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Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean.

There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators.

Estimation theory is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. However, in robust statistics, statistical theory goes on to consider the balance between having good properties, if tightly defined assumptions hold, and having worse properties that hold under wider conditions.

Background
An "estimator" or "point estimate" is a statistic (that is, a function of the data) that is used to infer the value of an unknown parameter in a statistical model. A common way of phrasing it is "the estimator is the method selected to obtain an estimate of an unknown parameter". The parameter being estimated is sometimes called the estimand. It can be either finite-dimensional (in parametric and semi-parametric models), or infinite-dimensional (semi-parametric and non-parametric models). If the parameter is denoted $$ \theta $$ then the estimator is traditionally written by adding a circumflex over the symbol: $$\widehat{\theta}$$. Being a function of the data, the estimator is itself a random variable; a particular realization of this random variable is called the "estimate". Sometimes the words "estimator" and "estimate" are used interchangeably.

The definition places virtually no restrictions on which functions of the data can be called the "estimators". The attractiveness of different estimators can be judged by looking at their properties, such as unbiasedness, mean square error, consistency, asymptotic distribution, etc. The construction and comparison of estimators are the subjects of the estimation theory. In the context of decision theory, an estimator is a type of decision rule, and its performance may be evaluated through the use of loss functions.

When the word "estimator" is used without a qualifier, it usually refers to point estimation. The estimate in this case is a single point in the parameter space. There also exists another type of estimator: interval estimators, where the estimates are subsets of the parameter space.

The problem of density estimation arises in two applications. Firstly, in estimating the probability density functions of random variables and secondly in estimating the spectral density function of a time series. In these problems the estimates are functions that can be thought of as point estimates in an infinite dimensional space, and there are corresponding interval estimation problems.

Definition
Suppose a fixed parameter $$\theta$$ needs to be estimated. Then an "estimator" is a function that maps the sample space to a set of sample estimates. An estimator of $$\theta$$ is usually denoted by the symbol $$\widehat{\theta}$$. It is often convenient to express the theory using the algebra of random variables: thus if X is used to denote a random variable corresponding to the observed data, the estimator (itself treated as a random variable) is symbolised as a function of that random variable, $$\widehat{\theta}(X)$$. The estimate for a particular observed data value $$x$$ (i.e. for $$X=x$$) is then $$\widehat{\theta}(x)$$, which is a fixed value. Often an abbreviated notation is used in which $$\widehat{\theta}$$ is interpreted directly as a random variable, but this can cause confusion.

Quantified properties
The following definitions and attributes are relevant.

Error
For a given sample $$ x $$, the "error" of the estimator $$\widehat{\theta}$$ is defined as
 * $$e(x)=\widehat{\theta}(x) - \theta,$$

where $$\theta $$ is the parameter being estimated. The error, e, depends not only on the estimator (the estimation formula or procedure), but also on the sample.

Mean squared error
The mean squared error of $$\widehat{\theta}$$ is defined as the expected value (probability-weighted average, over all samples) of the squared errors; that is,
 * $$\operatorname{MSE}(\widehat{\theta}) = \operatorname{E}[(\widehat{\theta}(X) - \theta)^2].$$

It is used to indicate how far, on average, the collection of estimates are from the single parameter being estimated. Consider the following analogy. Suppose the parameter is the bull's-eye of a target, the estimator is the process of shooting arrows at the target, and the individual arrows are estimates (samples). Then high MSE means the average distance of the arrows from the bull's eye is high, and low MSE means the average distance from the bull's eye is low. The arrows may or may not be clustered. For example, even if all arrows hit the same point, yet grossly miss the target, the MSE is still relatively large. However, if the MSE is relatively low then the arrows are likely more highly clustered (than highly dispersed) around the target.

Sampling deviation
For a given sample $$ x $$, the sampling deviation of the estimator $$\widehat{\theta}$$ is defined as
 * $$d(x) =\widehat{\theta}(x) - \operatorname{E}( \widehat{\theta}(X) ) =\widehat{\theta}(x) - \operatorname{E}( \widehat{\theta} ),$$

where $$ \operatorname{E}( \widehat{\theta}(X) ) $$ is the expected value of the estimator. The sampling deviation, d, depends not only on the estimator, but also on the sample.

Variance
The variance of $$\widehat{\theta}$$ is the expected value of the squared sampling deviations; that is, $$\operatorname{Var}(\widehat{\theta}) = \operatorname{E}[(\widehat{\theta} - \operatorname{E}[\widehat{\theta}]) ^2]$$. It is used to indicate how far, on average, the collection of estimates are from the expected value of the estimates. (Note the difference between MSE and variance.) If the parameter is the bull's-eye of a target, and the arrows are estimates, then a relatively high variance means the arrows are dispersed, and a relatively low variance means the arrows are clustered. Even if the variance is low, the cluster of arrows may still be far off-target, and even if the variance is high, the diffuse collection of arrows may still be unbiased. Finally, even if all arrows grossly miss the target, if they nevertheless all hit the same point, the variance is zero.

Bias
The bias of $$\widehat{\theta}$$ is defined as $$B(\widehat{\theta}) = \operatorname{E}(\widehat{\theta}) - \theta$$. It is the distance between the average of the collection of estimates, and the single parameter being estimated. The bias of $$\widehat{\theta}$$ is a function of the true value of $$\theta$$ so saying that the bias of $$\widehat{\theta}$$ is $$b$$ means that for every $$\theta$$ the bias of $$\widehat{\theta}$$ is $$b$$.

There are two kinds of estimators: biased estimators and unbiased estimators. Whether an estimator is biased or not can be identified by the relationship between $$\operatorname{E}(\widehat{\theta}) - \theta$$ and 0:
 * If $$\operatorname{E}(\widehat{\theta}) - \theta\neq0$$, $$\widehat{\theta}$$ is biased.
 * If $$\operatorname{E}(\widehat{\theta}) - \theta=0$$, $$\widehat{\theta}$$ is unbiased.

The bias is also the expected value of the error, since $$ \operatorname{E}(\widehat{\theta}) - \theta = \operatorname{E}(\widehat{\theta} - \theta ) $$. If the parameter is the bull's eye of a target and the arrows are estimates, then a relatively high absolute value for the bias means the average position of the arrows is off-target, and a relatively low absolute bias means the average position of the arrows is on target. They may be dispersed, or may be clustered. The relationship between bias and variance is analogous to the relationship between accuracy and precision.

The estimator $$\widehat{\theta}$$ is an unbiased estimator of $$\theta$$ if and only if $$B(\widehat{\theta}) = 0$$. Bias is a property of the estimator, not of the estimate. Often, people refer to a "biased estimate" or an "unbiased estimate", but they really are talking about an "estimate from a biased estimator", or an "estimate from an unbiased estimator". Also, people often confuse the "error" of a single estimate with the "bias" of an estimator. That the error for one estimate is large, does not mean the estimator is biased. In fact, even if all estimates have astronomical absolute values for their errors, if the expected value of the error is zero, the estimator is unbiased. Also, an estimator's being biased does not preclude the error of an estimate from being zero in a particular instance. The ideal situation is to have an unbiased estimator with low variance, and also try to limit the number of samples where the error is extreme (that is, have few outliers). Yet unbiasedness is not essential. Often, if just a little bias is permitted, then an estimator can be found with lower mean squared error and/or fewer outlier sample estimates.

An alternative to the version of "unbiased" above, is "median-unbiased", where the median of the distribution of estimates agrees with the true value; thus, in the long run half the estimates will be too low and half too high. While this applies immediately only to scalar-valued estimators, it can be extended to any measure of central tendency of a distribution: see median-unbiased estimators.

In a practical problem, $$\widehat{\theta}$$ can always have functional relationship with $$\theta$$. For example, A genetic theory states there is a type of leave, starchy green, occur with probability $$p_1=1/4\cdot(\theta + 2)$$, with $$0<\theta<1$$. For $$n$$ leaves, the random variable $$N_1$$, the number of starchy green leaves, can be modeled with a $$Bin(n,p_1)$$ distribution. The number can be used to express the following estimator for $$\theta$$: $$\widehat{\theta}=4/n\cdot N_1-2$$. One can show that $$\widehat{\theta}$$ is an unbiased estimator for $$\theta$$: $$E[\widehat{\theta}]=E[4/n\cdot N_1-2]$$ $$=4/n\cdot E[N_1]-2$$ $$=4/n\cdot np_1-2$$ $$=4\cdot p_1-2$$ $$=4\cdot1/4\cdot(\theta+2)-2$$ $$=\theta+2-2$$ $$=\theta$$.

