THE MICROSCOPE. 99 



to the full aperture of the objective; and this circle also should be 

 drawn upon the paper. The objective should then be removed, 

 and a well ruled micrometer placed upon the stage and drawn upon 

 the paper. The diameters of the two circles may now be obtained 

 in the usual way of measuring objects. The measurements are 

 best made in thousandths of an inch. If the diameter of the larger 

 circle now be divided by that of the smaller one, the numerical 

 aperture will be expressed by the quotient. This applies only to 

 those objectives which have a numerical aperture of more 

 than roo. 



If the magnifying power of the objective be measured, by the 

 rule of proportion the proper acting diameter of the back lens 

 for a numerical value of roo of any objective whose magnifying 

 power is known, may be ascertained; and even though it have far 

 less than 180 air, its numerical aperture may be obtained by 

 dividing this theoretical diameter by the acting diameter of the back 

 lens. The measurements of the diameters should be very accurately 

 made, otherwise the results will vary largely from the truth. The 

 use of the hemispherical lens is only required when the aperture of 

 the objective is more than roo. From the numerical aperture, the 

 angle in any immersion medium may be calculated by dividing 

 the numerical aperture by the refractive index of the fluid used, 

 which gives the sine of half the angle of aperture. The angle 

 which corresponds to this sine may then be obtained by reference 

 to a table of natural sines, which, after being multiplied by two, 

 gives the angle desired. 



SENSITIVE DENTINE. 



BY A. M. ROSS, M. D. 



ALMOST daily is the fact demonstrated in practice by the opera- 

 tor upon human teeth that the soft dentine immediately over- 

 lying the sound structure in the carious cavity, is, in many cases 

 more exquisitely sensitive than the sound structure itself. The ex- 

 cavator or sharp engine bur may be used with more freedom and 

 produce less pain after advancing beyond the softened structure. 

 This is found to be true in such a large majority of cases, by the ob- 

 serving dentist that he is sometimes led to believe that there is an 



