4 The Ohio Journal oj Science [Vol. XVI, No. 1, 



Some four years before the above quotations were written, 

 the author started to work up a course in Optics which should 

 aim, not only to give to the student a knowledge of the funda- 

 mental theory of lenses, but should also appl}^ those principles 

 to the methods of optical design and thus enable him to compute 

 the curves of the component lenses of a photographic objective. 

 This has now been fairly well worked out and is given in the 

 Arts college under the official titles "Astronomy, 107, 108, 109 

 and 110." The basis of this course is "A System of Applied 

 Optics," by H. Dennis Taylor, the inventor of the Cooke lens. 

 This splendid volume develops, from the standpoint of geometric 

 optics, a complete discussion of the formation of an image by a 

 combination of any number of lenses, but does not apply the 

 methods and formulae there developed to the actual design 

 of a photographic objective. The writer of this paper was, 

 therefore, compelled to work out this part of the theory for 

 himself and, as he had always felt that all mathematics should 

 ultimately end in arithmetic and that all arithmetic should 

 ultimately end in doing something, he resolved at the outset 

 that the course should end in laboratory work in the actual 

 computation, grinding and polishing of lenses. As to how well 

 this has succeeded, I will let the illustrations which accompany 

 this article speak for themselves. Suffice it to say that the 

 half tone cuts were made from five by seven enlargements from 

 negatives, one and three quarters by two and one-eighth inches, 

 taken with a lens designed and built at this observatory and 

 working at an aperture of F six. A peculiar feature of this lens 

 is that it is composed of four lenses all cut from the same piece 

 of crown glass. This lens beautifully illustrates the importance 

 of adding to the theoretical side of the course, the practical work 

 in the laboratory in construction and testing as this lens, 

 though in the main satisfactory, has one serious defect and 

 a defect which is very instructive in that it shows that at a certain 

 point in the design, the theory was weak and needed to be 

 extended and enlarged. It should be stated that this theoretical 

 investigation is now completed and ready to be put to the test 

 of practice. 



This Observatory possesses a well equipped instrument 

 shop, which was used for the practical side of this work and it 

 has seemed to me that a description of how we used the ordinary 

 tools of a machine shop, of what special appliances we were 