Unbiased

A desired property for estimators is the unbiased trait where an estimator is shown to have no systematic tendency to produce estimates larger or smaller than the provided probability. Additionally, unbiased estimators with smaller variances are preferred over larger variances because it will be closer to the "true" value of the parameter. The unbiased estimator with the smallest variance is known as the Minimum-variance unbiased estimator(MVUE).

To find if your estimator is unbiased it is easy to follow along the equation $$\operatorname{E}(\widehat{\theta}) - \theta=0$$, $$\widehat{\theta}$$. With estimator T with and parameter of interest $$\theta$$ solving the previous equation so it is shown as $$E[T] = \theta$$ the estimator is unbiased. Looking at the figure to the right despite $$\theta_2$$ being the only unbiased estimator. If the distributions overlapped and were both centered around $$\theta$$ then distribution $$\theta_1$$ would actually be the preferred unbiased estimator.

Expectation When looking at quantities in the interest of expectation for the model distribution there is an unbiased estimator which should satisfy the two equations below.
 * $$1. X_n = \tfrac{X_1 + X_2+ ... + X_n}{n}$$
 * $$2. E[\bar{X}_n] = \mu$$

Variance Similarly, when looking at quantities in the interest of variance as the model distribution there is also an unbiased estimator that should satisfy the two equations below.
 * $$1. S^2_n = \tfrac{1}{n-1}\sum_{i = 1}^n (X_i - X_n)^2$$
 * $$ 2. E[S^2_n] = \sigma^2$$

Note we are dividing by n - 1 because if we divided with n we would obtain an estimator with a negative bias which would thus produce estimates that are too small for $$\sigma^2$$. It should also be mentioned that even though $$S^2_n$$ is unbiased for $$\sigma^2$$ the reverse is not true.

Relationships among the quantities

 * The mean squared error, variance, and bias, are related: $$\operatorname{MSE}(\widehat{\theta}) = \operatorname{Var}(\widehat\theta) + (B(\widehat{\theta}))^2,$$ i.e. mean squared error = variance + square of bias. In particular, for an unbiased estimator, the variance equals the mean squared error.
 * The standard deviation of an estimator $$\widehat{\theta}$$ of $$\theta$$ (the square root of the variance), or an estimate of the standard deviation of an estimator $$\widehat{\theta}$$ of $$\theta$$, is called the standard error of $$\widehat{\theta}$$.
 * The bias-variance tradeoff will be used in model complexity, over-fitting and under-fitting. It is mainly used in the field of supervised learning and predictive modeling to diagnose the performance of algorithms.

Sampling Distribution
The sampling distribution can be shown by the estimator $$S = h(X_1,X_2,...,X_n)$$. represented by the random sample :$$X_1,X_2,...,X_n$$. The sampling distribution is equivalent to the probability distribution of the estimator S which can also be represented by the equation:

S = \tfrac{Y}{n} $$. where Y is the number of $$X_i$$ equal to zero and n is the number of trials. To understand why the expectation value is dependent on the probability ($$p_0$$) we need to understand the distribution. For example, in the sampling distribution for each i in the random dataset X it can be considered a success when X = 0. This makes Y is equal to the success of X = 0 in n trials. With the concept of Y either being a success or not it can be thought of as a binomial distribution with constant probability $$p_0$$. Therefore, the sampling distribution S can be seen as the distribution $$Bin(n,p_0)$$ making S a discrete random variable. As a result, the expectation for the sampling distribution can be thought of as
 * $$ E[S] = \tfrac{E[Y]}{n} = \tfrac{np_0}{n} = p_0 $$.

proving that the property holds regardless of what the value of $$p_0$$ is. This shows that despite $$p_0$$ values fluctuating between samples estimators can be on target regardless of the differences. 0, no matter how small, we have

\lim_{n\to\infty}\Pr\left\{ \left| t_n-\theta\right|<\varepsilon \right\}=1 $$.

The consistency defined above may be called weak consistency. The sequence is strongly consistent, if it converges almost surely to the true value.

An estimator that converges to a multiple of a parameter can be made into a consistent estimator by multiplying the estimator by a scale factor, namely the true value divided by the asymptotic value of the estimator. This occurs frequently in estimation of scale parameters by measures of statistical dispersion.

Fisher Consistency
An estimator can be considered Fisher Consistent as long as the estimator is the same functional of the empirical distribution function as the true distribution function. Following the formula:
 * $$\widehat{\theta} = h(T_n),     \theta  = h(T_\theta)$$

Where $$T_n$$ and $$T_\theta$$ is the empirical distribution function and theoretical distribution functions respectively. An easy example to see if something is Fisher consistent is to check the mean consistency and the variance. For example, to check consistency for the mean $$\widehat{\mu} = \bar{X}$$ and to check for variance confirm that $$\widehat{\sigma}^2 = SSD/n$$.

Asymptotic normality
An asymptotically normal estimator is a consistent estimator whose distribution around the true parameter θ approaches a normal distribution with standard deviation shrinking in proportion to $$1/\sqrt{n}$$ as the sample size n grows. Using $$\xrightarrow{D}$$ to denote convergence in distribution, tn is asymptotically normal if
 * $$\sqrt{n}(t_n - \theta) \xrightarrow{D} N(0,V),$$

for some V.

In this formulation V/n can be called the asymptotic variance of the estimator. However, some authors also call V the asymptotic variance. Note that convergence will not necessarily have occurred for any finite "n", therefore this value is only an approximation to the true variance of the estimator, while in the limit the asymptotic variance (V/n) is simply zero. To be more specific, the distribution of the estimator tn converges weakly to a dirac delta function centered at $$\theta$$.

The central limit theorem implies asymptotic normality of the sample mean $$\bar X$$ as an estimator of the true mean. More generally, maximum likelihood estimators are asymptotically normal under fairly weak regularity conditions — see the asymptotics section of the maximum likelihood article. However, not all estimators are asymptotically normal; the simplest examples are found when the true value of a parameter lies on the boundary of the allowable parameter region.

Efficiency
The efficiency of an estimator is used to estimate the quantity of interest in a "minimum error" manner. In reality, there is not an explicit best estimator; there can only be a better estimator. The good or not of the efficiency of an estimator is based on the choice of a particular loss function, and it is reflected by two naturally desirable properties of estimators: to be unbiased $$\operatorname{E}(\widehat{\theta}) - \theta=0$$ and have minimal mean squared error (MSE) $$\operatorname{E}[(\widehat{\theta} - \theta )^2]$$. These cannot in general both be satisfied simultaneously: an unbiased estimator may have a lower mean squared error than any biased estimator (see estimator bias). A function relates the mean squared error with the estimator bias.

$$ \operatorname{E}[(\widehat{\theta} - \theta )^2]=(\operatorname{E}(\widehat{\theta}) - \theta)^2+\operatorname{Var}(\theta)\ $$

The first term represents the mean squared error; the second term represents the square of the estimator bias; and the third term represents the variance of the sample. The quality of the estimator can be identified from the comparison between the variance, the square of the estimator bias, or the MSE. The variance of the good estimator (good efficiency) would be smaller than the variance of the bad estimator (bad efficiency). The square of an estimator bias with a good estimator would be smaller than the estimator bias with a bad estimator. The MSE of a good estimator would be smaller than the MSE of the bad estimator. Suppose there are two estimator, $$\theta_1$$ is the good estimator and $$\theta_2$$ is the bad estimator. The above relationship can be expressed by the following formulas.

$$\operatorname{Var}(\theta_1)<\operatorname{Var}(\theta_2)$$

$$|\operatorname{E}({\theta}_1) - \theta|<|\operatorname{E}({\theta_2}) - \theta|$$

$$\operatorname{MSE}(\theta_1)<\operatorname{MSE}(\theta_2)$$

Besides using formula to identify the efficiency of the estimator, it can also be identified through the graph. If an estimator is efficient, in the frequency vs. value graph, there will be a curve with high frequency at the center and low frequency on the two sides. For example: If an estimator is not efficient, the frequency vs. value graph, there will be a relatively more gentle curve. To put it simply, the good estimator has a narrow curve, while the bad estimator has a large curve. Plotting these two curves on one graph with a shared y-axis, the difference becomes more obvious.

