Slide rule

The slide rule known colloquially in the United States as a slipstick, is a mechanical analog computer. As graphical analog calculators, slide rules are related to nomograms, but the former are used for general calculations, whereas the latter are used for application-specific computations; the slide rule is used for multiplication and division, for functions such as exponents, roots and trigonometry, but not for addition or subtraction. Though similar in name and appearance to a standard ruler, the slide rule is not meant to be used for measuring length or drawing straight lines. Slide rules exist in a diverse range of styles and appear in a linear or circular form with a standardized set of markings essential to performing mathematical computations. Slide rules manufactured for specialized fields such as aviation or finance feature additional scales that aid in calculations particular to those fields. At its simplest, each number to be multiplied is represented by a length on a sliding ruler.

As the rulers each have a logarithmic scale, it is possible to align them to read the sum of the logarithms, hence calculate the product of the two numbers. The Reverend William Oughtred and others developed the slide rule in the 17th century based on the emerging work on logarithms by John Napier. Before the advent of the electronic calculator, it was the most used calculation tool in science and engineering; the use of slide rules continued to grow through the 1950s and 1960s as computers were being introduced. In its most basic form, the slide rule uses two logarithmic scales to allow rapid multiplication and division of numbers; these common operations can be error-prone when done on paper. More elaborate slide rules allow other calculations, such as square roots, exponentials and trigonometric functions. Scales may be grouped in decades, which are numbers ranging from 1 to 10, thus single decade scales C and D range from 1 to 10 across the entire width of the slide rule while double decade scales A and B range from 1 to 100 over the width of the slide rule.

In general, mathematical calculations are performed by aligning a mark on the sliding central strip with a mark on one of the fixed strips, observing the relative positions of other marks on the strips. Numbers aligned with the marks give the approximate value of the product, quotient, or other calculated result; the user determines the location of the decimal point in the result, based on mental estimation. Scientific notation is used to track the decimal point in more formal calculations. Addition and subtraction steps in a calculation are done mentally or on paper, not on the slide rule. Most slide rules consist of three linear strips of the same length, aligned in parallel and interlocked so that the central strip can be moved lengthwise relative to the other two; the outer two strips are fixed. Some slide rules have scales on both sides of the rule and slide strip, others on one side of the outer strips and both sides of the slide strip, still others on one side only. A sliding cursor with a vertical alignment line is used to find corresponding points on scales that are not adjacent to each other or, in duplex models, are on the other side of the rule.

The cursor can record an intermediate result on any of the scales. A logarithm transforms the operations of multiplication and division to addition and subtraction according to the rules log ⁡ = log ⁡ + log ⁡ and log ⁡ = log ⁡ − log ⁡. Moving the top scale to the right by a distance of log ⁡, by matching the beginning of the top scale with the label x on the bottom, aligns each number y, at position log ⁡ on the top scale, with the number at position log ⁡ + log ⁡ on the bottom scale; because log ⁡ + log ⁡ = log ⁡, this position on the bottom scale gives x y, the product of x and y. For example, to calculate 3×2, the 1 on the top scale is moved to the 2 on the bottom scale; the answer, 6, is read off the bottom scale. In general, the 1 on the top is moved to a factor on the bottom, the answer is read off the bottom where the other factor is on the top; this works because the distances from the "1" are proportional to the logarithms of the marked values: Operations may go "off the scale.

2008 Turkish Grand Prix

The 2008 Turkish Grand Prix was a Formula One motor race held on 11 May 2008 at the Istanbul Racing Circuit, Turkey. It was the fifth race of the 2008 Formula One season; the 58-lap race was won by Felipe Massa for the Ferrari team after starting from pole position. Lewis Hamilton finished second with Kimi Räikkönen third in the second Ferrari. Massa claimed pole, with teammate Räikkönen fourth, the two Ferrari cars sandwiching the McLarens of Heikki Kovalainen and Hamilton. At the first corner Räikkönen gave him a puncture; the safety car only remained out for one lap. During the course of the race, intending to make one more pit stop than both Ferrari drivers, was faster than Massa due to carrying a lighter fuel load and overtook him on lap 24. After Hamilton had made his third pit stop, he rejoined in second behind Massa but in front of the Championship leader, Räikkönen. Massa won the race, with Hamilton 3.779 seconds behind, Räikkönen a further half-second behind. The two BMW Sauber cars of Robert Kubica and Nick Heidfeld took fifth.

In the week running up to the grand prix, the Super Aguri team had withdrawn from Formula One, due to financial problems, leaving the sport with only ten teams. Massa's victory was his third consecutive pole position and victory in Turkey, having won the race from pole in 2006 and 2007. Rubens Barrichello celebrated his 257th Grand Prix start, breaking Riccardo Patrese's previous record of 256. Due to the race result, Räikkönen's lead in the Drivers' Championship was lowered to seven points. Massa rose to second from fourth, whilst Hamilton dropped to third, both drivers tying on 28 points but separated by Massa's two wins thus far to Hamilton's one. In the Constructors' Championship, Ferrari increased their lead to 22 points ahead of BMW Sauber, with McLaren a further two points behind in third; the Grand Prix was contested in ten teams of two. The teams known as "constructors", were Ferrari, BMW Sauber, Williams, Red Bull Racing, Toro Rosso, Force India and McLaren; this was two drivers fewer than in previous rounds of the 2008 season, due to the withdrawal of the Super Aguri team from the sport following the previous race.

