AND TRANSMITTED BY CERTAIN KINDS OF GLASS. 
249 
to interpose the substance in question between one of the mirrors and the photometer, 
and determine, by means of the photometer, the new position of equality. 
But, as such assumptions might be erroneous, the experiments were actually made in 
the following manner :—First, the glass plate was fixed on one side of the photometer, 
whose position was altered until both papers appeared equally bright; six readings 
having been thus made, the glass was then placed on the other side, and six more 
readings made. The glass was then replaced in its original position, and six more 
readings made, and so on. After thirty-six readings the photometer was reversed, 
and another set of thirty-six readings made in the same manner. In making the 
readings, the photometer was first placed too much to the right, and then moved to 
the left till the point at which the illumination was equal was reached ; it was then 
pushed to the left, and gradually moved back to the right, till the papers appeared 
equally bright, being thus brought to the position of equality alternately from one 
side and from the other. 
In order to prevent the possibility of any light reflected from the edges of the 
plates reaching the photometer, the plates were placed either close to it or close to 
one of the screens. For two sets of readings the glass was placed against the opening 
in the box enclosing the photometer, and for one set against the opening in the 
screen, except in the case of the thick piece of flint glass, which was too large and 
heavy to be carried by the block on which the photometer rested, and which was 
therefore always placed against one of the screens. The position of the glass made 
no ditterence in the measurements. 
The percentage transmitted of light falling upon the glass was calculated in the 
following manner: — Half the difiPerence between the means of each set of six observa¬ 
tions with the plate on either side of the photometer was taken ; half the distance 
between the two mirrors, plus or minus this quantity, together with the distance 
between the lamp and the mirrors, gave the two distances from the lamjo at which 
there was equality of illumination. The mirrors being 200 cm. apart and the lamp at a 
horizontal distance of 20 cm, from the middle of the line which joined their centres, 
the half difference wms added to or subtracted from 202.^^ 
Calling these distances a and 6, a being the lesser, a correction x had to be made in 
the value of a for the optical shortening of the path of the light due to its passage 
through the glass; this was calculated by the ordinary formula x = e{l — l/bi), 
where e is the thickness of the plate, and n its refractive index, the distance of the 
lamp from the glass being sufliciently great to allow the formula for perpendicular 
incidence to be used without introducing any sensible error. 
The percentage amount of light transmitted was given by the expression 
100 [a-xflb\ 
* Strictly speaking, the geometrical, and not the arithmetical, mean of the readings should have been 
taken, as the intensity of light vai-ies inversely as the square of the distance. Calling the two sources of 
light, to which the lamp and mirrors were equivalent, m and n, and the distance between them x, the 
MDCCCLXXXIX.—A. 2 K 
