Refraction near the horizon-an empirical approach. Part 1: terrestrial refraction of the dip: erratum

During leveling, the Earth's curvature and atmospheric refraction introduce deviations in the line of sight from a true horizontal reference. When the line of sight is leveled, it remains perpendicular to the plumb line only at a single point. Beyond this, it deviates due to the Earth’s curvature, represented by the correction C. For a sight distance D, the deviation can be derived using the relationship:This relationship shows that the deviation increases quadratically with distance. Over a...

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape...

The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...

Frustration occurs when people are obstructed or prevented from achieving a desired goal or fulfilling a perceived need. For example, when someone's input is ignored in a discussion, it can lead to feelings of frustration. Conflict, however, arises from opposing interests, goals, or actions. Conflicts can take various forms based on the nature of these opposing desires or goals.
One common type of conflict is the Approach–Approach Conflict. In this case, a person faces two desirable...

This lesson provides an in-depth discussion of the stereochemical outcomes in an SN1 reaction.
In the first step of an SN1 reaction, the bond between the electrophilic carbon and the leaving group ionizes to generate the carbocation intermediate. The second step of the mechanism is the nucleophilic attack.
In the formed carbocation, the positively charged carbon is sp2 hybridized with a trigonal planar geometry. As all the three substituents lie on the same plane, a plane of symmetry for the...

In an SN2 reaction, the reaction rate depends on both the type of nucleophile and the substrate. A hindered tertiary alkyl halide is practically inert to the SN2 mechanism despite using a strong nucleophile.
However, Sir Christopher Ingold and Edward D. Hughes, who studied the kinetics of various nucleophilic substitution reactions, noticed that a tertiary alkyl halide does undergo a nucleophilic substitution reaction in the presence of a weak nucleophile. While studying the substitution...