1 milligal/mile. (Dobrin 437). Accounting for this requires collecting gravimetric data over a sufficiently wide area in order to quantify the regional trend.

There are still other perturbations that affect high-precision surveys. The sun and moon cause tidal variation in local gravity with time, typically on the order of 0.1 milliGals. Changes in atmospheric pressure change the mass of the air column over your head, and these changes are on the order of 0.36 microGals/millibar. Rainfall can raise the water level, increasing gravity by about 0.04 milliGals per meter of retained water.

Gravimeters

 

Would-be geophysical prospectors may be unduly discouraged by the statement, in Grantville literature, that “gravimeters used in geophysical surveys have an accuracy of about 0.01 milligal” (EB15CD). As shown by the preceding analysis, one that can detect even a 1–20 milliGal anomaly may at least reveal the existence of a salt dome, and one with an accuracy of 0.1 milligals should be able to able to give some idea of its possible shape.

When you are measuring a tiny effect, you have to worry about instrument errors caused by its own physical limitations or its surroundings. There are essentially three approaches. First, you can attempt to isolate the instrument from the confounding factor. Second, you can construct the apparatus or conduct the experiment in such a way that the factor acts twice, in opposing sense, and thus cancels itself out. (This could be simply averaging out a random variation.) Finally, you can measure or predict the magnitude of the error, and adjust the raw data accordingly.

An absolute gravimeter measures gravity directly. A relative gravimeter—the more common kind—tells us how the gravity at position A compares with that at position B, but must be calibrated by using it alongside an absolute gravimeter.

Gravimeters use one of three principles: timing the oscillation of a swinging or twisting pendulum; measuring the elongation of a spring; or timing the free fall of an object.

Grantville literature reveals that until the 1950s, all absolute measurements were made with pendulum gravimeters; spring gravimeters can’t provide an absolute value, and it wasn’t possible until then to time a falling body with sufficient accuracy. Likewise, it teaches that until 1930, all relative measurements were made with pendulums, but these were superseded by spring-based instruments. (EB15CD).

Torsion balance. This was the first device used for gravity prospecting. (Pendulums, discussed below, were used previously to measure local gravity, but only for determining the shape of the earth). The balance had a horizontal bar suspended with a silk fiber. If a force was applied to one end of the bar, the bar would rotate, twisting the fiber. The fiber would of course try to untwist, thus supplying an opposing torque. The greater the applied force, the greater the twist angle attained. In 1777, Coulomb used this principle to measure electrostatic forces.

The torsion balance was used to determine the gravitational constant by measuring its deflection (Cavendish, 1798) or change in period of oscillation (Braun 1897) when a neighboring weight was moved from one side to another. (EB15CD/gravitation).

The Coulomb and Cavendish experiments were classic science experiments, and there may be useful descriptions of their apparatus in general science or physics textbooks that passed through the RoF. The physics majors in Grantville may also have duplicated one or both experiments in their college days.

In order to measure local gravity, Coulomb's device was modified by Eotvos (1901) so that the gravitational force on one end was greater than the force on the other. In essence, that meant placing weights on the ends in such a way that there was a vertical as well as a horizontal separation between them. If there was a localized gravitational anomaly, the "pull" on one weight could be at a slightly different angle and intensity than that on the other, and the component of the net force that acted horizontally and at right angles to the bar would cause the bar to rotate. (Dobrin2d, 201ff). Strictly speaking, the Eotvos torsion balance measured the gradient (the rate of change over distance) of the earth's gravitational field, not its value at a particular point. (SEG/Timelines).

The torsion balance is briefly described by Grantville literature (EB15CD/torsion balance). The device was light and compact, and accurate to perhaps 2 microgals (SEG). It helped prospectors discover 79 oil fields in the Gulf Coast in the Twenties and Thirties. However, measurements were extremely time-consuming, as, for each gravity determination, readings had to be taken in three different orientations, 120 degrees apart, and then one orientation repeated. Since the device took an hour to stabilize for each reading, that meant that a single gravity determination took four hours (and someone eventually had to solve a system of simultaneous equations to obtain the local gravity from the readings). The typical spacing between "stations" was a quarter or half mile.

