Such a solution of the problem is further facilitated by the fact that in these lenses more than two varieties of glass can be used to neutralise one another, while a natural mineral (fluorite) is also employed. From the glass-maker’s point of view, however, the problem of producing a satisfactory pair of glasses capable of entirely achromatising one another has yet to be solved. ---------+------+----+-------+------+------+------+------+------+----- | | | | | c-d | | d-f | | f-g′ Name. | n_{D}| ν | C-F. | C-D. | --- | D-F. | --- | F-G′.| --- | | | | | c-f. | | c-f. | | c-f. ---------+------+----+-------+------+------+------+------+------+----- Telescope| | | | | | | | | Crown |1·5254|61·7|·00852 |·00250| ·292 |·00602| ·707 |·00484| ·568 Telescope| | | | | | | | | Flint |1·5211|51·8|·001007|·00297| ·294 |·00710| ·705 |·00577| ·573 ---------+------+----+-------+------+------+------+------+------+----- The table of optical glasses given above, although brief as compared with the lists issued by French and German optical glass-makers, fairly covers the range of practically available glasses, and a rapid inspection will at once show how extremely limited this range really is. Thus the refractive index varies only between the limits 1·49 and 1·71, and even if we admit as practical glasses such extreme types--offered by some makers--as would extend this range to 1·40 in one direction and to 1·80 in the other, this does not affect the present argument. Of course, a glass of a refractive index as low as 1·0, or even 1·10, is not theoretically possible, since the mere density of any substance enters into the factors that affect its refractive index, and a glass having a density lower than that of water (whose refractive index is about 1·3) is scarcely conceivable. In the other direction, however, the limits met with in the case of glass are considerably exceeded by certain natural mineral substances. Thus the diamond has a refractive index of 2·42, while the garnets show refractive indices from 1·75 to 1·81. The values of ν found in the table of optical glasses are still more narrowly restricted, lying between 67 and 29, while such a mineral as fluorite shows a value of 95·4. These facts show that it is physically possible to obtain transparent substances having optical properties lying far beyond the limited range covered by our present optical glasses, and it scarcely needs showing that if such an extended range of materials were available greatly increased possibilities would be opened up to the designer of optical instruments. It is consequently interesting to inquire as to the actual causes which limit the range of optical glasses at present available. It will be found that these limits are set by the properties of glass itself. While the more ordinary kinds