We use Optical Character Recognition (OCR) during our scanning and processing workflow to make the content of each page searchable. You can view the automatically generated text below as well as copy and paste individual pieces of text to quote in your own work.
Text recognition is never 100% accurate. Many parts of the scanned page may not be reflected in the OCR text output, including: images, page layout, certain fonts or handwriting.
9 planet revolving in such an ellipse will pass through the distance from P to P 1 in the same time that it occupies to pass from P 5 to P 6 ; its rate of movement being much greater when near its perihelion, than when near its aphelion. The law which governs this variation, applying equally to the planets whose orbits are nearly circular, and to comets whose orbits are most eccentric, is very simply expressed in mathematical language, being as follows: The radius vector moves over equal areas in equal times. The radius vector is a line drawn from one of the foci of an ellipse to any point in the curve; thus, each of the lines 8 P, SPl, SP2, SP3, SP4, SP5, and S P 6, is a radius vector. Now, if We conceive the line 8 P to be travelling towards S P 1, it will move over the area or space included between these two lines and the curve that joins them; and whatever be the time which is occupied in this move- ment, exactly the same time will he required for the radius vector to pass over the same area in any other part of the orbit. Thus the space included between ^ P 1 and S P 2, and bounded on the outside by the curve, being equal to that between S P and SPl, the Part of the orbit between P 1 and P 2 will be traversed m the same time as that between P and Pi. In like manner, the portions between P 2 and P 3, between P 3 and P 4, between P 4 and P 5, and between P 5 and P 6, will all be traversed in equal times; the areas, or spaces included between the lines drawn from the focus to these points respectively, and bounded on the outside by the curve, being all equal. Thus, for example, the area included between the lines S P 5 and ® P 6, and bounded by the curve P 5, P 6, being equal f° the area between SP and SPl, and bounded by the curve P, P 1, the time occupied by the planet in Passing through the distance P 5, P 6, will be as great that required for its passage through the much longer distance P, P 1. If a circle were similarity divided into equal areas, as the radius vector is every- b 2