The other problem with the torsion balance was that it was so sensitive to surface topography, that it had good sensitivity only in flat terrain (Louisiana being ideal in this regard.)

Spring Gravimeters. If we suspend a weight on a spring, gravity will pull down the weight, fighting against the elastic restoring force of the spring. If the stretch is small, the elongation is proportional to the gravitational force. The spring may be linear or helical. To make the elongation observable, it's amplified by mechanical (levers) or optical means.

Despite its clear preference for spring gravimeters, Grantville literature (EB15CD) doesn’t say much about them. Herschel proposed a spring gravimeter in 1849, but it wasn’t sensitive enough. “The difficulties Herschel had encountered were overcome by choosing suitably stable material for the springs, by employing mechanical, electrical or optical devices to amplify the small displacements of the system, and by providing temperature control of compensation.”

That’s helpful, but doesn’t address several fundamental issues. First, to sense a 1 part in X change in gravity, you need to be able to detect a 1 part in X change in the elongation of the spring. So, for a sensitivity of 0.1 milligals (100 ppm) , you would need to be able to detect a change of 100 microns in a spring that initially is one meter long. And that also explains why temperature control is so important; a 1^oC change in temperature would change the length of even a quartz spring by 5.5 microns.

Secondly, there’s the problem of oscillation. Imagine a mass suspended by a spring. Press down on the mass, and release, it will oscillate up and down until friction and air resistance bring it to a halt. The sensitivity of a simple spring gravimeter is proportional to the square of the period of the oscillation. That of course means that it takes a lot more time to get a reading with a more sensitive unit. But that’s not all; for the system to have a period of 20 seconds, the spring length would have to be 100 meters! Plainly, we have to cheat.

The “Gulf gravimeter” used a spring wound into a helix; the force of gravity on the weight at the end caused the spring to both elongate and rotate, and the rotation caused the deflection of a light beam.

In the LaCoste-Romberg gravimeter (1934), a cantilevered spring, anchored above the hinge of a hinged beam with a weight at the far end, acts at an angle on a point near the far end; the component of the spring force perpendicular to the beam balances the weight at "normal" gravity so the beam is nearly horizontal. If the local gravity is different from normal, the weight will pivot up or down, changing both the elongation and the angle of action of the spring.

The unstretched length of the spring is as close to zero as possible. A mirror on the beam reflects a light beam, that illuminates a scale; this provides a further optical magnification. The mechanism is inside an insulated housing that communicates with a thermostat-controlled, battery-powered electric oven. (Dobrin 388). There may be a schematic diagram of this gravimeter in the 1977McGHEST at the Grantville high school library (cp. 2002McGHEST).

As an example of a modern instrument, EB15CD cites the “Worden gravimeter” (1948), but without providing any construction details; just performance characteristics (it can measure gravity of 0.01 milligals in a few minutes, and weighs just a few pounds).A "zero-length" fused quartz spring acts in opposition to a weighted arm about a torsion fiber. The spring mechanism is inside an evacuated thermos flask, and the spring is connected to differential expansion arms, all to minimize the effect of changes in temperature and pressure. (Dobrin 391).

Fused quartz is used because it has a very low coefficient of thermal expansion; Grantville engineers will know of this property. It is made by subjecting very pure silica to fusing temperatures (3200° F). Fused quartz was originally made by fusing natural Brazilian crystals.

Another low-coefficient material that the engineers will be yearning for is Invar, a nickel-steel alloy invented in 1896. Grantville literature almost certainly contains a reference book that reveals its composition (64% iron, 36% nickel) but if there are any alloying "tricks" they will need to be rediscovered. Local German supplies of nickel are probably adequate to meet the demand for making Invar for precision instruments.

In the seventeenth century, wood was used in low-coefficient applications (like the pendulums of a pendulum clock). Once borosilicate glass is available, it too will be an option.