Going into the race, Kimi Räikkönen was leading the Drivers' Championship, on 29 points. BMW Sauber drivers Robert Kubica and Nick Heidfeld were third and fifth, on 19 and 16 points respectively. In the Constructors' Championship Ferrari were leading on 47 points; the race was Rubens Barrichello's 257th Grand Prix, which broke the record for the number of Grand Prix starts held by Riccardo Patrese. The particular Grand Prix at which he broke this record was disputed, as there was some disagreement about what constituted a "start", such as the 2002 Spanish Grand Prix, where Barrichello entered but did not take part in the race on Sunday. Barrichello and Honda decided to make Turkey the site for their celebrations, issuing a statement that said, "In view of the lack of consensus regarding which specific race marks Rubens's 257th Grand Prix, Rubens will celebrate the milestone of 257 Grand Prix appearances at the Turkish Grand Prix", his Honda team gave him a special anniversary livery and helmet, both of which prominently featured the number 257.

Patrese said. The Super Aguri team had been in financial trouble since a proposed takeover deal backed by equity firm Dubai International Capital, under the "Magma Group" banner, failed to take effect. Early in the week before the Grand Prix, after team owner Aguri Suzuki revealed the extent of his difficulties, the team's trucks were blocked from entering the paddock by the Fédération Internationale de l'Automobile, Formula One's governing body; this decision was taken by the FIA after being informed by Honda's Formula One team CEO, Nick Fry, that Super Aguri, who used Honda engines and Honda-derived chassis, would not be racing at Istanbul Park. Suzuki admitted that his financial troubles could not be solved by existing primary sponsor SS United Group Oil & Gas Company, leaving the team with no choice but to withdraw from Formula One as of May 6. Super Aguri had competed in Formula One since the 2006 Bahrain Grand Prix. After scoring its first championship points after 22 race starts at the 2007 Spanish Grand Prix, the team finished ninth overall in the 2007 Constructors' Championship.

The Toro Rosso team's plan to introduce its new car, the STR3, at this race were postponed due to a lack of spare parts. This was due to an accident suffered by driver Sébastien Bourdais during testing prior to the previous race, which had resulted in the chassis sustaining heavy damage. Toro Rosso had used an updated version of its 2007 car, the STR2, for the first four races of the season, were now forced to race with it in Turkey as well; the team's other driver, Sebastian Vettel, said that he was "disappointed" that the new car was not ready. However, this was the last race in which the STR2 competed, as the STR3 subsequently made its début at the next race. Ferrari decided not to use a new nose for their car that had made its début at the previous race due to the low-downforce nature of the Turkish circuit. According to team manager Luca Baldisserri, "The cars used by Kimi and Felipe are to the same specification as those that were used in Spain, with the exception that at Istanbul Park we will not use the slotted nose.

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Chinese gunboat Fuxing

Fuxing was a wooden gunboat built for the Imperial Chinese Navy. She was built in 1870 at the Foochow Arsenal, the second such Meiyun-class gunboat constructed, alongside her sister ship Meiyun. Fuxing was based throughout her life at the Foochow Arsenal, there became involved in the Battle of Fuzhou at the opening of the Sino-French War, she was sunk during the battle by a spar torpedo. Fuxing was the third ship to be constructed at the Foochow Arsenal, after Meiyun and the transport Wannien Ching. All the ships of this period were constructed out of wood teak, she was 170 feet long overall. She had a beam of a draught of 9.8 ft. Fuxing displaced 515 long tons, she was sail rigged, in addition to her single steam engine powering a single shaft. The engine had an output of 400 indicated horsepower, she was armed with three Krupp guns. In July 1884, Fuxing was located at the Foochow Arsenal along with the corvette Yangwu and two flat-iron gunboats. From the middle of the month, the French Navy started sending ships nearby as the governments of France and China held negotiations in order to prevent a war.

The French forces became impatient, bombarded Formosa in early August. Despite the presence of the French navy near Foochow, more reinforcements were not sent to bolster the Chinese squadron. Negotiations ended on 21 August, the French squadron began clearing for action each day. On 23 August, they gave notice that the Chinese forces took no action. Just prior to 2pm, the French attack in the Battle of Fuzhou began, which marked the start of the active phase of the Sino-French War; the Chinese flagship Yangwu was destroyed 27 seconds as the French had sent forward torpedo boats equipped with spar torpedoes. While boat No 46 had impacted the Yangwu, Fuxing was damaged by a spar torpedo from boat No 45, it was sunk by another spar torpedo, this time from a pinnace launched from the French