232 PROCEEDINGS OF THE AMERICAN ACADEMY 



to the varying sensitiveness of the eye, to the effect of moonlight, 

 twilight, &c., and to various other causes, 



A still further simplification of this photometer may be effected by 

 substituting the diurnal motion of the earth for the scale as a measure 

 of the position of the star as regards the wedge. It is only necessary 

 to insert in the field a bar parallel to the edge of the wedge and place 

 it at right angles to the diurnal motion, so that a star in its transit 

 across the field will pass behind the bar and then undergo a continu- 

 ally increasing absorption as it passes towards the thicker portion of 

 the wedge. It will thus grow fainter and fainter, until it finally dis- 

 appears. It is now only necessary to measure the interval of time 

 from the passage behind the bar until the star ceases to be visible, to 

 determine the light. Moreover all stars, whether bright or faint, will 

 pass through the same phases, appearing in turn of the 10, 11, 12, &c., 

 magnitude, until they finally become invisible. For stars of the same 

 declination, the variation in the times will be proportioned to the vari- 

 ations in the thickness of the glass. But since the logarithm of the 

 light transmitted varies as the thickness of the glass, and the stellar 

 naagnitude varies as the logarithm of the light, it follows that the 

 time will vary as the magnitude. For stars of different declinations, 

 the times of traversing a given distance will be proportional to the 

 secant of the declination. If d, d' are the declinations of two stars 

 having magnitudes m and m', and i, t' are tlie times between their 

 transits over the bar and their disappearances, it follows tliat in' — m 

 z=zA{t sec 5 — t' sec 5'). For stars in the same declination calling 

 A sec 5 = -4' we have iv! — m = A! {t — <') . Accordingly the dis- 

 tance of the bar from the edge of the wedge is unimportant, and, as 

 in Professor Pritchard's form of the instrument, it is only necessary 

 to determine the value of a single constant, A. Various methods 

 may be employed to determine this quantity. Professor Pritchard 

 has recommended reducing the aperture of the telescope. Tliis 

 method is open to the objection that the images are enlarged by dif- 

 fraction when the aperture is diminished ; constant errors may thus 

 be introduced. Changing the aperture of a large telescope requires 

 some time, and in the interval the sensibility of the eye may alter. 

 These difficulties are avoided by the following method, which may be 

 employed at any time. Cover the wedge with a diaphi-agm in which 

 are two rectangular apertures, and place a uniformly illuminated sur- 

 face behind it. Bring the two rectangles into contact by a double 

 image prism, and measure their relative light by a Isicol. From 



