title: Puck (Glee)

text: In the season opener, "Audition", Puck is interviewed by blogger Jacob Ben Israel (Josh Sussman) and reveals that he had a vasectomy over the summer, saying it was the only responsible thing to do. Soon after the school year begins, Puck is arrested and sent to a juvenile detention center for driving his mother's car through a convenience store window and driving off with the ATM. He returns in "Never Been Kissed", but he is now on probation and helps Artie out in an attempt to satisfy his community service, although this is only initially because Puck claimed he was "helping a crip" and they misunderstood him. Though he acts tougher than ever to his classmates, Puck eventually confesses to Artie that he was terrified in juvie, and the two come to the agreement that Artie will tutor Puck, who has to pick up garbage to fulfill his community service requirements. In "Furt", Puck, Artie, Mike Chang (Harry Shum Jr.) and Sam Evans (Chord Overstreet) confront Dave Karofsky (Max Adler) in the boys locker room to get him to stop bullying Kurt Hummel (Chris Colfer). Because he was still on probation, Puck reluctantly had to watch the beat down between Sam and Karofsky, but despite not being allowed to fight and feeling helpless about it, he showed great restraint and was still praised for standing up for Kurt. "Special Education", Puck is asked by Will to find a new glee club member to replace Kurt, who has left McKinley and New Directions. He tries to recruit from the football team, but they lock him in a port-a-potty; he is rescued the next day by Lauren Zizes (Ashley Fink), who becomes the club's new twelfth member. Puck gets intimate with Rachel at her instigation, but leaves abruptly, realizing that he doesn't want to betray Finn for a second time, though Finn dumps Rachel when she confesses to him about it. Puck and Finn finally settle their differences in "The Sue Sylvester Shuffle", and they work together to help the football team win its first-ever championship.


title: Puck (Glee)

text: In the episode "Silly Love Songs", Puck unexpectedly falls for Lauren, and performs the song "Fat Bottomed Girls" by Queen, which expresses his love of Lauren's bigger body type, but Lauren is offended by the song. Santana, unhappy with being deserted by Puck, slaps Lauren in front of him to warn her away, and Lauren tosses her around like she was nothing, leaving her dazed. Puck immediately begs Lauren to go out with him. She ultimately agrees to go on a pre-Valentine's date with him, but stands him up. Puck clumsily tells Lauren he likes her, not because of her looks but because of her "badass-ness"; Lauren says she is not looking for something casual. They go out on Valentine's Day "as friends", though Puck is clearly hoping for more in the future. In the episode "Sexy", Lauren tells Puck she's decided to make a sex tape to help her become famous, to his delight, but their plans are dashed when substitute sex education teacher Holly Holliday (Gwyneth Paltrow) informs them that as both are underage it would be considered child pornography. As part of a class assignment in the episode "Original Song", Puck writes and sings a song for Lauren—"Big Ass Heart"—that she likes. In "Born This Way", Puck discovers that Lauren had been a child beauty queen; he tells her he will run a campaign for her to become that year's prom queen, and be her king. After candidate Quinn insults Lauren's candidacy, Puck helps Lauren dig up dirt on Quinn, but the tactic backfires. Neither Puck nor Lauren win the race for prom queen and king, but they remain a couple; they fly with the rest of New Directions to the nationals competition in New York City, where the glee club comes in twelfth out of fifty teams.


title: Puck (Glee)

text: Lauren breaks up with Puck at the beginning of school year and drops out of glee club, claiming that it is hurting her reputation. Shelby Corcoran, who adopted baby Beth, gets a teaching job at McKinley, and invites Puck and Quinn to be a part of Beth's life, provided they both become more responsible. Puck does so, and Shelby allows him to see Beth. Quinn decides she wants to regain custody of Beth, but Puck is torn, and tells Shelby of Quinn's plans. He spends increasing amounts of time with Beth, but then falls in love with Shelby. She sleeps with him once, though she tells him afterward she has made a mistake, to his disgust, and subsequently resigns from McKinley. One day his father visits him at work asking him for money for rent. This visit makes Puck fear that he might one day be like his father and visit Beth at work and ask her for money. He decides to be a father that Beth would be proud of and tries to do better in school and graduate with his class. After he fails his geography final and discovers that he is not graduating he decides to not care about grades and flunk out. In the episode "Props", he gets into a fight with Rick "The Stick" Nelson and pulls out a knife. Coach Beiste (Dot-Marie Jones) breaks up the fight and she informs Puck that he could get expelled from school for bringing the knife. He tells her that it's a prop knife that they used in their production of "West Side Story" and that he does not care since he is flunking out anyway. They have a heart to heart and the next day, she tells him that what he told her in their heart to heart the day before and it gave her the strength to leave her abusive husband. She told him that she owes him big time and that she talked to his geography teacher and she agreed to let Puck retake the test. In the season finale, Puck studies with Quinn's help and then retakes his final exam. He passes with a C− and graduates from McKinley.


title: Puck (Glee)

text: In the Season 4 premiere, it is revealed that Puck has a paternal half-brother named Jake (Jacob Artist) who he was not aware of, though the two are introduced to each other by Will in the following episode, "Britney 2.0", while Puck is briefly visiting Lima from his new home, Los Angeles. Jake later turns to Puck for advice over the phone on how to get Marley Rose (Melissa Benoist) to date him, and Puck subsequently invites Jake to visit him in California over the Christmas holiday; the two get matching tattoos. Puck decides to return to Lima to live, and the two Puckermans arrange for their mothers to meet on Christmas Day where the two families bond. Puck later starts dating Kitty (Becca Tobin) in order to keep her away from Jake and spoiling his budding relationship with Marley, though Puck and she break up when he moves into Finn's dorm room at the college Finn has just started attending, even though Puck is not enrolled there. He appears less frequently this season, despite still being credited as a series regular.


title: Puck (Glee)

text: Puck makes infrequent guest appearances starting from this season. Puck is devastated by Finn's death. In "The Quarterback", three weeks after the funeral, he steals a memorial tree planted for Finn and demands that Kurt, Finn's stepbrother, give him Finn's football jacket. Coach Beiste takes him to task for being drunk regularly after so many weeks, and the two mourn Finn together, but Beiste tells him he has to guide his own life without Finn's help, and asks him to replant the tree. When he later does so, he tells her that he intends to join the Air Force. In "100" Now in the Air Force, Puck comes back to McKinley to say goodbye to the Glee Club before it is disbanded. He sees Quinn and the two of them have a conversation. He is about to tell Quinn that he still has feelings for her when her boyfriend, Biff McIntosh, shows up and shows Puck that he is rude. Puck sings Avril Lavigne's song Keep Holding On to her hoping that this would win her heart, but she turns him down stating that she loves Biff. Later, Quinn and Biff are having dinner at Breadsticks when Santana, Puck, Mike, and Artie show up. They sit with Quinn at her table and Biff reveals that he doesn't know any thing about Quinn's past. Her friends tell her about her behavior in the episode The Purple Piano Project. Quinn asks Biff to get something out of the car for her and after he leaves, she asks her friends not to mention anything to Biff since she is ashamed of her past. Puck asks her if she is ever going to tell him about their relationship and their daughter, Beth, and she says that she will eventually. This somewhat angers Puck as he tells her that she can't hide from the past and should embrace it. A few days later, Puck is hanging by the school buses when he hears Quinn and Biff fighting. Biff becomes angry with her at the fact that she kept so much from him, including having a baby with Puck. He calls her a slut, causing Puck to snap and punch him. Biff punches Puck back, causing Puck to punch him once more and then throws him into the dumpster. He then tells Quinn that she can help Biff out of the dumpster or join her real friends in the choir room. Later, Puck and Quinn are in the locker room looking at Finn's plaque. Quinn tells Puck that Biff went back to Yale by himself, and the relationship is over. Puck reveals that he still has feelings for her and wants to get back together. Quinn tells Puck that she isn't going to look back to her past, as she wants to look into her future. Puck leaves the locker room heartbroken and storms down the hallway when Quinn runs after him and kisses him, agreeing to give their relationship another chance.


title: Puck (Glee)

text: Puck returns in "Homecoming" along with fellow New Directions alumni to help Rachel and Kurt rebuild the club. He is still dating Quinn. Later in the season he attends Santana and Brittany's (and eventually also Blaine Anderson (Darren Criss) and Kurt's) wedding in "A Wedding". He appears in the "Pilot" parallel episode "2009", taunting Tina Cohen-Chang's (then fake) stutter alongside Karofsky. He last appears in the series during the rededication of McKinley's auditorium to Finn Hudson and take a bow with the rest of the Glee Cast in the series finale.


title: Puck (Glee)

text: As Puck, Salling features in many songs that have been released as singles available for digital download and are also featured in the show's soundtrack albums. He usually accompanies himself on the guitar for solo songs, including "Sweet Caroline", "Only the Good Die Young", "Fat Bottomed Girls", and the song ostensibly composed by Puck, "Big Ass Heart".


title: Puck (Glee)

text: Neil Diamond's "Sweet Caroline" was his first solo number, in the episode "Mash-Up", and received favorable reviews from critics, and also from Diamond himself, who had initially been reluctant to license the number to the show. Following the episode's broadcast, Diamond posted his approval on the social networking website Twitter, writing: "Hey, so who's this guy Puck singing 'Sweet Caroline' so good, so good, so good on #Glee? Loved it!!" Raymund Flandez of "The Wall Street Journal" described Puck's voice on the song as "earthly, sensual and full", and "Entertainment Weekly" Michael Slezak said that Salling did "more than a serviceable job". "Sweet Caroline" was released as a single, available for digital download, and charted at number 34 in the US, 22 in Canada and 37 in Australia.


title: Puck (Glee)

text: Salling's performance as Puck received some positive reviews. Flandez said of Puck in the first-season episode "Mash-Up" that we finally saw him "emerging from his bonehead-punk exterior", and that he "wows us with his sensitive, cool guy turn as a solo singer" performing “Sweet Caroline”. In her review of the following episode, "Wheels", Emily VanDerWerff of "The A.V. Club" wrote, "Mark Salling just seems to have a ridiculous amount of chemistry with all of the female cast members in the show, and it's fun to see him and Dianna Agron get in that food fight. Again, fun stuff, but a serious emotional core that keeps the show grounded."


