[ 236 ] 

 XXX. Intelligence and Miscellaneous Articles. 



ON THE LIMITS OF THE EFFECTIVE POWER OF MICROSCOPES. 

 BY PROFESSOR HELMHOLTZ. 



A CCORDINGr to a general law of optical instruments, first ad- 

 -^ vanced by Lagrange, the more the magnifying is augmented the 

 narrower become the pencils of rays which pass from a single point 

 of the object through the instrument. The narrower the cones of 

 rays, the less becomes the brightness of the image, and the greater the 

 indistinctness occasioned by entoptic shadows and diffraction. If 

 the magnitude of the smallest perceptible objects is estimated from 

 the distance between each two bright lines which can be recognized 

 as separate from one another, this magnitude may be regarded as 

 equal to that which in the magnified image of the object equals the 

 width of the outer diffraction-fringes of each bright point. This 

 is a quantity dependent only on the angle of divergence of the in- 

 cident rays, and independent of the construction of the instrument. 

 Calling a the angle formed with the axis by the extreme rays of 

 the pencil from the axial point of the object, incident on and passing 

 through the instrument, at their starting-point, \ the wave-length 

 of the light in the medium in which the object is situated, e the 

 magnitude of the smallest recognizable distance on the object, 



e= X 



2 sin a' 



If the rays pass through a plane surface, in air, perpendicular to 

 the axis, and if the values of \ and a referred to air be denoted by 

 X and a , we can also write 



2 sin a Q 

 Our newer immersion microscopes make a nearly equal to a right 

 angle ; then e becomes equal to half the wave-length of the light 

 employed. For the middle greenish yellow light of the greatest 

 brightness we can put 



A = 0-00055 millim., 



6=0-000275 = 3^ millim. 



The more reliable of the newer measurements, especially those made 

 on objects which actually give a broad cone of light, have for their 

 result numbers (as ywi^ J^tUim., Harting) not much greater than 

 that. — Monatsbericht der Icon, jpreuss. Akad. September and October 

 1873, p. 625. 



EXPERIMENTAL RESEARCHES ON NEWTON'S COLOURED RINGS. 

 BY P. DESAINS. 



The experimental verification of the theory of Newton's rings 

 ordinarily consists only in measuring, under one or several inci- 

 dences, the diameters of a certain number of those rings. A good 

 micrometric screw permits the measurements to be made very con- 

 veniently and with much rigour. A screw can also be employed 

 for measuring directly the quantity by which the distance between 



