PHYSICAL AND MATHEMATICAL SCIENCES. 149
another kind. No sooner, however, did he find thishypothesis fail, than he plunged into fresh coinput,ations in pursuit of a new construction. He was, in thisinstance, led by a singular train and combination of ideasto one of those real laws which have since become thefoundation of physical astronomy.
His object was to investigate the real form of theorbit of Mars , from the motions of that planet as ob-served from the earth, itself in motion. Hence it wasnecessary to distinguish that apparent part of the in-equality of the planet’s motion, which is caused by theinequality of the earth’s motion in its orbit.
Considering, therefore, the earth’s orbit as circular,after many laborious trials, he at length deduced atolerably exact representation of the law of the earth’smotion in its orbit, by supposing the orbit to be de-scribed about the sun, which is not placed in the centre,but in a point from which, if lines be drawn to succes-sive points in the circumference, the areas of thesectors formed by these lines, and the intercepted por-tions of the circumference, will always he proportionalto the times in which those portions are described ;which, in other words, is called the law of the equabledescription of areas.
In considering the orbit circular, he assumed what isvery nearly true for that of the earth. In proceedingto carry on his investigations with respect to Mars , hecould now divest the subject of those difficulties whicharose from the inequalities of the earth’s motion; andhe soon found that no circular orbit would representthat of Mars ; nor would the equable description of areasabout a point within a circle represent its motion: itthen occurred to him that the form might he ellipticalor oval. But a number of subsidiary hypotheses wereyet to be framed and rejected in turn before the simpledoctrine of an elliptic orbit could really be established.The picture which Kepler presents to us of the work-ings of his mind while pursuing this research is full ofthe most intense interest. It would he impossible,l 3