Among unbiased estimators, there often exists one with the lowest variance, called the minimum variance unbiased estimator (MVUE). In some cases an unbiased efficient estimator exists, which, in addition to having the lowest variance among unbiased estimators, satisfies the Cramér–Rao bound, which is an absolute lower bound on variance for statistics of a variable.

Concerning such "best unbiased estimators", see also Cramér–Rao bound, Gauss–Markov theorem, Lehmann–Scheffé theorem, Rao–Blackwell theorem.

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title: Estimator


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Emerald

Emerald is a gemstone and a variety of the mineral beryl (Be3Al2(SiO3)6) colored green by trace amounts of chromium or sometimes vanadium. Beryl has a hardness of 7.5–8 on the Mohs scale. Most emeralds have many inclusions, so their toughness (resistance to breakage) is classified as generally poor. Emerald is a cyclosilicate.

Etymology
The word "emerald" is derived (via esmeraude and emeraude), from Vulgar Latin: esmaralda/esmaraldus, a variant of Latin smaragdus, which was via σμάραγδος (smáragdos; "green gem"). The Greek word may have a Semitic, Sanskrit or Persian origin. According to Webster's Dictionary the term emerald was first used in the 14th century.

Properties determining value

Emeralds, like all colored gemstones, are graded using four basic parameters known as "the four Cs": color, clarity, cut and carat weight. Normally, in grading colored gemstones, color is by far the most important criterion. However, in the grading of emeralds, clarity is considered a close second. A fine emerald must possess not only a pure verdant green hue as described below, but also a high degree of transparency to be considered a top gemstone.

This member of the beryl family ranks among the traditional "big four" gems along with diamonds, rubies and sapphires.

In the 1960s, the American jewelry industry changed the definition of emerald to include the green vanadium-bearing beryl. As a result, vanadium emeralds purchased as emeralds in the United States are not recognized as such in the United Kingdom and Europe. In America, the distinction between traditional emeralds and the new vanadium kind is often reflected in the use of terms such as "Colombian emerald".

Color
In gemology, color is divided into three components: hue, saturation, and tone. Emeralds occur in hues ranging from yellow-green to blue-green, with the primary hue necessarily being green. Yellow and blue are the normal secondary hues found in emeralds. Only gems that are medium to dark in tone are considered emeralds; light-toned gems are known instead by the species name green beryl. The finest emeralds are approximately 75% tone on a scale where 0% tone is colorless and 100% is opaque black. In addition, a fine emerald will be saturated and have a hue that is bright (vivid). Gray is the normal saturation modifier or mask found in emeralds; a grayish-green hue is a dull-green hue.

Clarity
Emeralds tend to have numerous inclusions and surface-breaking fissures. Unlike diamonds, where the loupe standard (i.e., 10× magnification) is used to grade clarity, emeralds are graded by eye. Thus, if an emerald has no visible inclusions to the eye (assuming normal visual acuity) it is considered flawless. Stones that lack surface breaking fissures are extremely rare and therefore almost all emeralds are treated ("oiled", see below) to enhance the apparent clarity. The inclusions and fissures within an emerald are sometimes described as jardin (French for garden), because of their mossy appearance. Imperfections are unique for each emerald and can be used to identify a particular stone. Eye-clean stones of a vivid primary green hue (as described above), with no more than 15% of any secondary hue or combination (either blue or yellow) of a medium-dark tone, command the highest prices. The relative non-uniformity motivates the cutting of emeralds in cabochon form, rather than faceted shapes. Faceted emeralds are most commonly given an oval cut, or the signature emerald cut, a rectangular cut with facets around the top edge.

Treatments
Most emeralds are oiled as part of the post-lapidary process, in order to fill in surface-reaching cracks so that clarity and stability are improved. Cedar oil, having a similar refractive index, is often used in this widely adopted practice. Other liquids, including synthetic oils and polymers with refractive indexes close to that of emeralds, such as Opticon, are also used. The least expensive emeralds are often treated with epoxy resins, which are effective for filling stones with many fractures. These treatments are typically applied in a vacuum chamber under mild heat, to open the pores of the stone and allow the fracture-filling agent to be absorbed more effectively. The U.S. Federal Trade Commission requires the disclosure of this treatment when an oil-treated emerald is sold. The use of oil is traditional and largely accepted by the gem trade, although oil-treated emeralds are worth much less than untreated emeralds of similar quality. Untreated emeralds must also be accompanied by a certificate from a licensed, independent gemology laboratory. Other treatments, for example the use of green-tinted oil, are not acceptable in the trade. Gems are graded on a four-step scale; none, minor, moderate and highly enhanced. These categories reflect levels of enhancement, not clarity. A gem graded none on the enhancement scale may still exhibit visible inclusions. Laboratories apply these criteria differently. Some gemologists consider the mere presence of oil or polymers to constitute enhancement. Others may ignore traces of oil if the presence of the material does not improve the look of the gemstone.

Emerald mines
Emeralds in antiquity were mined in Ancient Egypt at locations on Mount Smaragdus since 1500 BC, and India and Austria since at least the 14th century AD. The Egyptian mines were exploited on an industrial scale by the Roman and Byzantine Empires, and later by Islamic conquerors. Mining in Egypt ceased with the discovery of the Colombian deposits. Today, only ruins remain in Egypt.

Colombia is by far the world's largest producer of emeralds, constituting 50–95% of the world production, with the number depending on the year, source and grade. Emerald production in Colombia has increased drastically in the last decade, increasing by 78% from 2000 to 2010. The three main emerald mining areas in Colombia are Muzo, Coscuez, and Chivor. Rare "trapiche" emeralds are found in Colombia, distinguished by ray-like spokes of dark impurities.

Zambia is the world's second biggest producer, with its Kafubu River area deposits (Kagem Mines) about 45 km southwest of Kitwe responsible for 20% of the world's production of gem-quality stones in 2004. In the first half of 2011, the Kagem Mines produced 3.74 tons of emeralds.

Emeralds are found all over the world in countries such as Afghanistan, Australia, Austria, Brazil, Bulgaria, Cambodia, Canada, China, Egypt, Ethiopia, France, Germany, India, Kazakhstan, Madagascar, Mozambique, Namibia, Nigeria, Norway, Pakistan, Russia, Somalia, South Africa, Spain, Switzerland, Tanzania, the United States, Zambia, and Zimbabwe. In the US, emeralds have been found in Connecticut, Montana, Nevada, North Carolina, and South Carolina. In 1998, emeralds were discovered in the Yukon Territory of Canada.

Origin determinations
Since the onset of concerns regarding diamond origins, research has been conducted to determine if the mining location could be determined for an emerald already in circulation. Traditional research used qualitative guidelines such as an emerald's color, style and quality of cutting, type of fracture filling, and the anthropological origins of the artifacts bearing the mineral to determine the emerald's mine location. More recent studies using energy-dispersive X-ray spectroscopy methods have uncovered trace chemical element differences between emeralds, including ones mined in close proximity to one another. American gemologist David Cronin and his colleagues have extensively examined the chemical signatures of emeralds resulting from fluid dynamics and subtle precipitation mechanisms, and their research demonstrated the chemical homogeneity of emeralds from the same mining location and the statistical differences that exist between emeralds from different mining locations, including those between the three locations: Muzo, Coscuez, and Chivor, in Colombia, South America.

