In this paper, we investigated the natural lifts and curvatures of thespherical indicatries of the evolute in E3. Firstly, it is shown that theDarboux vektor of evolute curve and binormal vektor of the evolutecurve are linearly dependent, secondly the relations among the geodesiccurvatures and arc-lengths with respect to E3and S2 of the fixed polecurve (C?) and the spherical indicartix curves (T?),(N?),(B?) generatedby the unit vektor (C?) on S2 have been obtained and finally, thecondition being the natural lifts of the spherical indicatrix of the evolutecurve (α?) are an integral curve of geodesic spray has expressed.
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