title: Puck (Glee)

text: Television critics responded positively to the pairing of Puck and Lauren Zizes. Robert Canning of IGN said the "absolute best part" of the "Silly Love Songs" episode was Puck's "unexpected longing for Lauren Zizes." Emily VanDerWerff of "The A.V. Club" commented: "For me, the episode's highlight was the very sweet, funny courtship between Puck and Lauren. This may be because the writers have trouble writing for a self-professed bad boy, even though his escapades are straight out of Archie comics and not actually all that “bad” at all. But it's always fun to watch Salling sing, and it's always fun to watch him be smitten. Fink ends up being a good match for him, chemistry-wise, as she projects a confidence and certainty that makes it immediately obvious just what Puck sees in Lauren. The storyline also played out like both characters had something approaching real feelings." In the following episode, VanDerWerff found her relationship with Puck "a lot less assured" than before, but "Entertainment Weekly" Sandra Gonzalez deemed their scenes "as endearing as they are unrealistic", and E! Online's Jenna Mullins wrote that "the ice around [her] heart melted just a bit when Puck mouthed Lauren that little bit of encouragement at the start of her solo."


title: Puck (Glee)

text: Puck and Shelby's kiss in the "Pot o' Gold" episode was characterized as "creepy" and "super awkward" by "AOLTV" Crystal Bell, as either "super creepy" or "romantic" by BuddyTV's John Kubicek, and as "groan-inducing" in the "You're actually going to go there?" vein by Canning. Critics were polarized by Puck and Shelby's sexual encounter in the "I Kissed a Girl" episode. Kubicek declared that "the dumbest storyline Glee has ever done gets even dumber," MTV contributor Kevin Sullivan called it "the most divisive plot line of the season", and Bell asked, "Instead of these super creepy scenes between Puck and Shelby, can we please get more screen time for Shelby and Rachel?"


title: Puck (Glee)

text: In 2010, Salling was nominated for the Teen Choice Award for Choice TV: Breakout Star Male for his performance as Puck. His "Glee" castmate, Kevin McHale (Artie), was also nominated in that category, but neither actor won the award. In 2011, he was nominated for the Teen Choice Award for Choice TV: Scene Stealer Male along with "Glee" castmate Chris Colfer (Kurt); again, neither actor won.


title: Hooah

text: Hooah is a battle cry used by members of the United States Army, U.S. Air Force, and U.S. Space Force. Originally spelled "Hough", the battle cry was first used by members of the 2nd Cavalry Regiment during the Second Seminole War in 1841, after Seminole chief Coacoochee toasted officers of the regiment with a loud "Hough!", apparently a corruption of "How d'ye do!" Since WWII, the word has been widely used throughout the U.S. Army and gained a more general meaning of "anything and everything except 'no'.


title: Hooah

text: It is comparable to Oorah which the United States Marine Corps uses. The United States Navy and the United States Coast Guard use hooyah.


title: Hooah

text: The phrase originated with the U.S. Army Rangers and in the early 1980s was considered a trait of Ranger battalions, spreading locally through Fort Lewis, Washington and Fort Benning, Georgia, home of the three Ranger battalions at the time. By the late Eighties, it had spread through the majority of the Army's major and subordinate commands, quickly through leadership development schools and the more challenging courses such as Airborne, Air Assault, and Pathfinder. The speed with which it caught on is attributed to the rotation/Permanent Change of Station (PCS) of Rangers being reassigned from the "Bats" to one of the divisional units. On reassignment, their training could be put to use filling cadre slots as instructors or Black Hats by the divisions' G3 Training. As explained by senior instructor for Primary Leadership Development Course (PLDC) at Fort Ord, California in 1986, "Hooah" is always affirmative and used in various circumstances defined by the user's enthusiasm. Examples: upper case "HOOAH": "I totally agree, that's badass!"; or lower case "hooah", "yea got it, I'll get it done". Or it can be used as a question showing concern or need for clarification of intent: "Hooah?"


title: Drain-waste-vent system

text: In modern plumbing, a drain-waste-vent (or DWV) is a system that allows air to enter the plumbing system to maintain proper air pressure to enable the removal of sewage and greywater from a dwelling. Drain refers to water produced at fixtures such as sinks, and showers; waste refers to water from toilets. As the water runs down, proper venting is required to allow water to flow freely, and avoid a vacuum from being created. As the water runs down air must be allowed into the waste pipe either through a roof vent (external), or an internal vent.


title: Drain-waste-vent system

text: DWV systems maintain neutral air pressure in the drains, allowing free flow of water and sewage down drains and through waste pipes by gravity. It is critical that a sufficient downward slope be maintained throughout the drain pipes, to keep liquids and entrained solids flowing freely towards the main drain from the building. In some situations, a downward slope out of a building to the sewer cannot be created, and a special collection pit and grinding lift "sewage ejector" pump are needed. By contrast, potable water supply systems operate under pressure to distribute water up through buildings, and do not require a continuous downward slope in their piping.


title: Drain-waste-vent system

text: Every fixture is required to have an internal or external trap; double trapping is prohibited by plumbing codes due to its susceptibility to clogging. Every plumbing fixture must also have an attached vent. Without a vent, negative pressure from water leaving the system can cause a siphon which empties the trap. The top of stacks must be vented too, via a stack vent, which is sometimes called a stink pipe.


title: Drain-waste-vent system

text: All plumbing waste fixtures use traps to prevent sewer gases from leaking into the house. Through traps, all fixtures are connected to waste lines, which in turn take the waste to a "soil stack", a.k.a. "soil stack pipe", "soil vent pipe" or "main". At the building drain system's highest point, the drain-waste vent is attached, and rises (usually inside a wall) to and out of the roof. Waste exits from the building through the building's main drain and flows through a sewage line, which leads to a septic system or a public sewer. Cesspits are generally prohibited in developed areas. In the US, fixtures must have a vent (discharging into the "main stack" is not viewed as enough).


title: Drain-waste-vent system

text: The venting system, or plumbing vents, consists of a number of pipes leading from waste pipes to the outdoors, usually through the roof. Vents provide a means to release sewer gases outside instead of inside the house. Vents also admit oxygen to the waste system to allow aerobic sewage digestion, and to discourage noxious anaerobic decomposition. Vents provide a way to equalize the pressure on both sides of a trap, thereby allowing the trap to hold the water which is needed to maintain effectiveness of the trap, and avoiding "trap suckout" which otherwise might occur.


title: Drain-waste-vent system

text: A sewer pipe is normally at neutral air pressure compared to the surrounding atmosphere. When a column of waste water flows through a pipe, it compresses air ahead of it in the pipe, creating a "positive" pressure that must be released so it does not push back on the waste stream and downstream trap water seals. As the column of water passes, air must freely flow in behind the waste stream, or "negative" pressure results. The extent of these pressure fluctuations is determined by the fluid volume of the waste discharge.


title: Drain-waste-vent system

text: Excessive negative air pressure, behind a "slug" of water that is draining, can siphon water from traps at plumbing fixtures. Generally, a toilet outlet has the shortest trap seal, making it most vulnerable to being emptied by induced siphonage. An empty trap can allow noxious sewer gases to enter a building.


title: Drain-waste-vent system

text: On the other hand, if the air pressure within the drain becomes suddenly higher than ambient, this positive transient could cause waste water to be pushed into the fixture, breaking the trap seal, with serious hygiene and health consequences if too forceful. Tall buildings of three or more stories are particularly susceptible to this problem. Vent stacks are installed in parallel to waste stacks to allow proper venting in tall buildings and eliminate these problems.


title: Drain-waste-vent system

text: Most residential building drainage systems in North America are vented directly through the building roofs. The DWV pipe is typically ABS or PVC DWV-rated plastic pipe equipped with a flashing at the roof penetration to prevent rainwater from entering the buildings. Older homes may use copper, iron, lead or clay pipes, in rough order of increasing antiquity.


title: Drain-waste-vent system

text: Under many older building codes, a vent stack (a pipe leading to the main roof vent) is required to be within approx. a radius of the draining fixture it serves (sink, toilet, shower stall, etc.). To allow only one vent stack, and thus one roof penetration as permitted by local building code, sub-vents may be tied together inside the building and exit via a common vent stack, frequently the "main" vent. One additional requirement for a vent stack connection occurs when there are very long horizontal drain runs with very little slope to the run. Adding a vent connection within the run will aid flow, and when used with a cleanout allows for better serviceability of the long run.


title: Drain-waste-vent system

text: A blocked vent is a relatively common problem caused by anything from leaves, to dead animals, to ice dams in very cold weather, or a horizontal section of the venting system, sloped the wrong way and filled with water from rain or condensation. Symptoms range from bubbles in the toilet bowl when it is flushed, to slow drainage, and all the way to siphoned (empty) traps which allow sewer gases to enter the building.


title: Drain-waste-vent system

text: When a fixture trap is venting properly, a "sucking" sound can often be heard as the fixture vigorously empties out during normal operation. This phenomenon is harmless, and is different from "trap suckout" induced by pressure variations caused by wastewater movement "elsewhere" in the system, which is not supposed to allow interactions from one fixture to another. Toilets are a special case, since they are usually designed to self-siphon to ensure complete evacuation of their contents; they are then automatically refilled by a special valve mechanism.


title: Drain-waste-vent system

text: Mechanical vents (also called cheater vents) come in two types: Air admittance valves and check vents, the latter being a vent with a check valve.


title: Drain-waste-vent system

text: Air admittance valves (AAVs, or commonly referred to in the UK as Durgo valves and in the US as Studor vents and Sure-Vent®) are negative-pressure-activated, one-way mechanical valves, used in a plumbing or drainage venting system to eliminate the need for conventional pipe venting and roof penetrations. A discharge of wastewater causes the AAV to open, releasing the vacuum and allowing air to enter the plumbing vent pipe for proper pressure equalization.


title: Drain-waste-vent system

text: Since AAVs will only operate under negative pressure situations, they are not suitable for all venting applications, such as venting a sump, where positive pressures are created when the sump fills. Also, where positive drainage pressures are found in larger buildings or multi-story buildings, an air admittance valve could be used in conjunction with a positive pressure reduction device such as the PAPA positive air pressure attenuator to provide a complete venting solution for more complicated drainage venting systems.


title: Drain-waste-vent system

text: Using AAVs can significantly reduce the amount of venting materials needed in a plumbing system, increase plumbing labor efficiency, allow greater flexibility in the layout of plumbing fixtures, and reduce long-term roof maintenance problems associated with conventional vent stack roofing penetrations.


