1897-98-] Microscopy and some of its Uses. 313 



microscopy because one is dissatisfied with a mere stock of 

 scientific phrases, and wants rather to have vivid impressions 

 of scientific facts — because one has a desire to face the great 

 problem of life and its relations. This course has the singular 

 merit of being quite equal to the other from an aesthetic point 

 of view in regard to the beauty of the objects contemplated, 

 and furnishes besides an extremely grand and inexhaustible 

 source of interest. 



Many persons succeed fairly well in both these courses 

 with but little previous scientific knowledge. But previous 

 scientific knowledge is a great advantage, especially in the 

 second course. Indeed every microscopist should know a 

 little of the natural sciences, and at least as much of mathe- 

 matics up to trigonometry as can be learned from the articles 

 of an encyclopaedia. This is absolutely necessary if one 

 aspires to be an intelligent student. Opinions about micro- 

 scopes and lenses are often unscientific, and even mislead- 

 ing, and much mixed up with the personal equation : it is 

 therefore highly important that the student should be able, 

 concurrently with the use of the microscope, to make a 

 thorough study of its structure and of the properties of lenses, 

 and to understand the function of angle or aperture in an 

 objective, and generally to think and act for himself. 



It is further desirable that the student should have or 

 acquire some little mathematical knowledge to enable him to 

 appreciate the theories of Professor Abbe, which are fully 

 expounded in the second chapter of Carpenter, and which 

 form the most considerable addition to modern microscopic 

 science. Before Abbe's time the part aperture plays in an 

 objective was not well understood. The first part of his 

 theory put this matter on a scientific and clear basis. Agree- 

 ing that the rays of light from an object under the microscope 

 take the form of a cone of which the front lens is the base, 

 the vertical section of this cone gives an equal-sided triangle 

 which measures the angle of the objective, and gives one of 

 the factors. Bemembering next that different media, such as 

 glass, water, air, &c, refract light differently, and that com- 

 parison gives the index of refraction of a medium, we get the 

 other factor, and the merit of Abbe's researches consisted in 

 connecting these two factors — in showing; that in all cases the 