Pendulum Gravimeters. If the bob of a pendulum is drawn away from under its pivot point, and released, the force of gravity will cause it to swing back and forth. Friction and aerodynamic drag gradually reduce the amplitude (size) of the swings and bring it to rest.

If we imagine an ideal simple pendulum (no forces other than gravity, the bob is a point mass, the cord is massless), then for small amplitudes (angles of swing) the period approximates 2*pi*square root (length/local gravitational acceleration). A real pendulum's behavior is close enough to the ideal so that this relationship was discovered experimentally by Galileo.

The relationship meant that if gravity and length were constant, the period would also be constant, and you would have a means of measuring time. Pendulum clocks were conceived of by Galileo in 1637, and independently invented (and actually built) by Christian Huygens in 1656. In 1673 he published a treatise on the pendulum that established that the period was affected by amplitude and, for timekeeping accuracy, the amplitude had to be kept small. He also calculated the behavior of a ideal compound pendulum (we still ignore friction and air resistance, but the pendulum is a swinging rigid body), which is a better model of a real pendulum.

In 1666, Robert Hooke suggested that a pendulum clock could be used to measure the force of gravity. An ideal compound pendulum has a period which is the same as that of a simple pendulum with a length equal to the distance from the pivot point to the "center of oscillation." The center of oscillation is not readily determinable by calculation or observation, because its location is dependent on how the mass is distributed along the arm of the pendulum. Hence, in ordinary use, a pendulum is a relative gravimeter. The ratio of its periods at two different locations is the reciprocal of the ratio of the square roots of the local gravities. Initially, the standard surveying pendulum was the meter-long "seconds pendulum," one taking a second per swing (so period of two seconds) at "standard gravity." It was replaced around 1880 by the "half-second pendulum," only one-quarter the length.

Grantville literature ( CRC) has a table of "acceleration due to gravity and length of the seconds pendulum," including the "free air correction for altitude."

In 1672, Jean Richer discovered that a pendulum clock was 2.5 minutes/day slower in Cayenne, French Guiana than it was in Paris. He thus had detected the difference in gravitational force between the latitudes of Cayenne (4° 55' N) and Paris (48° 50' N); about 2.9 Gals.

It's amazing to me that so many books refer to this discovery without asking the following question: how did Richer tell that there a difference in the speed of the pendulum speed? After all, if the best clocks were pendulum clocks, any such clock brought to Cayenne would suffer the same slowdown. It's necessary to have a clock that tells time (at least over the short term) at least as accurately as a pendulum clock, but which works on a different principle so that it's unaffected by gravity.

We know that Richer made telescopic observations, and most likely his reference "clock" was an astronomical one; he counted the number of pendulum swings in a solar day (noon to noon), or in a sidereal day (star returns to same position in sky), or perhaps between two particular orientations of the moons of Jupiter. (Matthews 145).

To measure time by an “astronomical clock,” you need to at least account for the effect of the tilt of the earth’s axis and the ellipticity of its orbit around the sun (UT0, mean solar time). Desirably, you also correct for the wobble of the earth’s axis (UT1) and its annual and semi-annual variations (UT2). There are unpredictable irregularities in the spin rate that give rise to a time prediction error of about 60 milliseconds/year. (Allan). The preferred astronomical clock, by the way, is a photographic zenith tube, a telescope that photographs stars that pass directly overhead and records the time of transit. (Popular Mechanics, January 1948 p. 138).

For accuracy in measuring gravity (or time), there are a few confounding factors one must worry about: Is the rod stretched by the weight of the bob? Does it expand or contract with changes in temperature? Does it absorb moisture? Is it slowed down by friction at the pivot point or by air resistance? Is the density of air it's passing through changed by changes in atmospheric temperature or pressure?

In 1818, Kater invented the first reversible pendulum. This took advantage of Huygen's theorem that a pendulum has the same period when hung from its center of oscillation as from its pivot. EB11/Henry Kater refers to this "property of reciprocity," but doesn't provide any construction details. Neither does EB15CD.