title: Drain-waste-vent system

text: While some state and local building departments prohibit AAVs, the International Residential and International Plumbing Codes allow it to be used in place of a vent through the roof. AAVs are certified to reliably open and close a minimum of 500,000 times, (approximately 30 years of use) with no release of sewer gas; some manufacturers claim their units are tested for up to 1.5 million cycles, or at least 80 years of use. AAVs have been effectively used in Europe for more than two decades.


title: Drain-waste-vent system

text: An island fixture vent, sometimes colloquially called a "Chicago Loop", "Boston loop" or "Bow Vent", is an alternate way of venting the trap installed on an under counter island sink or other similar applications where a conventional vertical vent stack or air admittance valve is not feasible or allowed.


title: Drain-waste-vent system

text: As with all drains, ventilation must be provided to allow the flowing waste water to displace the sewer gas in the drain, and then to allow air (or some other fluid) to fill the vacuum which would otherwise form as the water flows down the pipe.


title: Drain-waste-vent system

text: An island fixture vent provides an elegant solution for this necessity: when the drain is opened, water displaces the sewer gas up to the sanitary tee, the water flows downward while sewer gas is displaced upward and toward the vent. The vent can also provide air to fill any vacuum created.


title: Drain-waste-vent system

text: The key to a functional island fixture vent is that the top elbow must be at least as high as the "flood level" (the peak possible drain water level in the sink). This is to ensure that the vent does not become a de facto drain should the actual drain get clogged.


title: Drain-waste-vent system

text: The cost of installation is high because of the number of elbows and small pieces of pipe required. The largest cost outlay with modern plastic drain pipes is labor. Use of street elbows is helpful.


title: Drain-waste-vent system

text: Alternately if moving sink to an island sink, install the P-trap below the floor of the island and vent off the top of the drain. Attach toward the trap and reverse 180 degrees so any water in the vent flows down the drain. Slope drain down, slope vent up, and attach to existing vent from previous existing fixture that is now abandoned. Patch previously existing drain to become vent. In Canada, the national plumbing code requires that the minimum trap arm be at least 2 times the pipe diameter, (e.g., 1.25 inch pipe needs a 2.5-inch trap arm, 1.5 pipe needs a 3-inch trap arm, etc.) and that the vent pipe be one size larger than the drain that it serves, also a cleanout is required on both the vent and the drain. The reason for this is in the event of a plugged sink, the waste water will back up and go down the vent, possibly plugging the vent (as it is under the countertop), and a clean-out would permit the cleaning of the pipes.


title: Drain-waste-vent system

text: All DWV systems require various sized fittings and pipes which are measured by their internal diameter of both the pipes and the fittings which, and in most cases are schedule 40 PVC wye's, tee's, elbows ranging from 90 degrees to 22.5 degrees for both inside diameter fitment (street) as well as outer diameter fitment (hub), repair and slip couplings, reducer couplings, and pipe which is typically ten feet in length. All DWV system fittings sizes are based on the inside diameter of the pipe that goes into the fittings. These are known as hub fittings. Sizes for hub fittings such as wye's and tee's and crosses are based on the inside diameter of the pipe that goes into the hub of the fittings. Items such as washer boxes and Studor vents are also measured by the internal diameter of the fittings.


title: Drain-waste-vent system

text: Schedule 40 PVC DWV systems are ideal for several different reasons and are replacing cast iron DWV systems in many municipalities in the US because of issues that cast iron systems present. Parts are no longer available for cast iron plumbing repairs or for installation due to being phased out for lighter and more sanitary materials.


title: Drain-waste-vent system

text: Since the advent of PVC and solvent weld adhesives, which is what holds the fittings together by melting the material into itself, along with the proper placement of support throughout the dwv system using strapping and jhooks as well as knowledge of boring holes in structural framing without comprising the integrity, a pvc dwv system can typically be installed by one individual experienced plumber as opposed to cast iron, which requires several people in order to install and remove.


title: Drain-waste-vent system

text: Most pvc dwv systems that replace cast iron systems require the complete removal of the cast iron in order to provide a proper functioning dwv system leaving only enough cast iron pipe (at the lowest point to the ground in which it tyes into the sewage) in order for a specialized rubber boot coupling, known as a fernco, to be installed in order to join the pvc system to waste drainage. A special fitting known as a test tee should immediately follow the installation of the fernco in order to adequately test the system to make sure no leaks are present and that adequate vent pressure is draining the waste water correctly.


title: Drain-waste-vent system

text: The means to properly test any dwv system is done with an inflatable apparatus known as a test ball which is placed in a test tee which should be located at the bottom most point of the system before going into the ground.


title: Crossing of cheques

text: A crossed cheque is a cheque that has been marked specifying an instruction on the way it is to be redeemed. A common instruction is for the cheque to be deposited directly to an account with a bank and not to be immediately cashed by the holder over the bank counter. The format and wording varies between countries, but generally, two parallel lines may be placed either vertically across the cheque or on the top left hand corner of the cheque. By using crossed cheques, cheque writers can effectively protect the instrument from being stolen or cashed by unauthorized persons.


title: Crossing of cheques

text: A crossed cheque generally is a cheque that only bears two parallel transverse lines, optionally with the words 'and company' or '& Co.' (or any abbreviation of them) on the face of the cheque, between the lines, usually at the top left corner or at any place in the approximate half (in width) of the cheque. In the UK, the crossing is across the cheque by the person who originally wrote the cheque (the drawer), or it can legitimately be added by the person the cheque is payable to (the payee), or even by the bank that the cheque is being paid into.


title: Crossing of cheques

text: Generally-crossed cheques can only be paid into a bank account, so that the beneficiary can be traced.


title: Crossing of cheques

text: Adding a crossing to a cheque increases its security in that it cannot be cashed at a bank counter but must be paid into an account in exactly the same name as the payee or indorsee indicated on the check.


title: Crossing of cheques

text: The words 'not negotiable' can be added to a crossing. The effect of such a crossing is that it removes the most important characteristic of a negotiable instrument (according to section 123).


title: Crossing of cheques

text: Where some customary instruction is written between the two parallel transverse lines (constituting crossing of cheque) that may result in imposing certain restrictions on the collecting or paying banker, it is called restrictive crossing.


title: Crossing of cheques

text: A crossing may have the name of a specific banker added between the lines. A cheque with such a crossing can only be paid into an account at that bank.


title: Crossing of cheques

text: The beneficiary bank can add an additional crossing to allow another bank, who are acting as their agent in collecting payment on cheques, to be paid the cheque on their behalf.


title: Crossing of cheques

text: The example is "State Bank of India". In these cases, the respective restrictions mandate to pay the cheque through State Bank of India (acting as collecting banker) only.


title: Crossing of cheques

text: A bank's failure to comply with the crossings amounts to a breach of contract with its customer. The bank may not be able to debit the drawer's account and may be liable to the true owner for his loss.


title: Platform for Life and Peace

text: Platform for Life and Peace (; PZZhM/ПЗЖМ or PLP) is a parliamentary group in Ukraine created after the ban on the Opposition Platform — For Life and the dissolution of the parliamentary group of the same name following the 2022 Russian invasion of Ukraine.


title: Platform for Life and Peace

text: The group explicitly announced that it did not include Viktor Medvedchuk, Vadym Rabinovych, Vadym Stolar, and their supporters, who had belonged to the prior Opposition Platform — For Life party. Some of these politicians had left Ukraine before the invasion started, or are perceived as proxies for Russia within Ukraine.


title: Platform for Life and Peace

text: According to Yuriy Boyko, the group contains "deputies willing to work for protecting Ukraine, helping the people, and rebuilding our country".


title: Give My Regards to Broad Street (film)

text: Give My Regards to Broad Street is a 1984 British musical drama film directed by Peter Webb. It stars Paul McCartney, Bryan Brown and Ringo Starr. The film covers a fictional day in the life of McCartney, who wrote the film for the screen, and McCartney, Starr and Linda McCartney all appeared as themselves. Despite "Give My Regards to Broad Street" being unsuccessful, both financially and critically, its soundtrack album sold well. The title is a take on George M. Cohan's classic show tune "Give My Regards to Broadway" and makes reference to London's Broad Street railway station, which would close in 1986.


title: Give My Regards to Broad Street (film)

text: Filming and recording of "Broad Street" began in November 1982, after the completion of "Pipes of Peace". Production on the album and film continued until July the following year. In the interim, "Pipes of Peace" and its singles were released, and the film project was thus scheduled for an autumn 1984 release once an appropriate amount of time had passed.


title: Give My Regards to Broad Street (film)

text: Paul (Paul McCartney) is stuck in a traffic jam in his chauffeur-driven car on his way to an interview. He daydreams that he is driving himself in a flashier car crammed with modern technology around the countryside when he gets a call from Steve (Bryan Brown) that Harry (Ian Hastings), a reformed criminal, is missing along with the master tapes he was supposed to give to the factory the previous day. Paul races to the studio to find that the police are already there investigating the matter, thinking that Harry is back to his old ways and plans to bootleg the tapes. The news gets worse when Mr. Rath (John Bennett), to whom the studio owes money, arrives with the news that he will take over the record company if the tapes aren't found by midnight.


title: Give My Regards to Broad Street (film)

text: Following the meeting, the film follows a day in the life of Paul and his work with wife Linda McCartney and friend Ringo Starr, which includes filming two videos, rehearsing in a loft, and recording performances for the radio. In between this, Paul wonders what Harry might have done: did he give the master tapes to be bootlegged, did he just run off, or was he murdered? During several songs, Paul has elaborate fantasies in various settings and costumes inspired by his predicament. Once the day is done, Paul goes out driving around London while his associates brace themselves for the takeover as midnight approaches. While driving towards Broad Street, Paul remembers that Harry was headed there when he last saw him and goes exploring the station. Eventually, he finds the blue case containing the tapes on a platform bench, and Harry in a small maintenance building nearby, where he had accidentally trapped himself looking for the toilet. They both laugh, and as they drive off, Paul informs Linda, and Linda informs the studio at the last minute, that the tapes have been found and the takeover is averted. Paul's chauffeur-driven car finally arrives at its destination and he is awoken from his slumber.


