The Mathematical Theory of Eclipses According to Chauvenets Transformation of B
The Mathematical Theory of Eclipses According to Chauvenets Transformation of B
Roberdeau Buchanan
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The equation m sin (M E) should read < unity. Compare page 479, line 2.
70. The Maximum Curve is correctly explained thus : As the earth is moving under the shadow in some different direction, the projection of the path over the earth's surface will not be its pro- jection on the fundamental plane, but will be, perhaps, the result- ant of the two motions. The northern and southern limiting curves will consequently not be formed by the element of the cone normal to the path, but by some other element swung around from the right angle by the angle E + some variable quantity. At the beginning 70 MAXIMUM CURVE. 85 and ending of these curves this variable is zero, and Q = E or Q = E 180 (CHAUVENET, i. , p. 481, Art. 311). Hence, for the be- ginning of the Maximum Curve, conceive a line crossing the path of the eclipse, making the variable angle E with the axis Y. As this line moves along the centre line, its intersection with the earth's sphere will generate the Maximum Curve in all cases ; and there are four special positions to be examined.
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