Kater's pendulum was a brass bar that could be pivoted around either of two knife blades. These were a fixed distance apart, measured initially with a microscope. There was a screw-driven moveable weight on the bar, and its position was adjusted until the periods of oscillation from the two pivot points was equal. He measured the period with the same precision clock used in the adjustment phase, calculated the local gravity, and applied various corrections.

By Kater’s day, of course, high precision mechanical clocks were available; several decades earlier, Harrison had built a marine chronometer accurate to one second per day. That’s good enough, by my calculations, for measuring gravity with a seconds pendulum to within about 20 milligals. Good enough for studying the shape of the Earth; not good enough for finding salt domes.

In general, with a pendulum, to achieve a sensitivity for measuring gravity of 1 part in X, we need to time the period to 0.5 parts in X. (Morrison 2.5). Thus, for 1 milliGal accuracy (1 ppm), we need to time the seconds pendulum to 0.5 ppm, or 0.04 seconds/day. And pendulums have been made with an absolute accuracy of 0.1 milligals.

The Kater pendulum could also be used to make relative gravity measurements, by just taking into account the change in the period when it was moved to a new location (since the length was constant).

In 1835, the mathematician Friedrich Bessel showed that as long as the two periods were close enough, the moveable weight wasn't needed, and that if the pendulum was symmetrical but weighted at one end, air drag errors would cancel out. The Repsold pendulum (1864) was based on these discoveries.

Von Sterneck (1887) solved the drag problem in another way, by placing the pendulum in a temperature-controlled vacuum. He also improved the readout. A similar device was constructed by Mendenhall (1890); it was, even in the 1920s, the world's best clock. (Wikipedia/Pendulum).

Unfortunately, neither EB11 nor EB15CD provide useful information about these pendulum designs. EB15CD/Clock does however briefly discuss the Shortt pendulum clock, which it calls the "most accurate mechanical timekeeper."

Another source of error was the effect of the swing on the pendulum stand. When the problem was recognized, it was first addressed by simply measuring the sway and mathematically correcting for it. Later, devices were built in which two pendulums swung out of phase to cancel out the effect.

Wikipedia says that Kater's accuracy was about 7 milliGals. However, EB15CD says that the reversible pendulum-based absolute gravity measurement made in Potsdam, 1906, which was the reference point for all local gravity data up until 1968, was in error by at least 15 milligals. Dobrin says that the later reversible pendulums measured gravity to 1 ppm, which is about 1 milliGal (Dobrin2d 204).

In the 1632verse, we can temporarily sidestep many of the historical problems with the use of pendulum gravimeters because we have access to twentieth century timekeeping technology. First, we have a limited number of highly accurate timepieces that are based on quartz crystals. The surveyor can borrow one, or perhaps can listen to time signals provided by a radio station equipped with such a clock.

Quartz crystal clocks use a quartz crystal as the oscillator. If the oscillation frequency isn’t quite right (the standard one is 32,768 Hertz), then this will create a systematic error. If you have a more accurate clock to compare it with, you can measure the frequency error and therefore the appropriate daily correction. For example, a comparison of three cheap ($6 apiece in 1997) LCD stopwatches with the Atomic Clock in Boulder, Colorado found frequency inaccuracies of 0.48 to 1.17 seconds/day—about 10 ppm. If you subtract out this constant rate error, what you are left with are the errors attributable to frequency instabilities; the most importance source of instability is temperature variation (but pressure, humidity, shock and vibration may also play a role). Over a period of 145 days, the residual time error varied slowly between -0.7 and 0.4 seconds, but the average day-to-day change was perhaps 50 milliseconds. (Allan) It is possible to devise methods of calibrating a clock to take into account the more common frequency instabilities, and reduce the (adjusted) daily clock error from one to one-tenth seconds or even less. And of course, we can start with one of the better up-time clocks to begin with. (An observatory grade quartz crystal clock has a frequency stability such that the maximum error is 0.1 ppb—about one second every 10 years. Anderson Institute. The best clock ...