text: the known eyeglass lens 1 illustrated in fig1 a has a lenticular grinding 2 in order to reduce the edge thickness . the rear and front surfaces 3 and 4 are spherical . as can be readily seen , such a lens does not satisfy esthetic demands . to an observer , it displays the so - called &# 34 ; bottom of the bottle &# 34 ; effect . fig1 b shows a known form of lens 5 , in which the rear surface 3 is spherical while the front surface 4 has the shape of an asphere of rotational symmetry . the optically usable diameter is designated 6 . within this region , the eyeglass lens is corrected ; outside , on the other hand , it passes , within an optically uncorrected region , continuously into the carrying border 7 . this lens also is not esthetically pleasing , since the fact that the front surface 4 is hollow in its central region and bead - shaped at its edges is esthetically disturbing . fig2 illustrates an eyeglass lens 8 designed in accordance with the present invention . the front surface 4 of this lens is spherical , while the rear surface 3 is developed as an asphere . the diameter 6 is the optically usable region , within which aberrations are optimally corrected . such optimal correction can be obtained in all cases by shaping the rear surface 3 , even when the lens is to have an anistigmatic action . the surface 3 in the optically usable region 6 may be an asphere of symmetry of rotation if the lens does not have astigmatic action . in this case the region 9 extends over the entire diameter symmetrically toward the carrying border . if the lens is to have an astigmatic action , then the surface 3 is developed as an atorus . even then , it is possible to keep the carrying border of the same thickness over its entire circumference and to make the sharply focusing region 6 circular by developing the region 9 asymmetrically . as can be noted by a comparison of fig2 with fig1 b , the lens 8 designed in accordance with this invention can be brought closer to the eye of the user than the known lens 5 , so that the value e * becomes smaller and thus the system magnification as well as the total magnification v are brought closer to a value of 1 . in the case of the known lens 10 in the plus range , illustrated in fig3 a , a relatively thin carrying border 11 is provided outside the optically usable diameter 6 . the rear and front surfaces 3 and 4 are spherical . it can be readily seen that such an eyeglass lens does not satisfy esthetic and optical demands . the known eyeglass lens 12 shown in fig3 b has a rear surface 3 which is spherical , while the front surface 4 has the shape of an asphere . outside of the optically useful diameter 6 , the front surface passes continuously into the border 13 , the curvature of the surface 4 changing . this surface 4 , strongly convex in its central region , passes in its outer region into a concave curvature . this is the reason why such a lens is also esthetically unpleasing . fig4 illustrates an eyeglass lens 14 according to this invention , having the same dioptric power and made of the same material ( allyl diglycol carbonate cr 39 ) as the known lens of fig3 b . both lens surfaces 3 and 4 have a convex shape in the region of the optically usable diameter 6 ; i . e ., the lens is of bi - form shape . the front surface 4 is convexly spherical , while the rear surface 3 is aspherical with a convex course in the region of the diameter 6 and a concave course in the marginal region 15 . within this region , the meridional inclination of the rear surface 3 approaches the inclination of the spherical front surface 4 , this transition being continuous . the rear surface 3 is continuously differentiable twice . its meridian section has the shape of a double flat figure s . as shown by a comparison of fig3 a and 3b with fig4 the front surface 4 of the bi - form is substantially flatter than those of the other lenses . such a flat front surface has the advantage that the forward protrusion with respect to the eyeglass frame is slight , so that such eyeglasses offer a pleasing appearance for an observer . furthermore , in the case of the lens of fig4 the center thickness can be kept less than that of known shapes , so that the lens is lighter . a saving in weight of about 10 percent is obtained as compared with the lens of fig3 b . the reduced center thickness and the flatter development of the front surface provide the advantage , in accordance with the above equation ( 1 ), that in the bi - form of fig4 the inherent magnification and thus the overall magnification v are considerably reduced as compared with previously known shapes . this provides the user with a very substantial advantage , which is perceptible also from an esthetic standpoint . a further substantial reduction in the center thickness and in the curvature of the front surface is possible if the lens is made from silicate glass , for instance from the glass sold by the schott glass firm under the designation basf 64 . a lens 16 made of this glass is shown in fig5 . in this lens also , the rear surface 3 is convex in its central region 6 , the shape passing into a concave course in the region 17 . some data of the bi - form eyeglass lenses of this invention , illustrated in fig4 and 5 , are compared with the data of a known lens according to fig3 b in the following table for plus lenses of a dioptric power of + 18 diopters . ______________________________________ known lens bi - form bi - form ( fig3 b ) ( fig4 ) ( fig5 ) ______________________________________material cr 39 cr 39 silicate n = 1 . 