Mr Herscliel at Achromatic Ohject-Glasscs,~ 
subjoined a table, calculated upon the rigorous formulae, the con- 
struction and employment of which will be explained presently. 
^ ^dly^ Another practical advantage afforded by this construc- 
tion, is, that the two interior surfaces approach in all cases so 
near to coincidence, that no -sensible error can arise from neglect- 
ing their difference, and figuring them on tools of equal radii. 
Indeed, for a dispersive ratio a little above the average, they 
would coincide rigorously, and this construction would be iden- 
tical with that of Glairaut above mentioned; and so nearly is 
this approach to equality sustained throughout the whole extent 
of the variations in the data, that even when the dispersive ration 
is so low as 0.75 : 1 (a case almost useless to consider), the dif- 
ference amounts to less than ^^^th part of the curvature of each. 
TABLE , — Dimensions qf an Aplanatic Double Object-glass. 
Refractive Index of Crown Lens, - 1.524 ) Focal Length, 1 0.000 
Refractive Index of Flint Lens, - 1.585 j 
•susq 
9^1 JO irSuot icao^ 
10.0000 
8.1818 
6.6667 
5.3846 
4.2858 
CO 
CO. 
•suaq 
UMOJO sq; jo qjSuoT inoo^ 
0^0 
«5 
o o 
CO CO 
g4 
' 4th Surface, Convex. 
‘lO 3un.!l JO xspul 
0 10*0 + JO aSuuqo 
u loj suipua JO uopuuu^ 
— 0.3962 
— 0.5033 
— 0.5659 
— 0.6323 
— 0.7570 
t- 
o 
»>} 
t- 
d 
1 
*If) uMoa 3 JO xopiu ‘jo^i 
oj 010*0 + JO 9§uuqD 
u aoj snipu^ jo uoiiuuu^ 
rH O 05 
Gvj CO 
C5 O O 
05 O 
d rH rH 
+ + + 
^ CO 1 
rH rH 1 
+ + 1 
-}- 1.0847 
‘saoipui ,gAi;.it?aj3jj 
9Aoqu 9q? joj snipe^ 
14.3697 
14.5353 
14.2937 
13.5709 
12.3154 
10.5186 
3d Sur- 
face, 
Con- 
cave. 
Radius. 
4.1575 
3.6006 
3.0640 

1 o 1 
1 -X) CO 
1 ■•0) 00 
1 0^ g4 1 
1.6450| 
2d Sur- 
face, 
Con- 
vex. 
: Radius. 
t- cvrco 
GVi CO QD 
CO CO 
GVJ V© O 
CO CO 
1 00 oj 1 CO 
O (W t- 
Of 1 o 
, O O 
1 O'? (^< 1 r— 1 
1st Surface, Convex, 
*19 JO xopuT -jau 
ot 010*0 + JO oSuuqa 
u joj suippa JO UOip3I.l^A 
— 0.0036 
— 0.0011 
+ 0.0037 
1 *0 1 OD 
^ 00 1© 
O O O 
d d d 
1 ++ 1 + 
•jf) UAVO.T 3 JO xaput -ja?! 
OIO’O + JO aSucqa 
u .loj sntpu^ JO uoijuuut^ 
-f- 0.0500 
+ 0.0740 
+ 0.0676 
-1- 0.0563 
+ 0.0335 
t- 
»-* 
o 
d 
! 
•saaipuj 9Aipuaja}j 
9Aoqc oq; aoj smptjjj 
6.7485 
6.7184 
6.7069 
6.7316 
6.8279 
7.0816 
1 
1 '•Oljt’U OAIS^adsTQ 
O *0 o 
AO 40 <©) 
d d'd 
0.65 
0.70 
0.751 
