Elements of astronomy ..with explanatory notes, and questions for examination . B is a straight line drawn from the centreof the sun through that of the earth, to the extremity ofthe shadow, and EB is the length of the shadow. Ourtask is to find how many miles long EB is. 349. We must first direct our attention to the trian-gle DEB. We know the extent of DE, for it is a radiusof the earth, and is miles long; moreover, EDBis a right angle ; for if a line (as ADB) touches the sur-face of a sphere at any point, and a line (as DE) is 1. Strictly speaking the shadow is not an exact cone, the
Elements of astronomy ..with explanatory notes, and questions for examination . B is a straight line drawn from the centreof the sun through that of the earth, to the extremity ofthe shadow, and EB is the length of the shadow. Ourtask is to find how many miles long EB is. 349. We must first direct our attention to the trian-gle DEB. We know the extent of DE, for it is a radiusof the earth, and is miles long; moreover, EDBis a right angle ; for if a line (as ADB) touches the sur-face of a sphere at any point, and a line (as DE) is 1. Strictly speaking the shadow is not an exact cone, the base of whichis a circle. It would be a cone if the earth was a perfect sphere but beingan ellipsoid the base of the shadow is an ellipse instead of a circle. When is an eclipse total? When partial? What is an appulse? What is theform of the shadow of a globe illumined by one of a greater size ? What does the lengthof the shadow depend upon 1 What is the form of the shadow of the earth ? Whenon/?est ? When shortest 1 Can its length be calculated 1 176 SOLAR SYSTEM. FIG. =^W drawn from the centre of the sphere to that point, theline drawn from the centre and the touching linealways make a right angle with each other. Now joinAE, and we thus form two angles ; viz., DAE which isthe surfs horizontal parallax, (Art. 94,) and AES which isthe suns apparent semi-diameter. In geometrical languageAES, is called the exterior angle of the triangle AEB,and is equal to the sum of the two angles ABE and B angle EBA, is therefore equal to the angle AES,diminished by the angle E AB; or in other words equalsthe difference between the suns apparent semi-diameterand his horizontal parallax. The value of the difference atthe suns mean distance is 15 Therefore, in thetriangle DEB, since we know the value of all the anglesand the length of one side, we proceed to select fromthe trigonometrical tables a similar triangle as D^B1,and institute a proportion as we have before shownbet
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