501 n = 1 . 501 glass n = 1 . 706outside diameter 67 66 66center thickness d 13 . 6 12 . 3 8 . 6radius of the front 29 . 70 43 . 74 61 . 39surface r . sub . 1radius of the rear 268 . 27 - 94 . 81 - 121 . 89surface r . sub . 2inherent magnification 1 . 18 1 . 10 1 . 06system magnification 1 . 35 1 . 35 1 . 35overall magnification v 1 . 60 1 . 49 1 . 43______________________________________ all dimensions are given in millimeters . in the case of an aspherical development of the surface in question the radii r 1 and r 2 are the radii of curvature in the center of the lens . a series of eyeglass lenses must cover a very wide range of dioptric powers , which also includes the region of severe ametropia defined earlier . for dioptric powers which lie outside the region of severe ametropia , eyeglass lenses are customarily developed in meniscus shape , i . e ., with convex front surface and concave rear surface . if the plus lenses were developed as bi - forms in accordance with fig4 and 5 for the entire range of severe ametropia , it might happen that a patient whose eyes are of different hyperopia might have , for the correction of his ametropia , eyeglasses one lens of which is of meniscus shape while the other has a bi - form . such glasses would not be satisfactory esthetically since the bi - form is less strongly curved on the front surface than the meniscus . for this reason , it is advantageous to provide also meniscus - shaped eyeglass lenses within the initial portion of the range of severe ametropia . these lenses are developed in accordance with the invention , i . e ., the rear surface is aspherical . by means of aspherical or atoric surfaces , it is possible to correct the aberrations with any curvature of the surface , so that both a meniscus - shaped and a bi - form shape of lens is possible for correction of the same aberrations . one illustrative embodiment of a meniscus - shaped lens developed in accordance with the invention and having a power of + 6 diopters is shown in fig7 . a lens of the same + 6 power developed in accordance with the above mentioned os no . 29 41 733 is shown in fig6 . this known lens 18 has a front surface 4 which is more strongly curved in its central region than the front surface of the new lens 20 in fig7 . furthermore , the curvature of the known lens 18 changes upon transition from the central region into the outer region 19 . in the new lens 20 of fig7 the rear surface 3 is more strongly curved in the region of the edge 21 than in the central region 6 . in this edge region 21 , the inclination of the rear surface 3 approaches that of the front surface 4 . since the front surface 4 of the lens of fig7 is flatter than that of the lens of fig6 and the value d 1 is therefore smaller , the total magnification v is less than in the known lens of fig6 . it can be noted from fig2 , 5 , and 7 that in all eyeglass lenses developed in accordance with the invention , the curvature of the rear surface 3 outside of the optically usable central region 6 is relatively great . this reduces the so - called &# 34 ; rear - mirror effect &# 34 ;, i . e ., visibility of objects of strong brightness reflected on the back surface , which is disturbing to the wearer of the glasses . such disturbing mirroring effects , on the other hand , are present in the known eyeglass lenses such as those illustrated in fig1 a , 1b , 3a , and 3b . this property of the new lenses of the present invention , in reducing the rear - mirror effect , therefore also increases the comfort of the wearer . the important feature that the eye - side surface of the lens is continuously differentiable twice , serves to distinguish the present lens from those lenses in which a radial section of the eye - side surface has two curves having a common point of tangency and having respective radii which , at that point of tangency , are unequal in either magnitude to more than a substantially infinitesimal extent , or sign ( plus or minus ), or both . such curves having the inequalities or differences just mentioned , at a common point of tangency , can not be continuously differentiable twice , within the meaning of that term as here used , and when such curves are used on eye - side eyeglass surfaces , the wearer &# 39 ; s observed image will appear to &# 34 ; jump &# 34 ; in magnification or in image quality when the line of sight moves across any point of tangency of such two curves . but , as already indicated , no such jump in image occurs when using the curvatures of the present invention . this expression &# 34 ; continuously differentiable twice &# 34 ; means that the second derivative of the curve is continuous ; that is , that the second derivative is a continuous function without steps .