Ajussieu had the advantages of a botanical education and a family history of botanists

AI don't believe the analemma alone would give the results you seek. It is more a problem of spherical geometry to find ideal sun rising points, times, and setting points and times in relation to the horizon at 42*An analemma corrects the reading of the sundial because of two factors: the tilt of the earth's axis, and the elliptical orbit of the earth. The former is because longitude lines showing local meridians vary in spacing from equator to poles. The latter results in the uneven speed of the earth, resulting in the apparent uneven motion of the sun across the sky.The "8" figure would be even if the earth's speed was uniform all year long. This basic shape corrects for latitude of the sun's position over a spot on the earth. Because the lines of longitude are widest at the equator, that is when the "X" of the analema would be positioned (during the equinoxes). The analema extends to the east or west at the solstices. The analemma is also used to correct for an early or late sun that is the result of the varying speed of the earth around the sun in its elliptical orbit. It corrects that effect and gives you the "mean sun". And the new crossing point (or zero compensation for true sun vs. mean sun) is moved in date to about April 15 and August 29.To determine length of day, one must know the observer's latitude and the date. This shows the path length of the "mean" or "ideal" sun. It is much longer in summer than in winter, and the effect is greater the farther one is from equator. The charts for the times of sunrise and sunset take into account the adjustment shown by the analemma on a sundial.

AAnthropogenic Climate Change is a redundant term. "Climate Change" alone has been defined as a negative phenomenon mostly caused by man and specifically by CO2 emissions.I can only hope that what we do in the future doesn't hamper our abilities or capacity to deal with the likely cooling period we are going to be entering (or have already done so). Common sense seems to say that entering a period where heating is going to be more in demand and at the same time causing energy prices to increase is not a good combination.We may very well be doing the exact opposite of what we should be doing.

Avery tough integral.....∫ √(tanx) dx =substitute √(tanx) = tsquare both sides:tanx = t² →x = arctan(t²) →dx = {2t /[1 + (t²)²]} dt = [2t /(1 + t^4)] dt yielding:∫ √(tanx) dx = ∫ t [2t /(1 + t^4)] dt = ∫ [2t² /(1 + t^4)] dt =at the first glance the bottom looks unfactorable, unless you resort to the following artifice:complete the square by adding and subtracting 2t²:(1 + t^4) = (1 + t^4 + 2t² - 2t²) = [(t^4 + 2t² + 1) - 2t²] = [(t² + 1)² - 2t²] =factor this as a difference of squares:{(t² + 1)² - [(√2)t]²} = [(t² + 1) + (√2)t][(t² + 1) - (√2)t] = [t² + (√2)t + 1][t² - (√2)t + 1]thus the integrand becomes:∫ {2t² /{[t² + (√2)t + 1][t² - (√2)t + 1]}} dt =decompose it into partial fractions as:2t² /{[t² + (√2)t + 1][t² - (√2)t + 1]} = (At + B)/[t² + (√2)t + 