title: Give My Regards to Broad Street (film)

text: The film was the result of a long-held ambition of McCartney, a lifelong film fan, to become involved in acting again after his success with the Beatles' films.


title: Give My Regards to Broad Street (film)

text: While "Give My Regards to Broad Street" was occasionally described in the press as McCartney's first film in 14 years, this was not in fact the case, as "Rockshow" had been released 4 years before, though it was mainly made up of Wings' concert footage.


title: Give My Regards to Broad Street (film)

text: "Broad Street" was one of the last film appearances of Sir Ralph Richardson, who plays an older man named Jim that McCartney visits late in the movie, looking for Harry. Some critics have pointed out Jim's similarity to McCartney's father (who was also named James; Richardson's character even refers to McCartney as "son") and appears to be something of a poet—the elder McCartney had his own jazz band in the 1940s. (McCartney has said that he actually based the character on Polonius, from William Shakespeare's "Hamlet".)


title: Give My Regards to Broad Street (film)

text: The 13-minute animated film "Rupert and the Frog Song" was shown in cinemas immediately preceding "Give My Regards to Broad Street". The short film contained the song "We All Stand Together", sung by McCartney and "the Frog Chorus". Simultaneously with the film's premiere in November, "We All Stand Together" was released as a single and became a hit in the UK, reaching #3.


title: Give My Regards to Broad Street (film)

text: A video game based on the film was released for the Commodore 64 and Sinclair ZX Spectrum home computers in 1985. The game was developed by Argus Press Software and released in their Mind Games series. The C64 version was also published by Mastertronic in the US (Cat. no. ICD-0082).


title: Give My Regards to Broad Street (film)

text: The game takes place after the action of the film and it is discovered that one track from the album was missing from the recovered tapes. The missing track was also going to be the lead single so without it, the studio is back in jeopardy. The player takes the role of McCartney who must travel around London to track down members of the band and other people who were at the original studio session to help piece the track back together. The game package contained a fold out map of London and profiles of the characters which the player needs to use to predict where to find them.


title: Give My Regards to Broad Street (film)

text: Although its soundtrack was a success, the film itself was met with negative reviews. It received a 21% positive rating on Rotten Tomatoes, based on reviews by 14 critics.


title: Give My Regards to Broad Street (film)

text: Roger Ebert of the "Chicago Sun-Times" gave the film one out of four stars, praising its music as "wonderful" but said it "is about as close as you can get to a nonmovie, and the parts that do try something are the worst." He particularly criticized the long and irrelevant dream sequences and the poor photography, and advised readers to buy the soundtrack album and not bother seeing the film itself.


title: Give My Regards to Broad Street (film)

text: "No More Lonely Nights", a song from the film, was nominated for a Golden Globe Award and a BAFTA Film Award for Best Original Song-Motion Picture.


title: Canoeing

text: Canoeing is an activity which involves paddling a canoe with a single-bladed paddle. Common meanings of the term are limited to when the canoeing is the central purpose of the activity. Broader meanings include when it is combined with other activities such as canoe camping, or where canoeing is merely a transportation method used to accomplish other activities. Most present-day canoeing is done as or as a part of a sport or recreational activity. In some parts of Europe canoeing refers to both canoeing and kayaking, with a canoe being called an "open canoe".


title: Canoeing

text: A few of the recreational forms of canoeing are canoe camping and canoe racing. Other forms include a wide range of canoeing on lakes, rivers, oceans, ponds and streams.


title: Canoeing

text: Canoeing is an ancient mode of transportation. Modern recreational canoeing was established in the late 19th century. In 1924, canoeing associations from Austria, Germany, Denmark and Sweden founded the "Internationalen Representation for Kanusport", forerunner of the International Canoe Federation. Canoeing became part of the Olympic Games in the summer of 1936. The main form of competitive sport was canoe sprint using a sprint canoe. Others include canoe polo, whitewater canoeing, canoe marathon, ICF canoe marathon, and playboating.


title: Canoeing

text: Most present-day canoeing is done as or as a part of a sport or recreational activity. In some parts of Europe, canoeing refers to both canoeing and kayaking, with a canoe being called an "Open canoe". A few of the recreational forms of canoeing are canoe camping and canoe racing such as canoe sprint and canoe marathons. Other forms include a wide range of canoeing on lakes, rivers, oceans, ponds and streams.


title: Canoeing

text: The summer Olympics include canoeing competitions. Canoe slalom (previously known as whitewater slalom) is a competitive sport with the aim to navigate a decked canoe or kayak through a course of hanging downstream or upstream gates on river rapids in the fastest time possible. It is one of the two kayak and canoeing disciplines at the Summer Olympics, and is referred to by the International Olympic Committee (IOC) as Canoe/Kayak Slalom. The other Olympic canoeing discipline is canoe sprint.


title: Canoeing

text: In his lifetime, according to the Guinness Book of World Records, Verlen Kruger paddled the most miles (over 100,000 miles) of anyone in the sport.


title: Bahun

text: Bahun () or Khas Brahmin () is a caste ("Varna") among Khas people of Nepal. Their origins are from the Indo-Aryan Khasa tribe of Nepal and South Asia. According to the 2011 Nepal census, Bahun is the second most populous group after Chhetri, another Varna within the hill Hindus in Nepal.


title: Bahun

text: According to 1854 "Muluki Ain" (Nepalese Legal Code), Bahuns were regarded as caste among sacred thread bearers (Tagadhari) and twice-born Hindus.


title: Bahun

text: Traditionally, Bahuns were members of the Khas community together with Chhetris and Hill Dalits. Possibly due to political power of the Khasa Malla kingdom, Khas Bahun and Khas Rajput (Chhetris) had high social status like plain Brahmins and Rajputs in the present-day western Nepal. Bahuns, regarded as upper class Khas group together with Chhetri, were associated mostly with the Gorkha Kingdom. Bahuns were original inhabitants of Karnali region of Nepal. The immigration of Brahmins into Nepal increased significantly from 1324 and continued up to 1769 due to the foreign invasion in the western portion of the Indian subcontinent.


title: Bahun

text: Bahuns were divided into two clans on the basis of residency. The Bahun residents east of Mahakali river were known as Purbiya Bahun and west of the river were known as Kumai Bahun. Kumai or Kumain is a direct derivative of Kumaoni, meaning residents of Kumaon.


title: Bahun

text: According to the 2011 Nepal census, Bahuns (referred as Hill-Brahmin) are the second most populous group after Chhetri with 12.2% of Nepal's population (or 32,26,903 people). Bahun are the second largest Hindu group with a population of 3,212,704 (99.6% of Bahuns). Bahuns are the largest group in 15 districts in Nepal: Jhapa, Morang, Kathmandu, Chitwan, Nawalparasi, Rupandehi, Kaski, Syangja, Parbat, Gulmi and Arghakhanchi. Among these, Bahuns in Parbat (35.7%), Arghakhanchi (32.8%), Syangja (30.9%), Chitwan (28.6%), Kaski (27.8%) and Gulmi (25.2%) consist more than 25% of the district population. Kathmandu has largest Bahun population with 410,126 people (23.5%).


title: Bahun

text: Bahuns have the highest civil service representation with 39.2% of Nepal's bureaucracy while having only 12.1% of Nepal's total population. The civil service representation to population ratio is 3.2 times for Bahuns which is fourth in Nepal. Chhetris represent 5.6 times in civil services to their percentage of population, which is the highest in Nepal. As per the Public Service Commission, Brahmins (33.3%) and Chhetris (20.01%) were two largest caste group to obtain governmental jobs in F.Y. 2017-18 even though 45% governmental seats are reserved for women, Madhesis, other caste and Tibetan tribes, people with disability and those from the backward regions. Similarly, in the fiscal 2018–19, Bahuns (34.87%) and Chhetris (19.63%) maintained 55% of their proportion in civil service as per Public Service Commission.


title: The Rubettes

text: The Rubettes are an English pop/glam rock band put together in 1974 after the release of "Sugar Baby Love", a recording assembled of studio session musicians in 1973 by the songwriting team of Wayne Bickerton, the then head of A&R at Polydor Records, and his co-songwriter, Tony Waddington, after their doo-wop and 1950s American pop-influenced songs had been rejected by a number of existing acts. Waddington paired the group with manager John Morris, the husband of singer Clodagh Rodgers and under his guidance, the band duly emerged at the tail end of the glam rock movement, wearing trademark white suits and cloth caps on stage. Their first release, "Sugar Baby Love" was an instant hit remaining at number one in the United Kingdom for four weeks in May 1974, while reaching number 37 on the US chart that August, and remains their best-known record. Subsequent releases were to be less successful, but the band continued to tour well into the 2000s with two line-ups in existence.


title: The Rubettes

text: The Rubettes' first and biggest hit was "Sugar Baby Love" (1974) which was a number one in the United Kingdom, going on to sell around 500,000 copies in the UK and three million copies globally. With three more songs, "Sugar Baby Love" was recorded for Polydor in October 1973 at Lansdowne Studios in Holland Park, London, by a group of session musicians featuring the distinctive falsetto and lead vocals of Paul Da Vinci (born: Paul Leonard Prewer). However, Da Vinci did not join the others to become a member of the band put together by John Richardson, and instead pursued solo work, having signed a contract with Penny Farthing Records. "Sugar Baby Love" was their only UK No. 1 and sole US Top 40 entry. In November 1974, "NME" music magazine reported that The Rubettes, The Glitter Band and Mud were among the UK bands who had roles in a new film titled "Never Too Young to Rock".


title: The Rubettes

text: The Rubettes, namely Alan Williams (whose vocals never appeared on the original 1973 recording of "Sugar Baby Love", but would front the group in 1974 and sing lead on all remaining songs), John Richardson, Pete Arnesen, Tony Thorpe, Mick Clarke and Bill Hurd, went on to have a number of other top ten hits across Europe during the mid-1970s, such as "Tonight", "Juke Box Jive" and "I Can Do It" sung by Alan Williams, mostly written by the Bickerton–Waddington songwriting team. The Rubettes' success encouraged Bickerton and Waddington to set up State Records, so that ten months after the release of "Sugar Baby Love", the fourth Rubettes single "I Can Do It" was on State (catalogue reference STAT 1). Two smaller hits, "Foe Dee Oh Dee" which made the Top 20 and "Little Darling", which unusually made the BBC Top 30 for only one week, followed on State records also sung by frontman Alan Williams.