Synthetic emerald

Both hydrothermal and flux-growth synthetics have been produced, and a method has been developed for producing an emerald overgrowth on colorless beryl. The first commercially successful emerald synthesis process was that of Carroll Chatham, likely involving a lithium vanadate flux process, as Chatham's emeralds do not have any water and contain traces of vanadate, molybdenum and vanadium. The other large producer of flux emeralds was Pierre Gilson Sr., whose products have been on the market since 1964. Gilson's emeralds are usually grown on natural colorless beryl seeds, which are coated on both sides. Growth occurs at the rate of 1 mm per month, a typical seven-month growth run produces emerald crystals 7 mm thick.

Hydrothermal synthetic emeralds have been attributed to IG Farben, Nacken, Tairus, and others, but the first satisfactory commercial product was that of Johann Lechleitner of Innsbruck, Austria, which appeared on the market in the 1960s. These stones were initially sold under the names "Emerita" and "Symeralds", and they were grown as a thin layer of emerald on top of natural colorless beryl stones. Later, from 1965 to 1970, the Linde Division of Union Carbide produced completely synthetic emeralds by hydrothermal synthesis. According to their patents (attributable to E.M. Flanigen), acidic conditions are essential to prevent the chromium (which is used as the colorant) from precipitating. Also, it is important that the silicon-containing nutrient be kept away from the other ingredients to prevent nucleation and confine growth to the seed crystals. Growth occurs by a diffusion-reaction process, assisted by convection. The largest producer of hydrothermal emeralds today is Tairus, which has succeeded in synthesizing emeralds with chemical composition similar to emeralds in alkaline deposits in Colombia, and whose products are thus known as “Colombian created emeralds” or “Tairus created emeralds”. Luminescence in ultraviolet light is considered a supplementary test when making a natural versus synthetic determination, as many, but not all, natural emeralds are inert to ultraviolet light. Many synthetics are also UV inert. Synthetic emeralds are often referred to as "created", as their chemical and gemological composition is the same as their natural counterparts. The U.S. Federal Trade Commission (FTC) has very strict regulations as to what can and what cannot be called a "synthetic" stone. The FTC says: "§ 23.23(c) It is unfair or deceptive to use the word "laboratory-grown", "laboratory-created", "[manufacturer name]-created", or "synthetic" with the name of any natural stone to describe any industry product unless such industry product has essentially the same optical, physical, and chemical properties as the stone named."

In culture and lore
Emerald is regarded as the traditional birthstone for May as well as the traditional gemstone for the astrological sign of Taurus (June/July)

Traditional alchemical lore ascribes several uses and characteristics to emeralds:

The virtue of the Emerald is to counteract poison. They say that if a venomous animal should look at it, it will become blinded. The gem also acts as a preservative against epilepsy; it cures leprosy, strengthens sight and memory, checks copulation, during which act it will break, if worn at the time on the finger.

According to French writer Brantôme (c. 1540–1614) Hernán Cortés had one of the emeralds which he had looted from Mexico text engraved, Inter Natos Mulierum non surrexit major ("Among those born of woman there hath not arisen a greater," Matthew 11:11), in reference to John the Baptist. Brantôme considered engraving such a beautiful and simple product of nature sacrilegious and considered this act the cause for Cortez's loss in 1541 of an extremely precious pearl (to which he dedicated a work, A beautiful and incomparable pearl), and even for the death of King Charles IX of France, who died (1574) soon afterward.

In American author L. Frank Baum's 1900 children's novel The Wonderful Wizard of Oz, and the 1939 MGM film adaptation, the protagonist must travel to an Emerald City to meet the eponymous character, the Wizard.

The chief deity of one of India's most famous temples, the Meenakshi Amman Temple in Madurai, is the goddess Meenakshi, whose idol is traditionally thought to be made of emerald.

title: Emerald


text:
Erie Canal

The Erie Canal is a historic canal in upstate New York that runs east–west between the Hudson River and Lake Erie. Completed in 1825, the canal was the first navigable waterway connecting the Atlantic Ocean to the Great Lakes, vastly reducing the costs of transporting people and goods across the Appalachians. The Erie Canal accelerated the settlement of the Great Lakes region, the westward expansion of the United States, and the economic ascendancy of New York state. It has been called "The Nation's First Superhighway."

A canal from the Hudson River to the Great Lakes was first proposed in the 1780s, but a formal survey was not conducted until 1808. The New York State Legislature authorized construction in 1817. Political opponents of the canal and its lead supporter New York Governor DeWitt Clinton, denigrated the project as "Clinton's Folly" and "Clinton's Big Ditch". Nonetheless, the canal saw quick success upon opening on October 26, 1825, with toll revenue covering the state's construction debt within the first year of operation. The westward connection gave New York City a strong advantage over all other U.S. ports and brought major growth to canal cities such as Albany, Utica, Syracuse, Rochester, and Buffalo.

The construction of the Erie Canal was a landmark civil engineering achievement in the early history of the United States. When built, the 363 mi canal was the second-longest in the world after the Grand Canal in China. Initially 40 ft wide and 4 ft deep, the canal was expanded several times, most notably from 1905 to 1918 when the "Barge Canal" was built and over half the original route was abandoned. The modern Barge Canal measures 351 mi long, 120 ft wide, and 12 ft deep. It has 34 locks, including the Waterford Flight, the steepest locks in the United States. When leaving the canal, boats must also traverse the Black Rock Lock to reach Lake Erie or the Troy Federal Lock to reach the tidal Hudson. The overall elevation difference is about 565 ft.

The Erie's peak year was 1855, when 33,000 commercial shipments took place. It continued to be competitive with railroads until about 1902, when tolls were abolished. Commercial traffic declined heavily in the latter half of the 20th century due to competition from trucking and the 1959 opening of the larger St. Lawrence Seaway. The canal's last regularly scheduled hauler, the Day Peckinpaugh, ended service in 1994.

Today, the Erie Canal is mainly used by recreational watercraft. It connects the three other canals in the New York State Canal System: the Champlain, Oswego, and Cayuga–Seneca. Some long-distance boaters take the Erie as part of the Great Loop. The canal has also become a tourist attraction in its own right—several parks and museums are dedicated to its history. The New York State Canalway Trail is a popular cycling path that follows the canal across the state. In 2000, Congress designated the Erie Canalway National Heritage Corridor to protect and promote the system.

Ambiguity in name
The waterway today referred to as the Erie Canal is quite different from the nineteenth-century Erie Canal. More than half of the original Erie Canal was destroyed or abandoned during construction of the New York State Barge Canal in the early 20th century. The sections of the original route remaining in use were widened significantly, mostly west of Syracuse, with bridges rebuilt and locks replaced. It was called the Barge Canal at the time, but that name fell into disuse with the disappearance of commercial traffic and the increase of recreational travel in the later 20th century.

Background
Before railroads, water transport was the most cost-effective way to ship bulk goods. A mule can only carry about 250 lb but can draw a barge weighing as much as 60000 lb along a towpath. In total, a canal could cut transport costs by about 95 percent.

In the early years of the United States, transportation of goods between the coastal ports and the interior was slow and difficult. Close to the seacoast, rivers provided easy inland transport up to the fall line, since floating vessels encounter much less friction than land vehicles. However, the Appalachian Mountains were a great obstacle to further transportation or settlement, stretching 1500 mi from Maine to Alabama, with just five places where mule trains or wagon roads could be routed. Passengers and freight bound for the western parts of the country had to travel overland, a journey made more difficult by the rough condition of the roads. In 1800, it typically took 2½ weeks to travel overland from New York to Cleveland, Ohio, (460 mi) and 4 weeks to Detroit (612 mi).

The principal exportable product of the Ohio Valley was grain, which was a high-volume, low-priced commodity, bolstered by supplies from the coast. Frequently it was not worth the cost of transporting it to far-away population centers. This was a factor leading to farmers in the west turning their grains into whiskey for easier transport and higher sales, and later the Whiskey Rebellion. In the 18th and early 19th centuries, it became clear to coastal residents that the city or state that succeeded in developing a cheap, reliable route to the West would enjoy economic success, and the port at the seaward end of such a route would see business increase greatly. In time, projects were devised in Virginia, Maryland, Pennsylvania, and relatively deep into the coastal states.

