The Philosophical magazine; a journal of theoretical, experimental and applied physics . the meridian; saythis is V, a vertex of the geo-desicline, and let the meridianthrough V meet the equatorin A; the geodesic line pro-ceeds from V to meet theequator in a point N, thenode, where A N is at most= 90°; and the undulationsare obtained by the repetition bIof this portion V N of thegeodesic line alternately oneach side of the equator andof the meridian. I consider in the present paper the series of geodesic lineswhich cut at right angles a gi veu meridian A C, or, say, a seriesof geodesic normals
The Philosophical magazine; a journal of theoretical, experimental and applied physics . the meridian; saythis is V, a vertex of the geo-desicline, and let the meridianthrough V meet the equatorin A; the geodesic line pro-ceeds from V to meet theequator in a point N, thenode, where A N is at most= 90°; and the undulationsare obtained by the repetition bIof this portion V N of thegeodesic line alternately oneach side of the equator andof the meridian. I consider in the present paper the series of geodesic lineswhich cut at right angles a gi veu meridian A C, or, say, a seriesof geodesic normals. It may be remarked that as V passesfrom the position A on the equator to the pole C, the angulardistance A N increases from a certain determinate value (equal, as will appear, to - 90°, if C, A are the polar and equatorial axes respectively) up to the value 90°; and it thus appears that,attending only to their course after they first meet the equator,the geodesic normals have an envelope resembling in its generalappearance the evolute of an ellipse (see fig. 1 and also fig. 2),.
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