THF HISTORY OF THE TELESOOPE. 107 



Tbe obvious r('(|uir<iii«Miis ure that in a good objective tlio li'-lit coui- 

 iii_i>' from a point in tlie object sliould be concentrated at a point in tiie 

 iinaji'c; but tliis, combined with a prescribed focal ]cn,ntli, may 1)6 re- 

 duced to tliree coiulitions: First, a lixed focal length; second, freedom 

 fr(tm color error; third, freedom iVom splierical alxn-ration for a partic- 

 ular color or wave lengtli of light. Now let us catalogue what provi- 

 sions we have for satisfying these conditions. They are, four surfaces, 

 wliieh uuist be spherical but may have any radii we please, the two 

 thicknesses of the two lenses, and the distance Avhicli se])arates the 

 lenses — tluit is, seven elements which may be varied to suit our require- 

 ments. As a matter of fact, however, on acconnt of the cost of the 

 material and the fact that glass is perfectly transparent, for powerful 

 telescopes we must make the lenses as thin as possible; and we shall 

 tind also that separating the lenses introduces errfU's away from the 

 axis which are, to say the least, undesirable. We have left, therefore, 

 only the four radii as arbitrary constants. These, however, are more 

 than enough to meet the three requirements. To make the problem 

 determinate we uuist add another condition. The suggestion of this 

 fourth condition and carrying- the ]>rol)lem to its solution is the work 

 of the great mathematicians who have directed their thought to it. 

 Clairault i)roposed to make the fourth condition that the two adjacent 

 surfaces should tit together and the lenses be cemented. This condition 

 would be, doubtless, of great value were it i)Ossible to cement large lenses 

 without changing their shapes to a degree which would quite spoil their 

 performance. ^Sir John llerschel published a very important i)aper in 

 1S21, in wliich he made the fourth condition that thesi»herical aberiation 

 should vanish, not only for objects at a very great distance, but also for 

 those at a moderate distance. In this ]»aper he computed a table, after- 

 wards greatly extended by Prof. IJaden Powell, for the a\'owed i)urpose 

 of aiding- the practical optician. It was tiiis feature undoubtedly which 

 brought his construction, not at all a good one as we shall see, into 

 more general use than any other for some time. But, as all nerschefs 

 tables were deiived from calculations whicli wholly disregarded the 

 tidckness of the lenses, I am (pute unable to see how they could have 

 been <»f any nmterial aid, and am inclined to suspect that the discredit 

 with which oi»ticians have received the dicta of mathematicians con- 

 cerning their instruments may have been due in part to this very fact. 

 It is a singular fact, for which 1 have in vain sought the explanation, 

 that r'raunhofer's objccti\es ar(^ of Just such a torm as to comply witii 

 the lleischelian solution, although they must have been made (piite 

 independently. 



(lauss made th<'f(»urth condition that another color or wave length 

 of light should be also free from s])herical aberration. This seems to 

 have been a tour deforce as a mathematician, not as a sober suggestion 

 of an improvement in ccuistiuction, for in a ])oint of fact the construc- 

 tion is very bad. It was generally believed that this con«lition could 



