370 Mr. J. S. Ames on the Concave Grating 



by r and /i, on which the various spectra are brought to a 

 focus ; and there is a second curve passing through K, v such 

 that, if the source of light be placed at any point of it, the 

 spectra will be brought to focus along the curve r, /m. These 

 two curves are then conjugate, and their properties have been 

 discussed by Mr. Baily in the Philosophical Magazine for 1883 

 (vol. XV. p. 183). 



If we make R=pcosv («'. e. place the slit on the circle 

 whose diameter is the radius of curvature of the grating), 

 r^=p cos fi ; that is, the two focal curves coincide. This case 

 is shown in fig. II. 



As is well known, this arrangement is mechanically secured 

 by placing the slit at the intersection of two beams set at 

 right angles, on which are ways to carry the grating and eye- 

 piece, these two being kept at a constant distance p apart by 

 an iron girder. Thus, in fig. III. the slit is at A, the grating 

 at B, and the eyepiece or camera at C. 



The reasons for putting the eyepiece at C, where /i = 0, are 

 easily found. Suppose the micrometer-eyepiece were placed 

 at D (fig. IV.), tangent to the focal circle. Let the eyepiece be 

 displaced along the tangent by an amount DD' or " a," 



a= ^ sin 2 (fi — $), 



da= one turn of micrometer, 

 = p Gos, 2 (/J, — 6)dfi = A. Z. ' 



But by theory of diffraction (see Ra3deigh, Encyc. Brit., 

 Wave Theory of Light, vol. xxiv. p. 437), 



A = -Tj (sin V + sm yu,), 



where a is grating- space and N the order of spectrum ; 



,^ (o , Aci) cos u 



,', aA,= =sj cos /u. rt/W. = :^- 



N ^^~N/3 cos 2(^-6/) • 



Or, if a photographic plate, bent to radius pj'l, were placed at 

 D, one scale-division A along plate 



(?\ = ^ cos fi d/j,, 



Aft) 



= ^cos/.. 



Now, if ^ = (i. e. if the micrometer-eyepiece or the camera- 