Topography
The Mohawk River (a tributary of the Hudson River) rises near Lake Ontario and runs in a glacial meltwater channel just north of the Catskill range of the Appalachian Mountains, separating them from the geologically distinct Adirondacks to the north. The Mohawk and Hudson valleys form the only cut across the Appalachians north of Alabama. A navigable canal through the Mohawk Valley would allow an almost complete water route from New York City in the south to Lake Ontario and Lake Erie in the west. Via the canal and these lakes, other Great Lakes, and to a lesser degree, related rivers, a large part of the continent's interior (and many settlements) would be made well connected to the Eastern seaboard.

Proposals

The idea of a canal to tie the East Coast to the new western settlements was discussed as early as 1724: New York provincial official Cadwallader Colden made a passing reference (in a report on fur trading) to improving the natural waterways of western New York.

Gouverneur Morris and Elkanah Watson were early proponents of a canal along the Mohawk River. Their efforts led to the creation of the "Western and Northern Inland Lock Navigation Companies" in 1792, which took the first steps to improve navigation on the Mohawk and construct a canal between the Mohawk and Lake Ontario, but it was soon discovered that private financing was insufficient. Christopher Colles, who was familiar with the Bridgewater Canal, surveyed the Mohawk Valley, and made a presentation to the New York state legislature in 1784, proposing a shorter canal from Lake Ontario. The proposal drew attention and some action but was never implemented.

Jesse Hawley had envisioned encouraging the growing of large quantities of grain on the western New York plains (then largely unsettled) for sale on the Eastern seaboard. However, he went bankrupt trying to ship grain to the coast. While in Canandaigua debtors' prison, Hawley began pressing for the construction of a canal along the 90 mi Mohawk River valley with support from Joseph Ellicott (agent for the Holland Land Company in Batavia). Ellicott realized that a canal would add value to the land he was selling in the western part of the state. He later became the first canal commissioner.

New York legislators became interested in the possibility of building a canal across New York in the first decade of the 19th century. Shipping goods west from Albany was a costly and tedious affair; there was no railroad yet, and to cover the distance from Buffalo to New York City by stagecoach took two weeks. The problem was that the land rises about 600 ft from the Hudson to Lake Erie. Locks at the time could handle up to 12 ft of lift, so even with the heftiest cuttings and viaducts, fifty locks would be required along the 360 mi canal. Such a canal would be expensive to build even with modern technology; in 1800, the expense was barely imaginable. President Thomas Jefferson called it "little short of madness" and rejected it.

Eventually, Hawley interested New York Governor DeWitt Clinton in the project. There was much opposition, and the project was ridiculed as "Clinton's folly" and "Clinton's ditch". In 1817, though, Clinton received approval from the legislature for $7 million for construction.

Construction
The original canal was 363 mi long, from Albany on the Hudson to Buffalo on Lake Erie. The channel was cut 40 ft wide and 4 ft deep, with removed soil piled on the downhill side to form a walkway known as a towpath. Its construction, through limestone and mountains, proved a daunting task. To move earth, animals pulled a "slip scraper" (similar to a bulldozer). The sides of the canal were lined with stone set in clay, and the bottom was also lined with clay. The Canal was built by Irish laborers and German stonemasons. All labor on the canal depended upon human and animal power or the force of water. Engineering techniques developed during its construction included the building of aqueducts to redirect water; one aqueduct was 950 ft long to span 800 ft of river. As the canal progressed, the crews and engineers working on the project developed expertise and became a skilled labor force.

The men who planned and oversaw construction were novices as surveyors and as engineers. There were no civil engineers in the United States. James Geddes and Benjamin Wright, who laid out the route, were judges whose experience in surveying was in settling boundary disputes. Geddes had only used a surveying instrument for a few hours before his work on the Canal. Canvass White was a 27-year-old amateur engineer who persuaded Clinton to let him go to Britain at his own expense to study the canal system there. Nathan Roberts was a mathematics teacher and land speculator. Yet these men "carried the Erie Canal up the Niagara escarpment at Lockport, maneuvered it onto a towering embankment to cross over Irondequoit Creek, spanned the Genesee River on an awesome aqueduct, and carved a route for it out of the solid rock between Little Falls and Schenectady—and all of those venturesome designs worked precisely as planned".

Construction began on July 4, 1817, at Rome, New York. The first 15 mi, from Rome to Utica, opened in 1819. At that rate, the canal would not be finished for 30 years. The main delays were caused by felling trees to clear a path through virgin forest and moving excavated soil, which took longer than expected, but the builders devised ways to solve these problems. To fell a tree, they threw rope over the top branches and winched it down. They pulled out the stumps with an innovative stump puller. Two huge wheels were mounted loose on the ends of an axle. A third wheel, slightly smaller than the others, was fixed to the center of the axle. A chain was wrapped around the axle and hooked to the stump. A rope was wrapped around the center wheel and hooked to a team of oxen. The mechanical advantage (torque) obtained ripped the stumps out of the soil. Soil to be moved was shoveled into large wheelbarrows that were dumped into mule-pulled carts. Using a scraper and a plow, a three-man team with oxen, horses and mules could build a mile in a year.

The remaining problem was finding labor; increased immigration helped fill the need. Many of the laborers working on the canal were Irish, who had recently come to the United States as a group of about 5,000. Most of them were Roman Catholic, a religion that raised much suspicion in early America because of its hierarchic structure, and many laborers on the canal suffered violent assault as the result of misjudgment and xenophobia.

Construction continued at an increased rate as new workers arrived. When the canal reached Montezuma Marsh (at the outlet of Cayuga Lake west of Syracuse), it was rumored that over 1,000 workers died of "swamp fever" (malaria), and construction was temporarily stopped. However, recent research has revealed that the death toll was likely much lower, as no contemporary reports mention significant worker mortality, and mass graves from the period have never been found in the area. Work continued on the downhill side towards the Hudson, and the crews worked on the section across the swampland when it froze in winter.

The middle section from Utica to Salina (Syracuse) was completed in 1820, and traffic on that section started up immediately. Expansion to the east and west proceeded simultaneously, and the whole eastern section, 250 mi from Brockport to Albany, opened on September 10, 1823, to great fanfare. The Champlain Canal, a separate but connected 64 mi north–south route from Watervliet on the Hudson to Lake Champlain, opened on the same date.

After Montezuma Marsh, the next difficulties were crossing Irondequoit Creek and the Genesee River near Rochester. The former ultimately required building the 1320 ft long "Great Embankment", to carry the canal at a height of 76 ft above the level of the creek, which ran through a 245 ft culvert underneath. The canal crossed the river on a stone aqueduct, 802 ft long and 17 ft wide, supported by 11 arches.

In 1823 construction reached the Niagara Escarpment, an 80 ft-high wall of hard dolomitic limestone. The route followed the channel of a creek that had cut a ravine steeply down the escarpment. The construction and operation of two sets of five locks along a 3 mi corridor soon gave rise to the community of Lockport. The 12 ft lift-locks had a total lift of 60 ft, exiting into a deeply cut channel. The final leg had to be cut 30 ft deep through another limestone mass, the Onondaga ridge. Much of that section was blasted with black powder, and the inexperience of the crews often led to accidents, and sometimes to rocks falling on nearby homes.

Two villages competed to be the terminus: Black Rock, on the Niagara River, and Buffalo, at the eastern tip of Lake Erie. Buffalo expended great energy to widen and deepen Buffalo Creek to make it navigable and to create a harbor at its mouth. Buffalo won over Black Rock, and grew into a large city, eventually encompassing its former rival.

Completion
In 1824, before the canal was completed, a detailed Pocket Guide for the Tourist and Traveler, Along the Line of the Canals, and the Interior Commerce of the State of New York, was published for the benefit of travelers and land speculators.

The entire canal was officially completed on October 26, 1825. The event was marked by a statewide "Grand Celebration", culminating in a series of cannon shots along the length of the canal and the Hudson, a 90-minute cannonade from Buffalo to New York City. A flotilla of boats, led by Governor Dewitt Clinton aboard Seneca Chief, sailed from Buffalo to New York City over ten days. Clinton then ceremonially poured Lake Erie water into New York Harbor to mark the "Wedding of the Waters". On its return trip, Seneca Chief brought back a keg of Atlantic Ocean water, which was poured into Lake Erie by Buffalo's Judge Samuel Wilkeson, who would later become mayor.