title: The Rubettes

text: In 1976 the band abandoned glam nostalgia to enter more serious territory. "Under One Roof" (1976) sung by John Richardson was a portrayal of a gay man disowned and later murdered by his father; along with Rod Stewart's "The Killing of Georgie" (1976), it was one of the few songs that tackled the topic of homophobia. Their most successful self-composed hit was the country rock styled ballad "Baby I Know" (1977) sung by Tony Thorpe, which reached number 10 in the UK and Germany in 1977. During this period the band continued to cater for the much bigger European market by continuing to release the more commercial pop singles all featuring lead vocals by Alan Williams such as "Julia" (1976), "Allez Oop" (1976), and "Ooh La La" (1977). The band became a quintet in early 1975 with the departure of Arnesen, and later became a quartet in mid-1976 when Hurd departed the band; to this day the original band has never expanded its line-up beyond four members. Whilst the band continued as a four-piece; Hurd joined Suzi Quatro's band, touring and playing on a number of worldwide hits, which included the Top 20 success "She's in Love with You" in 1979, before re-joining the Rubettes in 1982.


title: The Rubettes

text: In another attempt to get away from the 'doo-wop' glam image, Thorpe insisted that the trademark vocal harmonies were left off of his composition, "You're the Reason Why". Gerry Shury and the band out-voted him. The version with no vocal backing has been available as a bootleg recording in certain parts of Europe. In 1979, Thorpe and the band separated over musical differences. Thorpe can be heard on lead vocals on the last "Still Unwinding" track, "Does It Gotta Be Rock 'N' Roll". His guitar parts and backing vocals remained. After Thorpe's departure, the group's success began to dwindle. The band replaced Thorpe with Bob Benham; but he departed shortly thereafter and the band dissolved in 1980.


title: The Rubettes

text: The band reformed in 1982, with a line-up consisting of Williams, Clark, Hurd, and drummer Alex Bines to exploit the German market for 1970s nostalgia. This line-up remained relatively stable until 1999, with the only line-up changes being the departure of Clark in 1987, to be replaced first by Steve Kinch and then by Trevor Holliday, before he returned to the fold in 1993. In 1994, the group's profile was raised by the inclusion of "Sugar Baby Love" in the hit movie "Muriel's Wedding". This song was also featured in the 2005 Neil Jordan film "Breakfast on Pluto" soundtrack, and in a Safe Sex commercial.


title: The Rubettes

text: In 2002, the group hit the headlines once more when, following an acrimonious split and legal action, the Rubettes became the latest in a long line of bands (including the Beach Boys and Spandau Ballet) to end up in the courts in a dispute over ownership of the band's name. The court ruled that both Williams and Hurd could tour as the Rubettes, as long as it was clear which member was fronting the band.


title: The Rubettes

text: All was well until 2005 when Williams and Hurd were back in court following an appearance by Hurd's band on the German television station ZDF, with Williams claiming Hurd had breached the terms of the original agreement. On 2 February 2006, a High Court judge found that Hurd and Williams had both been guilty of breaching the 2002 agreement. Costs of the trial were, however, awarded to Williams in view of the severity of Hurd's breaches. Hurd appealed against this decision, but on 3 November 2006 the Appeal Court in London ruled against him, awarding the costs of the appeal to Williams. Hurd has since gone bankrupt.


title: The Rubettes

text: On 28 March 2008, "Sugar Baby Love" was declared to be the most successful oldie of all time by the German television station RTL.


title: The Rubettes

text: In March 2012, Thorpe digitally released the "No Hits, No Jazz Collection" and performed at Darwen Library Theatre with a live eight-piece band for his '50th Anniversary 1-Gig-Tour'. It featured session musicians Iain Reddy, Liam Barber, Justin Randall and Greg Harper. "You're the Reason Why" was played.


title: The Rubettes

text: In 2000, Williams formed his version of the band along with Clarke, Richardson, and ex-Kinks keyboardist Mark Haley.


title: The Rubettes

text: In May and June 2008, The Rubettes were part of the 'Glitz Blitz & 70s Hitz' tour of the UK alongside Sweet and Showaddywaddy.


title: The Rubettes

text: On 21 September 2014, as part of the Rubettes' 40th anniversary, it was announced that Alan Williams, John Richardson and Mick Clarke would return to the Olympia in Paris, the same venue at which the Rubettes made their first appearance in France in 1974 when "Sugar Baby Love" topped the French and European charts.


title: The Rubettes

text: In early 2015, this version of The Rubettes underwent their first line-up change when Mark Haley departed the band and was replaced by Steve Etherington.


title: The Rubettes

text: On 15 April 2016, at 'Theatre Severn' in Shrewsbury, UK they embarked on their first ever solo theatre tour with 40 dates throughout the UK. then continuing on to the 'Arena Loire', Angers, France on 4 November 2016 the first of 60 appearances at major 'Zenith' venues in France and Belgium as part of the 'Age Tendre, Tournée des Idoles' Tour, cumulating at the 'Forest National' in Brussels, Belgium's biggest venue, on 17 February 2017. Their latest compilation album 'La Légende Continue' (CLCD003) was released to coincide with the tour 31 November 2016.


title: The Rubettes

text: The band broke up in February 2019. A new Rubettes was formed with the original members John Richardson, Mick Clarke and Steve Etherington (producer/arranger since 1995).


title: The Rubettes

text: Following the dissolution of the original band; Hurd formed his version of the group with longtime drummer Alex Bines, vocalist Paul Da Vinci (who had performed lead vocal on "Sugar Baby Love"), bassist Billy Hill, and guitarist Rufus Rufell. Da Vinci departed the band in 2006 and was replaced by George Bird, and guitarist Rufell leaving in 2009 and replace by Ian Pearce.


title: The Rubettes

text: In 2010, Bill Hurd's Rubettes covered the 1997 Thorpe composition "Where the Angels Fear to Tread" on their album "21st Century Rock 'n' Roll" on Angel Air Records.


title: The Rubettes

text: 2013 saw the beginning of the most turbulent period in the band's history, as line-up instability was common for the next two years. First Bines, Hill, and Pearce all left the band to be replaced by Paul Callaby (drums), Ray Frost (guitars), and John Sorrell (bass) respectively; leaving Hurd as the last remaining 'founding member' of his version of the group left in the band. Late 2013 saw Bird depart the band to be replaced by Yvan Silva. By mid-2013 the band underwent a major personnel upheaval again, as everyone other than Hurd departed the band. The line-up then solidified with the arrival of vocalist Ken Butler, drummer Martin Clapson, and guitarist Dave Harding; with Mike Steed joining them on bass (on loan from The Marmalade) for a few months. The current line-up was completed in late 2014 with the departure of Steed and the arrival of Chris Staines in the bassist role. The band line up has remained fairly settled since 2014 with the only changes following the death of Ken Butler in 2018 saw the appointment of John Summerton (ex Flintlock) on guitar and vocals, and the arrival of drummer Damian Fisher.


title: The Rubettes

text: Founding members John Richardson, Mick Clarke, and Steve Etherington decided to break away from Alan Williams, and formed the Rubettes featuring John, Mick, and Steve on 15 February 2019.


title: The Rubettes

text: The band signed with Sobel Nation Records (distributed by Warner Brothers) and released a single on 20 June 2019 entitled "Ya Lovin' Rocks".


title: The Rubettes

text: The band has their own radio station playing only music from John Richardson, Mick Clarke, and Steve Etherington. "Jukebox Jive Radio" is a licensed radio station located on the official website for the Rubettes ft. John, Mick & Steve at www.therealrubettes.com.


title: The Rubettes

text: In July 2022 Alan Williams and his company won a High Court trial for the ownership of The Rubettes name, against Mick Clarke, John Richardson and Steve Etherington. Sitting in the High Court in London, Judge Pat Treacy ruled for Williams and said: "The defendants' conduct amounts to a misrepresentation sufficient to engage the tort of passing off. The claimants have succeeded."


title: Ramanujan's sum

text: In number theory, Ramanujan's sum, usually denoted "c"("n"), is a function of two positive integer variables "q" and "n" defined by the formula


title: Ramanujan's sum

text: Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes.


title: Ramanujan's sum

text: For integers "a" and "b", formula_2 is read ""a" divides "b"" and means that there is an integer "c" such that formula_3 Similarly, formula_4 is read ""a" does not divide "b"". The summation symbol


title: Ramanujan's sum

text: These formulas come from the definition, Euler's formula formula_11 and elementary trigonometric identities.


title: Ramanujan's sum

text: is also a root. Therefore, since there are "q" of them, they are all of the roots. The numbers formula_15 where 1 ≤ "n" ≤ "q" are called the "q"-th roots of unity. is called a primitive "q"-th root of unity because the smallest value of "n" that makes formula_16 is "q". The other primitive "q"-th roots of unity are the numbers formula_17 where ("a", "q") = 1. Therefore, there are φ("q") primitive "q"-th roots of unity.


title: Ramanujan's sum

text: Thus, the Ramanujan sum "c"("n") is the sum of the "n"-th powers of the primitive "q"-th roots of unity.


title: Ramanujan's sum

text: It is easily shown from the definition that "c"("n") is multiplicative when considered as a function of "q" for a fixed value of "n": i.e.


title: Ramanujan's sum

text: From the definition (or Kluyver's formula) it is straightforward to prove that, if "p" is a prime number,


title: Ramanujan's sum

text: This is called von Sterneck's arithmetic function. The equivalence of it and Ramanujan's sum is due to Hölder.


title: Ramanujan's sum

text: For a fixed value of "q" the absolute value of the sequence formula_39 is bounded by φ("q"), and for a fixed value of "n" the absolute value of the sequence formula_40 is bounded by "n".


title: Ramanujan's sum

text: If "f"("n") is an arithmetic function (i.e. a complex-valued function of the integers or natural numbers), then a convergent infinite series of the form:


title: Ramanujan's sum

text: Ramanujan found expansions of some of the well-known functions of number theory. All of these results are proved in an "elementary" manner (i.e. only using formal manipulations of series and the simplest results about convergence).


title: Ramanujan's sum

text: The expansion of the zero function depends on a result from the analytic theory of prime numbers, namely that the series


title: Ramanujan's sum

text: σ("n") is the divisor function (i.e. the sum of the "k"-th powers of the divisors of "n", including 1 and "n"). σ("n"), the number of divisors of "n", is usually written "d"("n") and σ("n"), the sum of the divisors of "n", is usually written σ("n").


