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XIV. — Further Observations on the Construction of the Prisms of M. 

 Nachet, for the Oblique Illumination of Transparent Objects on 

 Stage of the Microscope. By George Shadbolt, Esq. 



(Delivered verbally at the meeting of the Society in April, 1850). 



At the last meeting of this Society, which took place in March, I 

 had the honor of reading a short paper, descriptive of M. Nachet's 

 prisms, in wliich I put forth certain formulae for their construction, 

 but omitted the mathematical details of the mode in which these 

 formulae had been computed, from the conviction of the uninteresting 

 nature of such a demonstration to the great bulk of the members. 

 The correctness of them having, however, been called in question 

 (in perfect good feeling), or rather the propriety of adopting any 

 general formulae, I am compelled to trouble you with the details 

 alluded to, but will endeavour to do so with all possible perspicuity. 



One of the objections made to my formulae was, that even if they 

 were applicable to the ordinary glass, they might not be to every 

 kind of glass that might be made. My answer is, I only designed 

 the observations to apply to crown-glass, and any of greater density, 

 which, in fact, includes all in common use ; and I readily admit that 

 a glass might possibly be made which would not be applicable, in 

 consequence of its density being too low, but I do not see how this 

 affects the question. Another objection, relative to making the angle, 

 q, figs. 1 and 2, always an angle of forty-five degrees, I shall answer 

 in the course of my demonstration. 



Let the line z A, figs. 3, 4, 5, 6, represent the course of a ray 

 direct from the mirror to the object at A, on the stage of a 

 microscope, and let y A represent the course of a ray falling 

 obliquely at the angle desired ; then it is a sine qua non, that the 

 course of the ray must be diverted from z A to y A, by two internal 

 reflections in the prism. It is also necessary that two of the planes 

 of the prism, viz., d q and c b, figs. 1 and 2, be at right angles 

 respectively to y A and z A, in order that the rays may enter and 

 emerge perpendicularly, so as to obviate any refraction and conse- 

 quent dispersion of the light. It therefore only remains to determine 

 the relative inclination of the two lateral planes of the prism, with 

 their respective dimensions, and the focus of the lens required. If 

 the focus and aperture of the lens is first determined, the dimensions 

 of the various planes will be dependent thereon. 



It is a well-known law in optics, that when a ray of light is 