The Erie Canal was thus completed in eight years at a total length of 353 miles and cost $7.143 million (equivalent to $ million in ). It was acclaimed as an engineering marvel that united the country and helped New York City develop as an international trade center.

Problems developed but were quickly solved. Leaks developed along the entire length of the canal, but these were sealed using cement that hardened underwater (hydraulic cement). Erosion on the clay bottom proved to be a problem and the speed was limited to 4 mph.

Branch canals
Additional feeder canals soon extended the Erie Canal into a system. These included the Cayuga-Seneca Canal south to the Finger Lakes, the Oswego Canal from Three Rivers north to Lake Ontario at Oswego, and the Champlain Canal from Troy north to Lake Champlain. From 1833 to 1877, the short Crooked Lake Canal connected Keuka Lake and Seneca Lake. The Chemung Canal connected the south end of Seneca Lake to Elmira in 1833, and was an important route for Pennsylvania coal and timber into the canal system. The Chenango Canal in 1836 connected the Erie Canal at Utica to Binghamton and caused a business boom in the Chenango River valley. The Chenango and Chemung canals linked the Erie with the Susquehanna River system. The Black River Canal connected the Black River to the Erie Canal at Rome and remained in operation until the 1920s. The Genesee Valley Canal was run along the Genesee River to connect with the Allegheny River at Olean, but the Allegheny section, which would have connected to the Ohio and Mississippi rivers, was never built. The Genesee Valley Canal was later abandoned and became the route of the Genesee Valley Canal Railroad.

First Enlargement

The original design planned for an annual tonnage of 1.5 million tons (1.36 million metric tons), but this was exceeded immediately. An ambitious program to improve the canal began in 1834. During this massive series of construction projects, known as the First Enlargement, the canal was widened from 40 to 70 ft and deepened from 4 to 7 ft. Locks were widened and/or rebuilt in new locations, and many new navigable aqueducts were constructed. The canal was straightened and slightly re-routed in some stretches, resulting in the abandonment of short segments of the original 1825 canal. The First Enlargement was completed in 1862, with further minor enlargements in later decades.

Railroad competition

The Mohawk and Hudson Railroad opened in 1837, providing a bypass to the slowest part of the canal between Albany and Schenectady. Other railroads were soon chartered and built to continue the line west to Buffalo, and in 1842 a continuous line (which later became the New York Central Railroad and its Auburn Road in 1853) was open the whole way to Buffalo. As the railroad served the same general route as the canal, but provided for faster travel, passengers soon switched to it. However, as late as 1852, the canal carried thirteen times more freight tonnage than all the railroads in New York State combined. The New York, West Shore and Buffalo Railway was completed in 1884, as a route running closely parallel to both the canal and the New York Central Railroad. However, it went bankrupt and was acquired the next year by the New York Central. The canal continued to compete well with the railroads through 1902, when tolls were abolished.

Barge Canal

In 1903 the New York State legislature authorized construction of the New York State Barge Canal as the "Improvement of the Erie, the Oswego, the Champlain, and the Cayuga and Seneca Canals". In 1905, construction of the Barge Canal began, which was completed in 1918, at a cost of $96.7 million.

This new canal replaced much of the original route, leaving many abandoned sections (most notably between Syracuse and Rome). New digging and flood control technologies allowed engineers to canalize rivers that the original canal had sought to avoid, such as the Mohawk, Seneca, and Clyde rivers, and Oneida Lake. In sections that did not consist of canalized rivers (particularly between Rochester and Buffalo), the original Erie Canal channel was enlarged to 120 ft wide and 12 ft deep. The expansion allowed barges up to 2000 ST to use the Canal. This expensive project was politically unpopular in parts of the state not served by the canal, and failed to save it from becoming obsolete for commercial shipping.

Commercial decline
Freight traffic reached a total of 5.2 million short tons (4.7 million metric tons) by 1951. The growth of railroads and highways across the state, and the opening of the St. Lawrence Seaway in 1959, caused commercial traffic on the canal to decline dramatically during the second half of the 20th century. Since the 1990s, the canal system has been used primarily by recreational traffic.

New York State Canal System
In 1992, the New York State Barge Canal was renamed the New York State Canal System (including the Erie, Cayuga-Seneca, Oswego, and Champlain canals) and placed under the newly created New York State Canal Corporation, a subsidiary of the New York State Thruway Authority. While part of the Thruway, the canal system was operated using money generated by Thruway tolls. In 2017, the New York State Canal Corporation was transferred from the New York State Thruway to the New York Power Authority.

In 2000, Congress designated the Erie Canalway National Heritage Corridor, covering 524 mi of navigable water from Lake Champlain to the Capital Region and west to Buffalo. The area has a population of 2.7 million; about 75% of Central and Western New York's population lives within 25 mi of the Erie Canal.

There were some 42 commercial shipments on the canal in 2008, compared to 15 such shipments in 2007 and more than 33,000 shipments in 1855, the canal's peak year. The new growth in commercial traffic is due to the rising cost of diesel fuel. Canal barges can carry a short ton of cargo 514 mi on one gallon of diesel fuel, while a gallon allows a train to haul the same amount of cargo 202 mi and a truck 59 mi. Canal barges can carry loads up to 3000 ST, and are used to transport objects that would be too large for road or rail shipment. In 2012, the New York State Canal System as a whole was used to ship 42,000 tons of cargo.

Travel on the canal's middle section (particularly in the Mohawk Valley) was severely hampered by flooding in late June and early July 2006. Flood damage to the canal and its facilities was estimated as at least $15 million.

Original Canal
The Erie made use of the favorable conditions of New York's unique topography, which provided that area with the only break in the Appalachians south of the St. Lawrence River. The Hudson is tidal to Troy, and Albany is west of the Appalachians. It allowed for east–west navigation from the coast to the Great Lakes within US territory.

The canal began on the west side of the Hudson River at Albany, and ran north to Watervliet, where the Champlain Canal branched off. At Cohoes, it climbed the escarpment on the west side of the Hudson River—16 locks rising 140 ft—and then turned west along the south shore of the Mohawk River, crossing to the north side at Crescent and again to the south at Rexford. The canal continued west near the south shore of the Mohawk River all the way to Rome, where the Mohawk turns north.

At Rome, the canal continued west parallel to Wood Creek, which flows westward into Oneida Lake, and turned southwest and west cross-country to avoid the lake. From Canastota west, it ran roughly along the north (lower) edge of the Onondaga Escarpment, passing through Syracuse, Onondaga Lake, and Rochester. Before reaching Rochester, the canal uses a series of natural ridges to cross the deep valley of Irondequoit Creek. At Lockport the canal turned southwest to rise to the top of the Niagara Escarpment, using the ravine of Eighteen Mile Creek.

The canal continued south-southwest to Pendleton, where it turned west and southwest, mainly using the channel of Tonawanda Creek. From the Tonawanda south toward Buffalo, it ran just east of the Niagara River, where it reached its "Western Terminus" at Little Buffalo Creek (later it became the Commercial Slip), which discharged into the Buffalo River just above its confluence with Lake Erie. With Buffalo's re-excavation of the Commercial Slip, completed in 2008, the Canal's original terminus is now re-watered and again accessible by boats. With several miles of the Canal inland of this location still lying under 20th-century fill and urban construction, the effective western navigable terminus of the Erie Canal is found at Tonawanda.

Barge Canal
The new alignment began on the Hudson River at the border between Cohoes and Waterford, where it ran northwest with five locks (the so-called "Waterford Flight"), running into the Mohawk River east of Crescent. The Waterford Flight is claimed to be one of the steepest series of locks in the world.

While the old Canal ran next to the Mohawk all the way to Rome, the new canal ran through the river, which was straightened or widened where necessary. At Ilion, the new canal left the river for good, but continued to run on a new alignment parallel to both the river and the old canal to Rome. From Rome, the new route continued almost due west, merging with Fish Creek just east of its entry into Oneida Lake.