title: Ramanujan's sum

text: Euler's totient function φ("n") is the number of positive integers less than "n" and coprime to "n". Ramanujan defines a generalization of it, if


title: Ramanujan's sum

text: Von Mangoldt's function unless "n" = "p" is a power of a prime number, in which case it is the natural logarithm log "p".


title: Ramanujan's sum

text: "r"("n") is the number of way of representing "n" as the sum of 2"s" squares, counting different orders and signs as different (e.g., "r"(13) = 8, as 13 = (±2) + (±3) = (±3) + (±2).)


title: Ramanujan's sum

text: Ramanujan defines a function δ("n") and references a paper in which he proved that "r"("n") = δ("n") for "s" = 1, 2, 3, and 4. For "s" > 4 he shows that δ("n") is a good approximation to "r"("n").


title: Ramanujan's sum

text: formula_65 is the number of ways "n" can be represented as the sum of 2"s" triangular numbers (i.e. the numbers 1, 3 = 1 + 2, 6 = 1 + 2 + 3, 10 = 1 + 2 + 3 + 4, 15, ...; the "n"-th triangular number is given by the formula "n"("n" + 1)/2.)


title: Ramanujan's sum

text: The analysis here is similar to that for squares. Ramanujan refers to the same paper as he did for the squares, where he showed that there is a function formula_67 such that formula_68 for "s" = 1, 2, 3, and 4, and that for "s" > 4, formula_67 is a good approximation to formula_70


title: Tortious interference

text: Tortious interference, also known as intentional interference with contractual relations, in the common law of torts, occurs when one person intentionally damages someone else's contractual or business relationships with a third party, causing economic harm. As an example, someone could use blackmail to induce a contractor into breaking a contract; they could threaten a supplier to prevent them from supplying goods or services to another party; or they could obstruct someone's ability to honor a contract with a client by deliberately refusing to deliver necessary goods.


title: Tortious interference

text: A tort of negligent interference occurs when one party's negligence damages the contractual or business relationship between others, causing economic harm, such as, by blocking a waterway or causing a blackout that prevents the utility company from being able to uphold its existing contracts with consumers.


title: Tortious interference

text: Tortious interference with contract rights can occur when one party persuades another to breach its contract with a third party (e.g., using blackmail, threats, influence, etc.) or where someone knowingly interferes with a contractor's ability to perform his contractual obligations, preventing the client from receiving the services or goods promised (e.g., by refusing to deliver goods). The tortfeasor is the person who interferes with the contractual relationship between others. When a tortfeasor is aware of an existing contract and deliberately induces a breach by one of the contract holders, it is termed "tortious inducement of breach of contract."


title: Tortious interference

text: Tortious interference with business relationships occurs where the tortfeasor intentionally acts to prevent someone from successfully establishing or maintaining business relationships with others. This tort may occur when one party knowingly takes an action that causes a second party not to enter into a business relationship with a third party that otherwise would probably have occurred. An example is when a tortfeasor offers to sell a property to someone below market value knowing they were in the final stages of a sale with a third party pending the upcoming settlement date to formalize the sale writing. Such conduct is termed "tortious interference with a business expectancy".


title: Tortious interference

text: The above situations are actionable only if someone with actual knowledge of, and intent to interfere with, an existing contract or expectancy between other parties, acts improperly with malicious intent and actually interferes with the contract/expectancy, causing economic harm. Historically, there has not been actionable cause if the interference was merely . However, for some jurisdictions recognize such claims, although many do not. A tort of negligent interference occurs when one party's negligence damages the contractual or business relationship between others, causing economic harm, such as, by blocking a waterway or causing a blackout preventing the utility company from being able to uphold its existing contracts with consumers.


title: Tortious interference

text: An early—perhaps the earliest—instance of recognition of this tort occurred in "Garret v Taylor", 79 Eng. Rep. 485 (K.B. 1620). In that case, the defendant drove customers away from the plaintiff's quarry by threatening them with mayhem and also threatening to "vex [them] with suits." The King's Bench court said that “the defendant threatened violence to the extent of committing an assault upon ... customers of the plaintiff ... whereupon ‘they all desisted from buying.’’ The court therefore upheld a judgment for the plaintiff.


title: Tortious interference

text: In a similar case, "Tarleton v McGawley", 170 Eng. Rep. 153 (K.B. 1793), the defendant shot from its ship, "Othello", off the coast of Africa upon natives while "contriving and maliciously intending to hinder and deter the natives from trading with" plaintiff's rival trading ship, "Bannister". This action caused the natives (plaintiff's prospective customers) to flee the scene, depriving the plaintiff of their potential business. The King's Bench court held the conduct actionable. The defendant claimed, by way of justification, that the local native ruler had given it an exclusive franchise to trade with his subjects, but the court rejected this defense.


title: Tortious interference

text: The tort was described in the case of "Keeble v Hickeringill", (1707) 103 Eng. Rep. 1127, styled as a "trespass on the case". In that case, the defendant had used a shotgun to drive ducks away from a pond that the plaintiff had built for the purpose of capturing ducks. Thus, unlike the foregoing cases, here the actionable conduct was not directly driving the prospective customers away, but rather eliminating the subject matter of the prospective business. Although the ducks had not yet been captured, the Justice Holt wrote for the court that "where a violent or malicious act is done to a man's occupation, profession, or way of getting a livelihood, there an action lies in all cases." The court noted that the defendant would have the right to draw away ducks to a pond of his own, raising as a comparison a 1410 case in which the court deemed that no cause of action would lie where a schoolmaster opened a new school that drew students away from an old school.


title: Tortious interference

text: Wrongful interference: the unified theory which treated causing loss by unlawful means as an extension of the tort of inducing a breach of contract was abandoned; inducing breach of contract and causing loss by unlawful means were two separate torts.


title: Tortious interference

text: inducing a breach of contract was a tort of accessory liability, and an intention to cause a breach of contract was a necessary and sufficient requirement for liability; a person had to know that he was inducing a breach of contract and to intend to do; that a conscious decision not to inquire into the existence of a fact could be treated as knowledge for the purposes of the tort; that a person who knowingly induced a breach of contract as a means to an end had the necessary intent even if he was not motivated by malice but had acted with the motive of securing an economic advantage for himself; that, however, a breach of contract which was neither an end in itself nor a means to an end but was merely a foreseeable consequence of a person's acts did not give rise to liability; and that there could be no secondary liability without primary liability, and therefore a person could not be liable for inducing a breach of contract unless there had in fact been a breach by the contracting party.


title: Tortious interference

text: Causing loss by unlawful means: acts against a third party counted as unlawful means only if they were actionable by that third party if he had suffered loss; that unlawful means consisted of acts intended to cause loss to the claimant by interfering with the freedom of a third party in a way which was unlawful as against that third party and which was intended to cause loss to the claimant, but did not include acts which might be unlawful against a third party but which did not affect his freedom to deal with the claimant. Strict liability for conversion applied only to an interest in chattels and not to chooses in action; this was too radical to impose liability for pure economic loss on receivers who had been appointed and had acted in good faith. This also left open the position where they breached the duty of good faith.


title: Tortious interference

text: In the United Kingdom, a trade union encouraging or facilitating workers to take strike action commits tortious interference with the employees' contracts of employment, unless the action is conducted in accordance with Part V of the Trade Union and Labour Relations (Consolidation) Act 1992, as amended.


title: Tortious interference

text: Although the specific elements required to prove a claim of tortious interference vary from one jurisdiction to another, they typically include the following:


title: Tortious interference

text: The first element may, in employment-at-will jurisdictions, be held fulfilled in regards to a previously unterminated employer/employee relationship.


title: Tortious interference

text: In California, these are the elements of negligent interference with prospective economic advantage, which the plaintiff must establish:


title: Tortious interference

text: Some cases add that a defendant acts negligently only if "the defendant owes the plaintiff a duty of care."


title: Tortious interference

text: California and most jurisdictions hold that there is a privilege to compete for business. “Under the privilege of free competition, a competitor is free to divert business to himself as long as he uses fair and reasonable means. Thus, the plaintiff must present facts indicating the defendant’s interference is somehow wrongful—i.e., based on facts that take the defendant’s actions out of the realm of legitimate business transactions.” "[T]he competition privilege is defeated only where the defendant engages in unlawful or illegitimate means." "


title: Tortious interference

text: "Wrongful" in this context means “independently wrongful”—that is, "blameworthy" or " independently wrongful apart from the interference itself." This may be termed use of improper means. “Commonly included among improper means are actions which are independently actionable, violations of federal or state law or unethical business practices, e.g., violence, misrepresentation, unfounded litigation, defamation, trade libel or trade mark infringement.” Other examples of "wrongful conduct" are "fraud, misrepresentation, intimidation, coercion, obstruction or molestation of the rival or his servants or workmen."


title: Tortious interference

text: Typical legal damages for tortious interference include economic losses, if they can be proven with certainty, and mental distress. Additionally punitive damages may be awarded if malice on the part of the wrongdoer can be established.


title: Tortious interference

text: Equitable remedies may include injunctive relief in the form of a negative injunction that would be used to prevent the wrongdoer from benefiting from any contractual relationship that may arise out of the interference, i.e., the performance of a singer who was originally contracted with the plaintiff to perform at the same time.


title: Tortious interference

text: Tortious interference with an expected inheritance - One who, by fraud, duress or other tortious means intentionally prevents another from receiving from a third person an inheritance or gift that he would otherwise have received, is subject to liability to the other for loss of the inheritance or gift.


title: History of the Panama Canal

text: The idea of the Panama Canal dates back to 1513, when Vasco Núñez de Balboa first crossed the isthmus of Panama. The narrow land bridge between North and South America was a fine location to dig a water passage between the Atlantic and Pacific Oceans. The earliest European colonists recognized this, and several proposals for a canal were made.


title: History of the Panama Canal

text: By the late nineteenth century, technological advances and commercial pressure allowed construction to begin in earnest. Noted canal engineer Ferdinand de Lesseps led the initial attempt by France to build a sea-level canal. Beset by cost overruns due to the severe underestimation of the difficulties in excavating the rugged terrain, heavy personnel losses to tropical diseases, and political corruption in France surrounding the financing of the massive project, the canal was only partly completed.


