42 Transactions of the Ajiefican Institute. 



and that is what is called defining power. By this is meant the 

 powers of delineation of the outlines of the objects observed. Great 

 powers of enlargement seem to be supposed by many to be the most 

 important property; but Avithout sharp definition, no magnifying 

 power is of any value, for definition is necessary that the object may 

 properly be seen at all. Great magnifying power is indeed for many 

 purposes a disadvantage rather than the contrary. To see an object 

 in whole, or any considerable part, it is generally indispensable that 

 the power should be low ; and it should always be remembered that 

 when the power is high enough to permit us to see what we want to 

 see, to increase it Avould be worse than useless. The field on the 

 stage commanded by a power of one hundred is hardly more than the 

 twentieth of an inch in diameter. With a power of one or two 

 thousand, a puncture of a fine needle in a card would more than 

 represent the entire space w^hich the observer could see at a single 

 view. Hence, except for the very minutest objects, high powers 

 define only details of structure, not by any means forms and outlines. 

 Defining power being secured, we need next either penetrating power, 

 or resolving power, according to the uses we expect to make of the 

 instrument. By penetrating power is meant a certain conmiand of 

 the parts of the object which are above or below the plane of the true 

 focus. This property the eye itself possesses in an eminent degree. 

 It furnishes us notions of the relations of parts to each other which 

 cannot be obtained when every point out of an absolutely true focus 

 is utterly confused. Penetrating power can only be satisfactorily 

 secured with objectives of which the magnifying power is low. 

 Resolving power is a name for the degree of efficiency of the instru- 

 ment in separating fine lines or other delicate markings on the surface 

 of the object observed. This quality is only secured by making what 

 is called the angular aperture of the objective large. The angular 

 aperture is the degree of spread wliich can be given to the pencil of 

 rays which the objective will transmit. It is by means of the most 

 oblique rays that the minute tracery upon the surface of an object is 

 made most conspicuous. The reason of this will easily appear from 

 the diagram exhibited. The relative distinctness of such markings, 

 as shown on the scale of a butterfly's wing in this other figure, Avith 

 different angles of aperture, Avill further illustrate this peculiarity. 

 Kesolving power and penetrating power are, for obvious reasons, to 

 a certain extent antagonistic to each other. Ilence, both are not to 

 be sought for in the same objective. 



