^0 Royal Society, 



then it is clear that the quantic is reduced to zero by each of the ope- 

 rations of the entire system, but this property is not by any means 

 confined to the quantic ; and any function having the property in 

 question, i. e. every function which is reduced to zero by each ope- 

 ration of the entire system, is said to be a co variant of the quantic. 

 The definition is afterwards still further generalized, and its connec- 

 tion explained with the methods given, in the memoir ' On Linear 

 Transformations,* Camb. and Dub. Math. Journal, Old Series, t. iv., 

 and New Series, t. i., and the ' Memoire sur les Hyperd<§terminants,' 

 Crelle, t. xxx., and some other theorems given in relation to the 

 subject. The latter part of the memoir relates to the theory of 

 the quantic (*)(j:', y)"*, and to the number of and relations between 

 the CO variants, and as part of such theory to the beautiful law of 

 reciprocity of MM. Sylvester and Hermite. 



May 1 1 . — The Earl of Rosse, President, in the Chair. 



The following paper was read : — " On the relation of the Angular 

 Aperture of the Object-Glasses of Compound Microscopes to their 

 penetrating power and to Oblique Light." By J. W. Griffith, M.D., 

 F.L.S. 



The explanation given by Dr. Goring and others of the advantage 

 of increased angular aperture in microscopic objective- glasses ap- 

 pears to the author to be correct, as applied to the case of opake ob- 

 jects, and accordingly his remarks in the present communication 

 have reference to transparent objects only. 



It is known that delicate markings on a transparent object, such 

 as the valve of a Gyrosigma, may be rendered more distinctly visible 

 by using an object-glass of large aperture, by bringing the mirror to 

 one side, and by placing a central stop jn the object-glass or the con- 

 denser or in both ; the increased distinctness produced in these seve- 

 ral ways being due to the illumination of the object by oblique light. 

 Experiment also shows that the degree of obliquity of the light re- 

 quisite varies with the delicacy or fineness of the markings, being 

 greater as these are more delicate ; so that the finest markings re- 

 quire tbe most oblique light which can possibly be obtained to ren- 

 der them evident, and the angular aperture of the object-glass must 

 necessarily be proportionately large, otherwise none of these oblique 

 rays could enter it. 



If the parts of an object which refract the light are large in pro- 

 portion to the power of the object-glass and of irregular form, they 

 will refract a certain number of rays, so that these cannot enter the 

 object-glass; hence certain parts will become dark, and will map out, as 

 it were, in the image formed of the object, the structural peculiarities 

 of the same. But if the parts are minute, of a curved form and ap- 

 proximatively symmetrical, they will act upon the light transmitted 

 through them in the manner of lenses, and their luminous or dark 

 appearance will vary according to the relation of the foci of these to 

 that of the object-glass. Thus the parts of an object may appear 

 dark and defined, from the refraction of the light out of the field of 

 the microscope ; alsO) from the concentration or dispersion of por- 