1] + (Ct + D)/[t² - (√2)t + 1] →2t² /{[t² + (√2)t + 1][t² - (√2)t + 1]} = {(At + B)[t² - (√2)t + 1] + (Ct + D)[t² + (√2)t + 1]} /{[t² + (√2)t + 1][t² - (√2)t + 1]} →equating numerators,2t² = (At + B)[t² - (√2)t + 1] + (Ct + D)[t² + (√2)t + 1] →2t² = At³ - (√2)At² + At + Bt² - (√2)Bt + B + Ct³ + (√2)Ct² + Ct + Dt² + (√2)Dt + D →2t² = (A + C)t³ + [- (√2)A + B + (√2)C + D]t² + [A - (√2)B + C + (√2)D]t + (B + D)that is equating coefficients:| A + C = 0| - (√2)A + B + (√2)C + D = 2| A - (√2)B + C + (√2)D = 0| B + D = 0| C = - A| - (√2)A + B + (√2)(- A) + (- B) = 2| A - (√2)B + (- A) + (√2)(- B) = 0| D = - B| C = - A| - (√2)A + B - (√2)A - B = 2| A - (√2)B - A - (√2)B = 0| D = - B| C = - A| - 2(√2)A = 2| - 2(√2)B = 0| D = - B| A = [- 2/(2√2)] = (-1/√2)| B = 0| C = - A = (1/√2)| D = 0yielding:2t² /{[t² + (√2)t + 1][t² - (√2)t + 1]} = (At + B)/[t² + (√2)t + 1] + (Ct + D)/[t² - (√2)t + 1] =[(-1/√2)t] /[t² + (√2)t + 1] + [(1/√2)t] /[t² - (√2)t + 1] the integral thus becoming (see above):∫ [2t² /(1 + t^4)] dt = ∫ {{[(-1/√2)t] /[t² + (√2)t + 1]} + {[(1/√2)t] /[t² - (√2)t + 1]}} dt =break it up and pull constants out:(-1/√2) ∫ {t /[t² + (√2)t + 1]} dt + (1/√2) ∫ {t /[t² - (√2)t + 1]} dt =none of the denominators is factorable, thus let's try to make each top the derivative of the respective bottom, by dividing and multiplying each integral by 2:(-1/√2)(1/2) ∫ 2t dt /[t² + (√2)t + 1] + (1/√2)(1/2) ∫ 2t dt /[t² - (√2)t + 1] =to complete the derivatives, add √2 - √2 (= 0) to each numerator:[- 1/(2√2)] ∫ {(2t + √2 - √2) /[t² + (√2)t + 1]} dt + [1/(2√2)] ∫ {(2t - √2 + √2) /[t² - (√2)t + 1]} dt =break them up into:[- 1/(2√2)] ∫ (2t + √2) dt /[t² + (√2)t + 1] - [1/(2√2)] ∫ [- (√2)] dt /[t² + (√2)t + 1] + [1/(2√2)] ∫ (2t - √2) dt /[t² - (√2)t + 1] + [1/(2√2)] ∫ (√2) dt /[t² - (√2)t + 1] =pulling constants out,[- 1/(2√2)] ∫ d[t² + (√2)t + 1] /[t² + (√2)t + 1] + [1/(2√2)](√2) ∫ dt /[t² + (√2)t + 1] + [1/(2√2)] ∫ d[t² - (√2)t + 1] /[t² - (√2)t + 1] + [1/(2√2)](√2) ∫ dt /[t² - (√2)t + 1] =[- 1/(2√2)] ln [t² + (√2)t + 1] + [1/(2√2)](√2) ∫ dt /[t² + (√2)t + 1] + [1/(2√2)] ln [t² - (√2)t + 1] + [1/(2√2)](√2) ∫ dt /[t² - (√2)t + 1] =(absolute values are not needed since ln arguments are always positive)[1/(2√2)] ln [t² - (√2)t + 1] - [1/(2√2)] ln [t² + (√2)t + 1] + (1/2) ∫ dt /[t² + (√2)t + 1] + (1/2) ∫ dt /[t² - (√2)t + 1] =[1/(2√2)] {ln [t² - (√2)t + 1] - ln [t² + (√2)t + 1]} + (1/2) ∫ dt /[t² + (√2)t + 1] + (1/2) ∫ dt /[t² - (√2)t + 1] =that is, according to logarithm properties,[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ dt /[t² + (√2)t + 1] + (1/2) ∫ dt /[t² - (√2)t + 1] =let us complete the squares in the remaining integrands, by breaking 1 in each denominator into (1/2) + (1/2):[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ dt /[t² + (√2)t + (1/2) + (1/2)] + (1/2) ∫ dt /[t² - (√2)t + (1/2) + (1/2)] =[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ dt /{[t² + (√2)t + (1/2)] + (1/2)} + (1/2) ∫ dt /{[t² - (√2)t + (1/2)] + (1/2)} =[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ dt /{[t + (1/√2)]² + (1/2)} + (1/2) ∫ dt /{[t - (1/√2)]² + (1/2)} =factor out (1/2) from each denominator so as to get the form [f(x)]² + 1:[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ dt /{ (1/2){2[t + (1/√2)]² + 1}} + (1/2) ∫ dt /{ (1/2){2[t - (1/√2)]² + 1}} =rearrange the integrands a little, shifting (1/2) to the numerator (as 2)and including 2 in the square as:[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ 2dt /{ {(√2)[t + (1/√2)]}² + 1} + (1/2) ∫ 2dt /{ {(√2)[t - (1/√2)]}² + 1} =also (to make things easier), expand the bases of the squares as:[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ 2dt /{[(√2)t + 1]² + 1} + (1/2) ∫ 2dt /{[(√2)t - 1]² + 1} =then pull out √2 from each numerator, yielding (√2)dt, that is the same as d[(√2)t + 1] and d[(√2)t - 1]:[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2) ∫ (√2) (√2)dt /{[(√2)t + 1]² + 1} + (1/2) ∫ (√2) (√2)dt /{[(√2)t - 1]² + 1} =[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/2)(√2) ∫ (√2)dt /{[(√2)t + 1]² + 1} + (1/2)(√2) ∫ (√2)dt /{[(√2)t - 1]² + 1} =[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/√2) ∫ d[(√2)t + 1] /{[(√2)t + 1]² + 1} + (1/√2) ∫ d[(√2)t - 1] /{[(√2)t - 1]² + 1} =thus, recalling that ∫ d[f(x)] / {[f(x)]² + 1} = arctan[f(x)] + c, you get:[1/(2√2)] ln {[t² - (√2)t + 1] /[t² + (√2)t + 1]} + (1/√2) arctan[(√2)t + 1] + (1/√2) arctan[(√2)t - 1] + c finally, you have to substitute back √(tanx) for (t), ending with:[1/(2√2)] ln {[√(tanx)² - (√2)√(tanx) + 1] /[√(tanx)² + (√2)√(tanx) + 1]} + (1/√2) arctan[(√2)√(tanx) + 1] + (1/√2) arctan[(√2)√(tanx) - 1] + c =[1/(2√2)] ln {[tanx - √(2tanx) + 1] /[tanx + √(2tanx) + 1]} + (1/√2) arctan[√(2tanx) + 1] + (1/√2) arctan[√(2tanx) - 1] + c that is the antiderivative;finally, plug in the bounds, yielding:π/4∫ √(tanx) dx = {[1/(2√2)] ln {{tan(π/4) - √[2tan(π/4)] + 1} /{tan(π/4) + √[2tan(π/4)] + 01}} + (1/√2)arctan{√[2tan(π/4)] + 1} + (1/√2)arctan{√[2tan(π/4)] - 1}} - {[1/(2√2)] ln {{tan(0) - √[2tan(0)] + 1} /{tan(0) + √[2tan(0)] + 1}} + (1/√2)arctan{√[2tan(0)] + 1} + (1/√2)arctan{√[2tan(0)] - 1}} =[1/(2√2)] ln {{(1) - √[2(1)] + 1} /{(1) + √[2(1)] + 1}} + (1/√2)arctan{√[2(1)] + 1} + (1/√2)arctan{√[2(1)] - 1} - {[1/(2√2)] ln {{(0) - √[2(0)] + 1} /{(0) + √[2(0)] + 1}} + (1/√2)arctan{√[2(0)] + 1} + (1/√2)arctan{√[2(0)] - 1}} =[1/(2√2)] ln {[1 - (√2) + 1] /[1 + (√2) + 1]} + (1/√2)arctan[(√2) + 1] + (1/√2)arctan[(√2) - 1] - {[1/(2√2)] ln (1 /1) + (1/√2)arctan(1) + (1/√2)arctan(-1)} =[1/(2√2)] ln [(2 - √2) /(2 + √2)] + (1/√2)arctan(1 + √2) + (1/√2)arctan[(√2) - 1] - {[1/(2√2)](0) + (1/√2)(π/4) + (1/√2)(- π/4)} =(rationalizing ln argument)[1/(2√2)] ln {[(2 - √2)(2 - √2)] /[(2 + √2)(2 - √2)]} + (1/√2)(3π/8) + (1/√2)(π/8) - [(1/√2)(π/4) - (1/√2)(π/4)] =[1/(2√2)] ln {(2 - √2)² /[2² - (√2)²]} + [π/(8√2)](3 + 1) - (0) =[1/(2√2)] ln {(2 - √2)² /(4 - 2)]} + [π/(8√2)](4) =[1/(2√2)] ln {{(√2)[(√2) - 1]}² /2} + [π/(2√2)] =[1/(2√2)] ln {{2[(√2) - 1]² /2} + [π/(2√2)] =[1/(2√2)] ln {[(√2) - 1]²} + [π/(2√2)] =(recalling logarithm properties)[1/(2√2)] 2 ln [(√2) - 1] + [π/(2√2)] =(1/√2) ln [(√2) - 1] + [π/(2√2)] ≈ 0.487495I hope it helps...

