H. M. Parkhurst on the Photo-mapper. 39 
placed parallel to the axis of the telescope, pointing toward 
the object-glass. The further end of this magnitude-bar is con- 
nected at right angles by a connecting-rod with universal joints, 
with the upright arm of a lever, the lower arm of which is the 
lower supporting-bar. The length of this upright arm and of 
the magnitude-bar must be equal, In photo-mapping I place 
the prism always in the meridian, to avoid the complicated ad- 
justments which would be necessary if its position were to be 
varied, 
or south 
being thus equalized with that of a standard artificial star, or 
extinguished, as the case may be, a magnitude mark is impressed 
bes mapped in its proper position, 
and the distance upon the map, of the magnitude mark from 
A perpendicular plate, with a circular hole through which the 
connecting-rod passes, furnishes a convenient point from which 
to measure with dividers when the instrument is used without 
the mapper. a 
Thus far I have spoken of the “cone” of rays, as if the aper- 
ture were circular. If it were so, the scale of magnitudes 
would not be one of equal parts. It may be made one of equal 
parts by placing over the object-glass an outer dia m with 
an aperture of suitable form, and making the aperture of the 
inner diaphragm of corresponding form. : a 
Let «=2-5[y] be the equation of a logarithmic curve. Then, 
the area between any two ordinates of that curve will be 
25MAy; M being Modulus. Constructing for the object-glass 
of 6 inches aperture a diaphragm bounded by four such curves, 
with values of « ranci i } 
right and left, and a similar inner diaphragm of one-eighth the 
Piragm will leave an area corresponding to stars exactly one 
magnitude smaller. The motion of he star-point will be one- 
Seventh greater, and of the star-key still greater, according to 
the seale of the map. ee 
But while the object-glass is limited, the inner aperture may 
