784 
SUMMARY OF CURRENT RESEARCHES RELATING TO 
From the following table it is seen that making use of this three- 
termed relation, the error of the transverse aberration (z — Z) A : z is not 
greater than 3 /x. 
A 
d or 
A 
d a- 
0*3 
- 2*2 a 
1*5 
+ 3 • 0 p, 
0.5 
- 2*9 
1*7 
+ 2*7 
0*7 
- 2*7 
1*9 
+ 0*8 
0*9 
- 1*6 
2*1 
- 1*8 
1*1 
0 
2*3 
- 3*0 
1*3 
+ 2*0 
2*5 
+ 3*0 
Thus in the correction of such a 1/6 in., it is justifiable to make use 
of the rules drawn from the three-termed relation, and to proceed by the 
same relation with the approximate determination of the focal plane. 
The distance of this plane (£ f ) is therefore found as follows : — 
Comparing 
z = a~bh 2 -\-ch 4: and 
, W A 4 
* = “-Pypi + *yt. 
we have c = y : A' 4 , y = c A' 4 : thus with central illumination 
(A' = 1 • 25) ; y = 0 • 949 ; by use of all zones (A' = 2 • 5) ; y = 15 • 18. 
Further we have from equation (2) as distance of union of tbe yellow- 
green rays of height of emergence A* = 0*866 A' : 
for A' = 1*25 z* = 164*79 
A' = 2*50 162*27 
and consequently, since £' = z* -f- ~ y, as distance of the focal plane: 
for central illumination : £' = 164*85 
by use of all zones: £' = 163*22 
The difference of 1*63 mm. corresponds to a lowering of the 
objective system (whose magnification N = 43) of 1 * 63 : N 2 = 0 * 0008 
mm. which is smaller than its penetrating power. For the rest see 
Dippel, c Mikroskopie/ p. 344. The transverse aberration (o*) in the 
focal plane can now be calculated. It is given by the formula 
1. For direct light (£ = 164*85) : 
A 
Co 
O-D 
o- E 
0- F 
0*1 
-f 6* 3/x 
-f 3*9/x 
+ 2-5/x 
+ 1-9/x 
~h 1’1/t 
0*3 
+18*1 
4-10*9 
4- 6*9 
4- 5*0 
4- 2*8 
0*5 
+27-6 
4-16*0 
+ 9*5 
4- 6*4 
4- 3*0 
0*7 
-f-33*7 
-j-17* 9 
+ 9*2 
+ 5*2 
4- i*o 
0*9 
-f35*5 
4-16*0 
+ 5*7 
+ 1*0 
- 3*2 
1*1 
4-33*0 
4-10*6 
- 0*8 
- 5*8 
- 9*1 
1*3 
4-27*1 
4- 1-7 
-10*1 
-14*7 
-15*8 