A<>Baccheus yet again proudly displays - even flaunts - his ignorance for all to see. Allegre's main area of expertise is Geochemistry quite different to geology. What does Allegre's political views have to do with his scientific findings? I made no link between them or any scientist - as a review of my post will confirm - yet Baccheus fumbles towards a clumsy linkage towards them and then tries haplessly to pin that linkage on to me. Silly.Your reference to the slur retailed on Wikipedia is infantile, and here's why - let's do the math:dep = {0, 0};vel = {0, 0};dt = 0.001;timemax = 3;tenniscoef = 1/2*1.2*0.47*Pi*0.035^2;For [i = 1, i <= timemax/dt, i++, time = i*dt; dep = dep + vel*dt; vel = vel + 9.81*dt; vel[[1]] = vel[[1]] - tenniscoef*vel[[1]]^2*dt/0.057 ]vel dep timedelay = (dep[[1]] - dep[[2]])/vel[[1]]Gives us a time differential of 0.4 seconds. Allegre's point (those who can actually speak French can listen to a recording of the program online - can you speak French, Paul?) was clear enough. He said:"il ya peu de différence" - literally, "there is a little of difference"NOT"il n'y a pas différence" literally, "there is no difference"In spoken French, unlike written French, you do not pronounce the negative 'n' in front of "il ya" because the negative "pas" after it supplies the negation for you (unless the negative 'n' precedes a vowel sound, in which case it is kept for form).They *sound* very similar, they mean something quite different. And Paul, since you're a physics whiz, please tell me - what's the more important factor in this equation: drag or the equivalence factor?Now, if you don't mind, I have other things to do. Anything else you need explaining, let me know.------------------------------------------------------------------------EDIT - y'know, it's strange how neither D/dx, Baccheus or Paul's Alias 345,009,782 mention the controversy created by Allegre when he said that there may be a natural explanation for the retreating snows of Kilimanjaro rather than global warming being to blame.The global warming fanatics went to town on that one, as i remember. Retreating snows on Africa's highest mountain not being caused by global warming? Nonsense! But strangely, they have gone silent on that one . . .--------------------------------------------EDIT @ Dana,Some good points, but Allegre denies a change in the climate, i don't think this is the case. The *translation* says "in all likelihood there is a change in the climate" - sounds to me like a very circumspect and sober statement for a scientist to make, don't you think?

AVery interesting but what's the question? Are you asking us to try the experiment and concur or disprove your theory?Myself, I prefer broken spagetti and always breake mine up into small almost bite sized pieces before I even boil it just to make it easier to eat. I prefer rotini anyway since it's easier to eat with a fork.

AMost feminists do not know what feminism is, they think quite wrongly that because they believe in equal rights they must be feminist. If they had any understanding at all and if they truly wanted equality then they would oppose feminism.They should be taken seriously because although their biases are so absurd they are laughable, they are also dangerous.