From Oneida Lake, the new canal ran west along the Oneida River, with cutoffs to shorten the route. At Three Rivers, the Oneida River turns northwest, and was deepened for the Oswego Canal to Lake Ontario. The new Erie Canal turned south there along the Seneca River, which turns west near Syracuse and continues west to a point in the Montezuma Marsh. There the Cayuga and Seneca Canal continued south with the Seneca River, and the new Erie Canal again ran parallel to the old canal along the bottom of the Niagara Escarpment, in some places running along the Clyde River, and in some places replacing the old canal. At Pittsford, southeast of Rochester, the canal turned west to run around the south side of Rochester, rather than through downtown. The canal crosses the Genesee River at the Genesee Valley Park, then rejoins the old path near North Gates.

From there it was again roughly an upgrade to the original canal, running west to Lockport. This reach of 64.2 mi from Henrietta to Lockport is called "the 60‑mile level" since there are no locks and the water level rises only 2 ft over the entire segment. Diversions from and to adjacent natural streams along the way are used to maintain the canal's level. It runs southwest to Tonawanda, where the new alignment discharges into the Niagara River, which is navigable upstream to the New York Barge Canal's Black Rock Lock and thence to the Canal's original "Western Terminus" at Buffalo's Inner Harbor.

Freight boats
Canal boats up to 3.5 ft in draft were pulled by horses and mules walking on the towpath. The canal had one towpath, generally on the north side. When canal boats met, the boat with the right of way remained on the towpath side of the canal. The other boat steered toward the berm (or heelpath) side of the canal. The driver (or "hoggee", pronounced HO-gee) of the privileged boat kept his towpath team by the canalside edge of the towpath, while the hoggee of the other boat moved to the outside of the towpath and stopped his team. His towline would be unhitched from the horses, go slack, fall into the water and sink to the bottom, while his boat coasted with its remaining momentum. The privileged boat's team would step over the other boat's towline, with its horses pulling the boat over the sunken towline without stopping. Once clear, the other boat's team would continue on its way.

Pulled by teams of horses, canal boats moved slowly, but methodically, shrinking time and distance. Efficiently, the smooth, nonstop method of transportation cut the travel time between Albany and Buffalo nearly in half, moving by day and by night. Migrants took passage on freight boats, camping on deck or on top of crates.

Passenger boats
Packet boats, serving passengers exclusively, reached speeds of up to 5 mph and ran at much more frequent intervals than the cramped, bumpy stagecoach wagons. These boats, measuring up to 78 ft long and 14.5 ft wide, made ingenious use of space, accommodating up to 40 passengers at night and up to three times as many in the daytime. The best examples, furnished with carpeted floors, stuffed chairs, and mahogany tables stocked with books and current newspapers, served as sitting rooms during the days. At mealtimes, crews transformed the cabin into a dining room. Drawing a curtain across the width of the room divided the cabin into ladies' and gentlemen's sleeping quarters at night. Pull-down tiered beds folded from the walls, and additional cots could be hung from hooks in the ceiling. Some captains hired musicians and held dances.

Sunday closing debate
The New York State Legislature debated closing the locks of the Erie Canal on Sundays, when they convened in 1858. However, George Jeremiah and Dwight Bacheller, two of the bill's opponents, argued that the state had no right to stop canal traffic on the grounds that the Erie Canal and its tributaries had ceased to be wards of the state. The canal at its inception had been imagined as an extension of nature, an artificial river where there had been none. The canal succeeded by sharing more in common with lakes and seas than it had with public roads. Jeremiah and Bacheller argued, successfully, that just as it was unthinkable to halt oceangoing navigation on Sunday, so it was with the canal.

Economic impact
The Erie Canal greatly lowered the cost of shipping between the Midwest and the Northeast, bringing much lower food costs to Eastern cities and allowing the East to ship machinery and manufactured goods to the Midwest more economically. To give an example, the cost to transport a barrel of flour from Rochester to Albany dropped from $3 (before the canal) to 75¢ on the canal. The canal also made an immense contribution to the wealth and importance of New York City, Buffalo and New York State. Its impact went much further, increasing trade throughout the nation by opening eastern and overseas markets to Midwestern farm products and by enabling migration to the West. The port of New York became essentially the Atlantic home port for all of the Midwest. Because of this vital connection and others to follow, such as the railroads, New York would become known as the "Empire State" or "the great Empire State".

The Erie Canal was an immediate success. Tolls collected on freight had already exceeded the state's construction debt in its first year of official operation. By 1828, import duties collected at the New York Customs House supported federal government operations and provided funds for all the expenses in Washington except the interest on the national debt. Additionally, New York State's initial loan for the original canal had been paid by 1837. Although it had been envisioned as primarily a commercial channel for freight boats, passengers also traveled on the canal's packet boats. In 1825 more than 40,000 passengers took advantage of the convenience and beauty of canal travel. The canal's steady flow of tourists, businessmen and settlers lent it to uses never imagined by its initial sponsors. Evangelical preachers made their circuits of the upstate region, and the canal served as the last leg of the Underground Railroad ferrying runaway slaves to Buffalo near the Canada–US border. Aspiring merchants found that tourists were reliable customers. Vendors moved from boat to boat peddling items such as books, watches and fruit, while less scrupulous "confidence men" sold remedies for foot corns or passed off counterfeit bills. Tourists were carried along the "northern tour," which ultimately led to the popular honeymoon destination Niagara Falls, just north of Buffalo.

As the canal brought travelers to New York City, it took business away from other ports such as Philadelphia and Baltimore. Those cities and their states started projects to compete with the Erie Canal. In Pennsylvania, the Main Line of Public Works was a combined canal and railroad running west from Philadelphia to Pittsburgh on the Ohio River, opened in 1834. In Maryland, the Baltimore and Ohio Railroad ran west to Wheeling, West Virginia, then a part of Virginia, also on the Ohio River, and was completed in 1853.

The canal played a major role in the growth of Standard Oil, as founder John D. Rockefeller used the canal as a cheaper form of transportation – in the summer months when it was not frozen – to get his refined oil from Cleveland to New York City. In the winter months his only options were the three trunk lines: the Erie Railroad, the New York Central Railroad, or the Pennsylvania Railroad.

Migratory impact
New ethnic Irish communities formed in some towns along its route after completion, as Irish immigrants were a large portion of the construction labor force. A plaque honoring the canal's construction is located in Battery Park in southern Manhattan.

Because so many immigrants traveled on the canal, many genealogists have sought copies of canal passenger lists. Apart from the years 1827–1829, canal boat operators were not required to record passenger names or report them to the New York government. Some passenger lists survive today in the New York State Archives, and other sources of traveler information are sometimes available.

The canal allowed Buffalo to grow from just 200 settlers in 1820 to more than 18,000 people by 1840.

Cultural impact
The Canal also helped bind the still-new nation closer to Britain and Europe. Repeal of Britain's Corn Law resulted in a huge increase in exports of Midwestern wheat to Britain. Trade between the United States and Canada also increased as a result of the repeal and a reciprocity (free-trade) agreement signed in 1854. Much of this trade flowed along the Erie.

Its success also prompted imitation: a rash of canal-building followed. Also, the many technical hurdles that had to be overcome made heroes of those whose innovations made the canal possible. This led to an increased public esteem for practical education. Chicago, among other Great Lakes cities, recognized the importance of the canal to its economy, and two West Loop streets are named "Canal" and "Clinton" (for canal proponent DeWitt Clinton).

Concern that erosion caused by logging in the Adirondacks could silt up the canal contributed to the creation in 1885 of another New York National Historic Landmark, the Adirondack Park.

Many notable authors wrote about the canal, including Herman Melville, Frances Trollope, Nathaniel Hawthorne, Harriet Beecher Stowe, Mark Twain, Samuel Hopkins Adams and the Marquis de Lafayette, and many tales and songs were written about life on the canal. The popular song "Low Bridge, Everybody Down" by Thomas S. Allen was written in 1905 to memorialize the canal's early heyday, when barges were pulled by mules rather than engines.