title: History of the Panama Canal

text: Interest in a U.S.-led canal effort picked up as soon as France abandoned the project. Initially, the Panama site was politically unfavorable in the U.S. for a variety of reasons, including the taint of the failed French effort and the unfriendly attitude of the Colombian government (at the time, the owner of the land) towards the U.S. continuing the project. The U.S. first sought to construct a canal through Nicaragua instead.


title: History of the Panama Canal

text: French engineer and financier Philippe-Jean Bunau-Varilla played a key role in changing American attitudes. Bunau-Varilla had a large stake in the failed French canal company and stood to profit on his investment only if the Panama Canal was completed. Extensive lobbying of American lawmakers, coupled with his support of a nascent independence movement among the Panamanian people, led to a simultaneous revolution in Panama and the negotiation of the Hay–Bunau-Varilla Treaty which secured both independence for Panama and the right for the U.S. to lead a renewed effort to construct the canal. Colombia's response to the Panamanian independence movement was tempered by an American military presence; this is often cited as a classic example of the era of gunboat diplomacy.


title: History of the Panama Canal

text: American success hinged on two factors. First was converting the original French sea-level plan to a more realistic lock-controlled canal. The second was controlling the diseases which had decimated workers and management alike under the original French attempt. Initial chief engineer John Frank Stevens built much of the infrastructure necessary for later construction; slow progress on the canal itself led to his replacement by George Washington Goethals. Goethals oversaw the bulk of the excavation of the canal, including appointing Major David du Bose Gaillard to oversee the most daunting project, the Culebra Cut through the roughest terrain on the route. Almost as important as the engineering advances were the healthcare advances made during the construction, led by William C. Gorgas, an expert in controlling tropical diseases such as yellow fever and malaria. Gorgas was one of the first to recognize the role of mosquitoes in the spread of these diseases and, by focusing on controlling the mosquitoes, greatly improved worker conditions.


title: History of the Panama Canal

text: On 7 January 1914, the French crane boat "Alexandre La Valley" became the first to make the traverse, and on 1 April 1914 the construction was officially completed with the hand-over of the project from the construction company to the Canal Zone government. The outbreak of World War I caused the cancellation of any official "grand opening" celebration, but the canal officially opened to commercial traffic on 15 August 1914 with the transit of the "SS Ancon".


title: History of the Panama Canal

text: During World War II, the canal proved a vital part of American military strategy, allowing ships to transfer easily between the Atlantic and Pacific. Politically, the canal remained a territory of the United States until 1977, when the Torrijos–Carter Treaties began the process of transferring territorial control of the Panama Canal Zone to Panama, a process completed on 31 December 1999.


title: History of the Panama Canal

text: The Panama Canal continues to be a viable commercial venture and a vital link in world shipping, and is periodically upgraded. The Panama Canal expansion project started construction in 2007 and began commercial operation on 26 June 2016. The new locks allow the transit of larger Post-Panamax and New Panamax ships, which have greater cargo capacity than the original locks could accommodate.


title: History of the Panama Canal

text: The idea of a canal across Central America was revived during the early 19th century. In 1819, the Spanish government authorized the construction of a canal and the creation of a company to build it.


title: History of the Panama Canal

text: Although the project stalled for some time, a number of surveys were made between 1850 and 1875. They indicated that the two most-favorable routes were across Panama (then part of Colombia) and Nicaragua, with a third route across the Isthmus of Tehuantepec in Mexico another option. The Nicaraguan route was surveyed.


title: History of the Panama Canal

text: After the 1869 completion of the Suez Canal, France thought that an apparently similar project to connect the Atlantic and Pacific Oceans could be carried out with little difficulty. In 1876 a limited company, La Société Civile Internationale du Canal Interocéanique par l'isthme du Darien was created at the initiative of the Société de Géographie, dean of geography societies, to fill in gaps in the geographical knowledge of the Central American area for the purpose of building an interoceanic canal.


title: History of the Panama Canal

text: On March 20, 1878, the Société Civile obtained an exclusive 15 years concession from the Colombian government to build a canal across the isthmus of Panama, which at the time was a Department of Colombia; the waterway that would revert to the Colombian government after 99 years without compensation.


title: History of the Panama Canal

text: Ferdinand de Lesseps, who was in charge of the Suez Canal construction, headed the project. His enthusiastic leadership and his reputation as the man who had built the Suez Canal persuaded speculators and ordinary citizens to invest nearly $400 million in the project.


title: History of the Panama Canal

text: However, despite his previous success, Lesseps was not an engineer. The construction of the Suez Canal, essentially a ditch dug through a flat, sandy desert, presented few challenges. Although Central America's mountainous spine has a low point in Panama, it is still above sea level at its lowest crossing point. The sea-level canal proposed by de Lesseps would require a great deal of excavation through a variety of unstable rock, rather than Suez's sand.


title: History of the Panama Canal

text: Less-obvious barriers were the rivers crossing the canal, particularly the Chagres, which flows strongly during the rainy season. Since the water would be a hazard to shipping if it drained into the canal, a sea-level canal would require the river's diversion.


title: History of the Panama Canal

text: The most serious problem was tropical diseases, particularly malaria and yellow fever, whose methods of transmission were unknown at the time. The legs of hospital beds were placed in cans of water to keep insects from crawling up them, but the stagnant water was an ideal breeding place for mosquitoes (carriers of the diseases).


title: History of the Panama Canal

text: In May 1879, the Congrès International d'Etudes du Canal Interocéanique (International Congress for Study of an Interoceanic Canal), led by Lesseps, convened in Paris. Among the 136 delegates of 26 countries, 42 were engineers and made technical proposals before the congress. The others were speculators, politicians, and friends of Lesseps, for whom the purpose of this congress was only to launch fundraising by legitimizing Lesseps' own decision, based on the Lucien Bonaparte-Wyse and Armand Réclus plan, through a so-called international scientific approval, since he was convinced that a sea-level canal, dug through the mountainous spine of Central America, could be completed at least as easily as the Suez Canal.


title: History of the Panama Canal

text: In reality, only 19 engineers approved the chosen plan, and only 1 of those had visited Central America.


title: History of the Panama Canal

text: While the Americans abstained because of their own plan through Nicaragua, the five delegates from the French Society of Engineers all refused. Among them were Gustave Eiffel and Adolphe Godin de Lépinay, the general-secretary of the Société de Géographie, who was the only one to propose a lake-and-locks project. Designer in particular of the large gauge canal between Bordeaux and Narbonne, the road between Sétif and Bougie, and of the railway lines connecting Philippeville to Constantine, Algeria, Algiers to Constantine, Athens to Piraeus, he also supervised the construction of the rail link between Veracruz and Córdoba, Mexico, losing two-thirds of his workers to tropical disease.


title: History of the Panama Canal

text: Godin de Lépinay's plan was to build a dam across the Chagres River in Gatún, near the Atlantic, and another on the Rio Grande, near the Pacific, to create an artificial lake accessed by locks. Digging less and avoiding unsanitary work and the danger of flooding was his priority, with an estimated lower cost of $100,000,000 () and 50,000 lives saved, as mentioned in the motivation for his negative review. All was said. The bankruptcy of the Lesseps project is described clearly, without ambiguity. It will be technical and financial, as Godin de Lépinay had planned. Unfortunately, his innovative plan, the only profitable as said by the Americans engineers, received no serious attention from the congress. Had it been adopted, the Panama Canal might well have been completed by the French instead of by the United States.


title: History of the Panama Canal

text: Following the congress, the Compagnie Universelle du Canal Interocéanique de Panama, in charge of the construction, whose president was Lesseps, acquired the Wyse Concession from the Société Civile.


title: History of the Panama Canal

text: The engineering congress estimated the Lesseps project's cost at $214 million; on February 14, 1880, an engineering commission revised the estimate to $168.6 million. Lesseps reduced this estimate twice, with no apparent justification: on February 20 to $131.6 million and on March 1 to $120 million. The congress estimated seven or eight years as the time required to complete the canal; Lesseps reduced this estimate to six years (the Suez Canal required ten).


title: History of the Panama Canal

text: The proposed sea-level canal would have a uniform depth of , a bottom width of and a width at water level of about ; the excavation estimate was . A dam was proposed at Gamboa to control flooding of the Chagres River, with channels to drain water away from the canal. However, the Gamboa dam was later found impracticable and the Chagres River problem was left unsolved.


title: History of the Panama Canal

text: Construction of the canal began on January 1, 1881, with digging at Culebra beginning on January 22. A large labor force was assembled, numbering about 40,000 in 1888 (nine-tenths of whom were afro-Caribbean workers from the West Indies). Although the project attracted good, well-paid French engineers, retaining them was difficult due to disease. The death toll from 1881 to 1889 was estimated at over 22,000, of whom as many as 5,000 were French citizens.


title: History of the Panama Canal

text: By 1885 it had become clear to many that a sea-level canal was impractical, and an elevated canal with locks was preferable; de Lesseps resisted, and a lock canal plan was not adopted until October 1887. By this time increasing mortality rates, as well as financial and engineering problems coupled with frequent floods and mudslides, indicated that the project was in serious trouble. Work continued under the new plan until May 15, 1889, when the company went bankrupt and the project was suspended. After eight years the canal was about two-fifths completed, and about $234.8 million had been spent.


title: History of the Panama Canal

text: The company's collapse was a scandal in France, and the antisemitic Edouard Drumont exploited the role of two Jewish speculators in the affair. One hundred and four legislators were found to have been involved in the corruption, and Jean Jaurès was commissioned by the French parliament to conduct an inquiry which was completed in 1893.


title: History of the Panama Canal

text: It soon became clear that the only way to recoup expenses for the stockholders was to continue the project. A new concession was obtained from Colombia, and in 1894 the Compagnie Nouvelle du Canal de Panama was created to finish the canal. To comply with the terms of the contract, work began immediately on the Culebra excavation while a team of engineers began a comprehensive study of the project. They eventually settled on a plan for a two-level, lock-based canal.


title: History of the Panama Canal

text: The new effort never gained traction, mainly because of US speculation that a canal through Nicaragua would render one through Panama useless. The most men employed on the new project was 3,600 (in 1896), primarily to comply with the terms of the concession and to maintain the existing excavation and equipment in saleable condition. The company had already begun looking for a buyer, with an asking price of $109 million.


