1882.] 



MICROSCOPICAL JOURNAL. 



69 



the results of using the telescopic 

 measure are so unsatisfactory as to be 

 practically useless. Third, that the 

 measure of the angular aperture of any 

 objective is the angle at the principal 

 focus for rays of the convergence with- 

 in the tube for which the lens is correct- 

 ed, keeping in view the fact that this 

 principal focus is not at the object, 

 but between it and the lens. Fourth, 

 that this measurement should be 

 taken also with a tube of the length, 

 and ocular of the diameter, for which 

 the objective was constructed. 



If these conclusions are found to 

 be sound, it will not be difficult to 

 make the practical application. The 

 angle of any objective may of course 

 be easily computed by any one who 

 has the formula on which it is made; 

 but the microscopist will be satisfied 

 with methods of measurement that 

 are approximately true. If, in high 

 powers the telescopic angle of field 

 does not differ sensibly from the angle 

 at the principal focus of the micro- 

 scope, the common method may still 

 be used. In low powers the experi- 

 ments herein detailed show that by 

 the aid of a common table of chords 

 or of tangents, and a couple of simple 

 measurements, the angle may be quick- 

 ly determined. I will only add that 

 whilst choosing to make use of the 

 pin-hole diaphragm in the former of 

 these experiments because the circu- 

 lar field gave a stricter application of 

 theory, and there was then no refrac- 

 tion of rays between the object and 

 the lens, yet the observations were 

 repeated with a slit .00 15 -inch in 

 width, and with the same results as 

 above described. Even with the three- 

 inch objective the whole field was il- 

 luminated and was of full-size, though 

 the light was much reduced. 



It may be worth while to recollect 

 that in the method of measuring the 

 angles of objectives used some years 

 ago by Mr. Tolles, Dr. Woodward 

 and others, rays from the lamp were 

 thrown down the microscope tube, and 

 their crossing at the principal focus 

 was ocularly demonstrated and mea- 



sured in a square of crown-glass with 

 ground surfaces. This was in true 

 accordance with the principles stated 

 above; though, when parallel rays 

 were used, the angle attributed to the 

 objective was evidently less than if the 

 rays of proper convergence (3' /and a' 

 I' fig. 24) were used. The fact that this 

 was a different method with different 

 results from that in which the tele- 

 scopic field is made the criterion 

 of the angle, does not seem to have 

 attracted attention. In the opinion 

 of the writer, the facts which have 

 been stated and the proper conclu- 

 sions from them, only recall us to the 

 original and elementary idea of the 

 aperture of a single lens, namely, the 

 angle formed at the principal focus 

 by the emergent refracted rays which 

 have passed the lens, the convergence 

 or divergence of these rays, when in- 

 cident upon the other side of the 

 lens, being given. Each point in the 

 object from ^ to <^ is the apex of a 

 pencil of rays, all of different angles. 

 In this infinity of pencils it would 

 appear arbitrary to select one as of 

 special significance. The boundary 

 of the whole cone at the principal 

 focus, however, is that which, from 

 the beginning of optical investigation 

 has been treated as one of the funda- 

 mental elements in the discussion of 

 the properties of lenses. 



Microscopical Laboratories. 



BY PROF. J. W. S. ARNOLD. 



The articles in the February and 

 March numbers of your valuable 

 Journal upon the subject of micro- 

 scopical laboratories are of especial 

 interest to me, as, for nearly fifteen 

 years, I have been constantly teach- 

 ing practical histology and allied sub- 

 jects. It has been my fortune to 

 come in contact with students of all 

 ages, and from almost every part of the 

 world. The young and the old, the 

 uninitiated and the advanced student 

 pursuing special investigation, have 

 been under my care and supervision 