Consisting of a massive stone aqueduct that carried boats over incredible cascades, Little Falls was one of the most popular stops for American and foreign tourists. This is shown in Scene 4 of William Dunlap's play A Trip to Niagara, where he depicts the general preference of tourists to travel by canal so that they could experience a combination of artificial and natural sights. Canal travel was, for many, an opportunity to take in the sublime and commune with nature. The play also reflects the less enthusiastic view of some who saw movement on the canal as tedious.

The Erie Canal changed property law in New York. Most importantly, it expanded the government's right to take private property. Cases surrounding the newly built Erie Canal expanded condemnation theory to permit canal builders to appropriate private land and broadened the meaning of "public use" in the 5th Amendment to the U.S. Constitution. The canal also had an impact on water access jurisprudence as well as nuisance law.

The canal today
Today, the Erie Canal is used primarily by recreational vessels, though it remains served by several commercial barge-towing companies.

The canal is open to small craft and some larger vessels from May through November each year. During winter, water is drained from parts of the canal for maintenance. The Champlain Canal, Lake Champlain, and the Chambly Canal, and Richelieu River in Canada form the Lakes to Locks Passage, making a tourist attraction of the former waterway linking eastern Canada to the Erie Canal. In 2006 recreational boating fees were eliminated to attract more visitors.

The Erie Canal is a destination for tourists from all over the world, and has inspired guidebooks dedicated to exploration of the waterway. An Erie Canal Cruise company, based in Herkimer, operates from mid-May until mid-October with daily cruises. The cruise goes through the history of the canal and also takes passengers through Lock 18.

Aside from transportation, numerous businesses, farms, factories and communities alongside its banks still utilize the canal's waters for other purposes such as irrigation for farmland, hydroelectricity, research, industry, and even drinking. Use of the canal system has an estimated total economic impact of $6.2 billion annually.

Old Erie Canal
Today, the reconfiguration of the canal created during the First Enlargement is commonly referred to as the "Improved Erie Canal" or the "Old Erie Canal", to distinguish it from the canal's modern-day course. Existing remains of the 1825 canal abandoned during the Enlargement are officially referred to today as "Clinton's Ditch" (which was also the popular nickname for the entire Erie Canal project during its original 1817–1825 construction).

Sections of the Old Erie Canal not used after 1918 are owned by New York State, or have been ceded to or purchased by counties or municipalities. Many stretches of the old canal have been filled in to create roads such as Erie Boulevard in Syracuse and Schenectady, and Broad Street and the Rochester Subway in Rochester. A 36‑mile (58 km) stretch of the old canal from the town of DeWitt, New York, east of Syracuse, to just outside Rome, New York, is preserved as the Old Erie Canal State Historic Park. In 1960 the Schoharie Crossing State Historic Site, a section of the canal in Montgomery County, was one of the first sites recognized as a National Historic Landmark.

Some municipalities have preserved sections as town or county canal parks, or have plans to do so. Camillus Erie Canal Park preserves a 7 mi stretch and has restored Nine Mile Creek Aqueduct, built in 1841 as part of the First Enlargement of the canal. In some communities, the old canal has refilled with overgrowth and debris. Proposals have been made to rehydrate the old canal through downtown Rochester or Syracuse as a tourist attraction. In Syracuse, the location of the old canal is represented by a reflecting pool in downtown's Clinton Square and the downtown hosts a canal barge and weigh lock structure, now dry. Buffalo's Commercial Slip is the restored and re-watered segment of the canal which formed its "Western Terminus".

In 2004, the administration of New York Governor George Pataki was criticized when officials of New York State Canal Corporation attempted to sell private development rights to large stretches of the Old Erie Canal to a single developer for $30,000, far less than the land was worth on the open market. After an investigation by the Syracuse Post-Standard newspaper, the Pataki administration nullified the deal.

Parks and museums
Parks and museums related to the Old Erie Canal include (listed from east to west):
 * Day Peckinpaugh ship; restoration and conversion to a floating museum was planned for completion in 2012 by the New York State Museum
 * Watervliet Side Cut Locks, located at Watervliet and listed on the National Register of Historic Places in 1971
 * Enlarged Erie Canal Historic District (Discontiguous), a national historic district located at Cohoes, New York listed on the National Register of Historic Places in 2004
 * Cohoes Falls Park, 231 N. Mohawk St., Cohoes, New York, offers, looking away from the river, a dramatic view of abandoned and dry Erie Canal lock 18, high above.
 * Enlarged Double Lock No. 23, Old Erie Canal, Rotterdam
 * Schoharie Crossing State Historic Site at Fort Hunter
 * Old Erie Canal State Historic Park, 36-mile linear park from Rome to DeWitt
 * Erie Canal Village, near Rome
 * Canastota Canal Town Museum, Canastota
 * Chittenango Landing Canal Boat Museum, near Chittenango
 * Erie Canal Museum in downtown Syracuse
 * Camillus Erie Canal Park in Camillus
 * Jordan Canal Park in Jordan, town of Elbridge
 * Enlarged Double Lock No. 33 Old Erie Canal, St. Johnsville
 * Erie Canal Lock 52 Complex, a national historic district located within the Old Erie Canal Heritage Park at Port Byron and Mentz in Cayuga County; listed on the National Register of Historic Places in 1998
 * Seneca River Crossing Canals Historic District, a national historic district located at Montezuma and Tyre in Cayuga County; listed on the National Register of Historic Places in 2005
 * Centerport Aqueduct Park near Weedsport; listed on the National Register of Historic Places in 2000
 * Lock Berlin Park near Clyde
 * Macedon Aqueduct Park near Palmyra
 * Old Erie Canal Lock 60 Park in Macedon
 * Perinton Park in Perinton near Fairport
 * Genesee Valley Park in the city of Rochester
 * Spencerport Depot & Canal Museum, Spencerport
 * Niagara Escarpment "Flight of Five" locks at Lockport
 * Erie Canal Discovery Center, 24 Church Street, Lockport (Locks 34 and 35)
 * Canalside Buffalo at the Canal's "Western Terminus"

Records and research
Records of the planning, funding, design, construction, and administration of the Erie Canal are vast and can be found in the New York State Archives. Except for two years (1827–1829), the State of New York did not require canal boat operators to maintain or submit passenger lists.

Locks
The following list of locks is provided for the current canal, from east to west. There are a total of 36 (35 numbered) locks on the Erie Canal.

All locks on the New York State Canal System are single-chamber; the dimensions are 328 ft long and 45 ft wide with a minimum 12 ft depth of water over the miter sills at the upstream gates upon lift. They can accommodate a vessel up to 300 ft long and 43.5 ft wide. Overall sidewall height will vary by lock, ranging between 28 and 61 ft depending on the lift and navigable stages. Lock E17 at Little Falls has the tallest sidewall height at 80 ft.

Distance is based on position markers from an interactive canal map provided online by the New York State Canal Corporation and may not exactly match specifications on signs posted along the canal. Mean surface elevations are comprised from a combination of older canal profiles and history books as well as specifications on signs posted along the canal. The margin of error should normally be within 6 in.

The Waterford Flight series of locks (comprising Locks E2 through E6) is one of the steepest in the world, lifting boats 169 ft in less than 2 mi.

All surface elevations are approximate.

 * Denotes federally managed locks.

There is a 2 ft natural rise between locks E33 and E34 as well as a 1.5 ft natural rise between Lock E35 and the Niagara River.

There is no Lock E1 or Lock E31 on the Erie Canal. The place of "Lock E1" on the passage from the lower Hudson River to Lake Erie is taken by the Troy Federal Lock, located just north of Troy, New York, and is not part of the Erie Canal System proper. It is operated by the United States Army Corps of Engineers. The Erie Canal officially begins at the confluence of the Hudson and Mohawk rivers at Waterford, New York.

Although the original alignment of the Erie Canal through Buffalo has been filled in, travel by water is still possible from Buffalo via the Black Rock Lock in the Niagara River to the canal's modern western terminus in Tonawanda, and eastward to Albany. The Black Rock Lock is operated by the United States Army Corps of Engineers.

Oneida Lake lies between locks E22 and E23, and has a mean surface elevation of 370 ft. Lake Erie has a mean surface elevation of 571 ft.

title: Erie Canal