title: History of the Panama Canal

text: In the US, a congressional Isthmian Canal Commission was established in 1899 to examine possibilities for a Central American canal and recommend a route. In November 1901, the commission reported that a US canal should be built through Nicaragua unless the French were willing to sell their holdings for $40 million. The recommendation became law on June 28, 1902, and the New Panama Canal Company was compelled to sell at that price.


title: History of the Panama Canal

text: Although the French effort was effectively doomed to failure from the beginning due to disease and a lack of understanding of the engineering difficulties, it was not entirely futile. The old and new companies excavated of material, of which was taken from the Culebra Cut. The old company dredged a channel from Panama Bay to the port at Balboa, and the channel dredged on the Atlantic side (known as the French canal) was useful for bringing in sand and stone for the locks and spillway concrete at Gatún.


title: History of the Panama Canal

text: Detailed surveys and studies (particularly those carried out by the new canal company) and machinery, including railroad equipment and vehicles, aided the later American effort. The French lowered the summit of the Culebra Cut along the canal route by , from . An estimated of excavation, valued at about $25.4 million, and equipment and surveys valued at about $17.4 million were usable by the Americans.


title: History of the Panama Canal

text: The 1848 discovery of gold in California and the rush of would-be miners stimulated US interest in building a canal between the oceans. In 1887, a United States Army Corps of Engineers regiment surveyed canal possibilities in Nicaragua. Two years later, the Maritime Canal Company was asked to begin a canal in the area and chose Nicaragua. The company lost money in the panic of 1893, and its work in Nicaragua ceased. In 1897 and 1899, the United States Congress charged a canal commission with researching possible construction; Nicaragua was chosen as the location both times.


title: History of the Panama Canal

text: Although the Nicaraguan canal proposal was made redundant by the American takeover of the French Panama Canal project, increases in shipping volume and ship sizes have revived interest in the project. A canal across Nicaragua accommodating post-Panamax ships or a rail link carrying containers between ports on either coast have been proposed.


title: History of the Panama Canal

text: Theodore Roosevelt believed that a US-controlled canal across Central America was a vital strategic interest of the country. This idea gained wide circulation after the destruction of the USS "Maine" in Cuba on February 15, 1898. Reversing a Walker Commission decision in favor of a Nicaraguan canal, Roosevelt encouraged the acquisition of the French Panama Canal effort. George S. Morison was the only commission member who argued for the Panama location. The purchase of the French-held land for $40 million was authorized by the June 28, 1902 Spooner Act. Since Panama was then part of Colombia, Roosevelt began negotiating with that country to obtain the necessary rights. In early 1903 the Hay–Herrán Treaty was signed by both nations, but the Senate of Colombia failed to ratify the treaty.


title: History of the Panama Canal

text: Roosevelt implied to Panamanian rebels that if they revolted, the US Navy would assist their fight for independence. Panama declared its independence on November 3, 1903, and the USS "Nashville" impeded Colombian interference. The victorious Panamanians gave the United States control of the Panama Canal Zone on February 23, 1904, for $10 million in accordance with the November 18, 1903 Hay–Bunau-Varilla Treaty.


title: History of the Panama Canal

text: The United States took control of the French property connected to the canal on May 4, 1904, when Lieutenant Jatara Oneel of the United States Army was presented with the keys during a small ceremony. The new Panama Canal Zone Control was overseen by the Isthmian Canal Commission (ICC) during construction.


title: History of the Panama Canal

text: The first step taken by the US government was to place all the canal workers under the new administration. The operation was maintained at minimum strength to comply with the canal concession and keep the machinery in working order. The US inherited a small workforce and an assortment of buildings, infrastructure and equipment, much of which had been neglected for fifteen years in the humid jungle environment. There were no facilities in place for a large workforce, and the infrastructure was crumbling.


title: History of the Panama Canal

text: Cataloguing assets was a large job; it took many weeks to card-index available equipment. About 2,150 buildings had been acquired, many of which were uninhabitable; housing was an early problem, and the Panama Railway was in a state of decay. However, much equipment (such as locomotives, dredges and other floating equipment) was still serviceable.


title: History of the Panama Canal

text: Although chief engineer John Findley Wallace was pressured to resume construction, red tape from Washington stifled his efforts to obtain heavy equipment and caused friction between Wallace and the ICC. He and chief sanitary officer William C. Gorgas were frustrated by delay, and Wallace resigned in 1905. He was replaced by John Frank Stevens, who arrived on July 26, 1905. Stevens quickly realized that serious investment in infrastructure was necessary and determined to upgrade the railway, improve sanitation in Panama City and Colón, renovate the old French buildings and build hundreds of new ones for housing. He then began the difficult task of recruiting the large labor force required for construction. Stevens' approach was to press ahead first and obtain approval later. He improved drilling and dirt-removal equipment at the Culebra Cut for greater efficiency, revising the inadequate provisions in place for soil disposal.


title: History of the Panama Canal

text: No decision had been made about whether the canal should be a lock or a sea-level one; the ongoing excavation would be useful in either case. In late 1905, President Roosevelt sent a team of engineers to Panama to investigate the relative merits of both types in cost and time. Although the engineers voted eight to five in favor of a sea-level canal, Stevens and the ICC opposed the plan; Stevens' report to Roosevelt was instrumental in convincing the president of the merits of a lock canal and Congress concurred. In November 1906 Roosevelt visited Panama to inspect the canal's progress, the first trip outside the United States by a sitting president.


title: History of the Panama Canal

text: Whether contract employees or government workers would build the canal was controversial. Bids for the canal's construction were opened in January 1907, and Knoxville, Tennessee-based contractor William J. Oliver was the low bidder. Stevens disliked Oliver, and vehemently opposed his choice. Although Roosevelt initially favored the use of a contractor, he eventually decided that army engineers should carry out the work and appointed Major George Washington Goethals as chief engineer (under Stevens' direction) in February 1907. Stevens, frustrated by government inaction and the army involvement, resigned and was replaced by Goethals.


title: History of the Panama Canal

text: The US relied on a stratified workforce to build the canal. High-level engineering jobs, clerical positions, skilled labor and jobs in supporting industries were generally reserved for Americans, with manual labor primarily by cheap immigrant labor. These jobs were initially filled by Europeans, primarily from Spain, Italy and Greece, many of whom were radical and militant due to political turmoil in Europe. The US then decided to recruit primarily from the British and French West Indies, and these workers provided most of the manual labor on the canal.


title: History of the Panama Canal

text: The Canal Zone originally had minimal facilities for entertainment and relaxation for the canal workers apart from saloons; as a result, alcohol abuse was a great problem. The inhospitable conditions resulted in many American workers returning home each year.


title: History of the Panama Canal

text: A program of improvements was implemented. Clubhouses were built, managed by the YMCA, with billiard, assembly and reading rooms, bowling alleys, darkrooms for camera clubs, gymnastic equipment, ice cream parlors, soda fountains and a circulating library. Member dues were ten dollars a year, with the remaining upkeep (about $7,000 at the larger clubhouses) paid by the ICC. The commission built baseball fields and arranged rail transportation to games; a competitive league soon developed. Semi-monthly Saturday-night dances were held at the Hotel Tivoli, which had a spacious ballroom.


title: History of the Panama Canal

text: These measures influenced life in the Canal Zone; alcohol abuse fell, with saloon business declining by 60 percent. The number of workers leaving the project each year dropped significantly.


title: History of the Panama Canal

text: The work done thus far was preparation, rather than construction. By the time Goethals took over, the construction infrastructure had been created or overhauled and expanded from the French effort and he was soon able to begin construction in earnest.


title: History of the Panama Canal

text: Goethals divided the project into three divisions: Atlantic, Central and Pacific. The Atlantic Division, under Major William L. Sibert, was responsible for construction of the breakwater at the entrance to Limon Bay, the Gatún locks and their approach channel, and the Gatun Dam. The Pacific Division (under Sydney B. Williamson, the only civilian division head) was responsible for the Pacific entrance to the canal, including a breakwater in Panama Bay, the approach channel, and the Miraflores and Pedro Miguel locks and their associated dams. The Central Division, under Major David du Bose Gaillard, was responsible for everything in between. It had arguably the project's greatest challenge: excavating the Culebra Cut (known as the Gaillard Cut from 1915 to 2000), which involved cutting through the continental divide down to above sea level.


title: History of the Panama Canal

text: By August 1907, 765,000 m³ (1,000,000 cubic yards) per month was being excavated; this set a record for the rainy season; soon afterwards this doubled, before increasing again. At the peak of production, 2,300,000 m³ (3,000,000 cubic yards) were being excavated per month (the equivalent amount of spoil from the Channel Tunnel every 3½ months).


title: History of the Panama Canal

text: One of the greatest barriers to a canal was the continental divide, which originally rose to above sea level at its highest point. The effort to cut through this barrier of rock was one of the greatest challenges faced by the project.


title: History of the Panama Canal

text: Goethals arrived at the canal with Major David du Bose Gaillard of the US Army Corps of Engineers. Gaillard was placed in charge of the canal's Central Division, which stretched from the Pedro Miguel locks to the Gatun Dam, and dedicated himself to getting the Culebra Cut (as it was then known) excavated.


title: History of the Panama Canal

text: The scale of the work was massive. Six thousand men worked in the cut, drilling holes in which a total of of dynamite were placed to break up the rock (which was then removed by as many as 160 trains per day). Landslides were frequent, due to the oxidation and weakening of the rock's underlying iron strata. Although the scale of the job and the frequent, unpredictable slides generated chaos, Gaillard provided quiet, clear-sighted leadership.


title: History of the Panama Canal

text: On May 20, 1913, Bucyrus steam shovels made a passage through the Culebra Cut at the level of the canal bottom. The French effort had reduced the summit to over a relatively narrow width; the Americans had lowered this to above sea level over a greater width, and had excavated over of material. About of this material was in addition to the planned excavation, due to landslides. Dry excavation ended on September 10, 1913; a January slide had added of earth, but it was decided that this loose material would be removed by dredging when the cut was flooded.


title: History of the Panama Canal

text: Two artificial lakes are key parts of the canal: Gatun and Miraflores Lakes. Four dams were constructed to create them. Two small dams at Miraflores impound Miraflores Lake, and a dam at Pedro Miguel encloses the south end of the Culebra Cut (essentially an arm of Lake Gatun). The Gatun Dam is the main dam blocking the original course of the Chagres River, creating Gatun Lake.