796 Transactions of the Society. 



yield for tlie same distance of projection (T). The value of — which 



I shall denote by the sign [N] may be conveniently called the 

 normal ami^lification (the own propter amplification) of the ob- 

 objective, because it is realized when the objective is used without 

 an eye-piece, as a " simple Microscope." 

 We have now 



N = [N] ;/ 



and conversely 



The value of v, which was defined above by the quotient -, and 



.... y 



which indicates the enlargement of the dissipation-circles by the 

 ocular, is therefore also the quotient of the total amplification of 

 the Microscope by the normal amphfication of the objective, and 

 thus expresses the increase of i^oiver, beyond the normal power of 

 the objective, which is obtained in the compound Microscope by the 

 tube and ocular combined. I shall, therefore, call the quantity v 

 the siqjer-ampUfication which is applied to a system, or which it 

 has to bear when it is the objective of a compound Microscope with 

 a given length of the tube and a given ocular. 



^Ye arrive now at the proposition : — When an objective (for 

 which the constant visual angle of the inherent dissipation of light 

 is given) is used with any length of tube and with any power of the 

 ocular, the angular dissipation is always increased in the ultimate 

 image in proportion to the super-amplification which the objective 

 has to bear, i. e. according to the quotient of the total amplification 

 of the Microscope by the normal amplification of the objective. 



The foregoing considerations lead to a comprehensive expression 

 and measure of the combined effect of tube and ocular in the com- 

 pound Microscope, which holds good (as may be shown) in regard to 

 all functions of the instrument. If, for example, we know that the 

 objective of a Microscope has a focal length f = ^ inch — which 

 gives the normal amplification [N] = 20, for a distance of vision 

 Z = 10 inches — and that this objective is used for a power of 

 N = 200, we have a super-amplification y = 10. We have thereby 

 analyzed the composition of the total power of the instrument as 

 between objective and ocular, or the manner of co-operation of these 

 two elements of the composite system, in quite a general manner ; 

 and we know that all essential conditions of the optical performance 

 remain the same as long as the same value of i/ is maintained, 

 whatever may be the pai-ticular conditions as to length of tube and 

 depth of ocular. At the same time we have established a numerical 

 test of the strain to which an objective must be submitted in order 

 to obtain a certain total power of the Microscope. We know that 



