The following method has been developed to obtain the tangents to a curve accurately and rapidly with no more than a i/4-3/8.in. diameter cylindrical rod of Perspex or glass used as a lens. The rod is laid roughly tangentially to the curve near to the point P at which the slope is required. It is then rolled over the paper till the image of P appears on the axis of the rod. The rod is twisted in the plane of the paper until the image of the part of the curve near P lies exactly along the axis of the rod. The magnification of the cylindrical lens ( x 5 or 6) increases the accuracy v i t h which this can be done. But a further check is obtained if a short pencil stroke is made across the curve at P:this, viewed through the rod, will appear as a line almost exactly normal to the rod axis, however carelessly the stroke is drawn. This line, therefore, gives a secondary criterion for setting the slope of the rod: the image of the stroke must appear to cut the image of the curve at right angles.