60 Capt. Rater’s experiments for determining the 
obtained when the knife edges are viewed as dark objects on 
a light ground ; and on the contrary, the same quantity to 
be added when they are seen as light objects on a dark 
ground. 
From the few experiments I have made, this quantity ap- 
pears to be the same, whatever may be the relative illumina- 
tion of the object and its ground, so long as the difference of 
character is preserved. On the cause of this extraordinary 
fact I can hazard no conjecture, and it remains an interesting 
subject for future investigation. 
Of the expansion of the pendulum. 
The composition of brass is so various, that probably no 
two specimens possess precisely the same rate of expansion. 
It became therefore necessary to determine the expansion of 
the pendulum by direct experiment, instead of adopting the 
conclusions of others, and for this purpose the following 
method was used. A trough of deal was made of a length 
sufficient to receive the bar intended for the pendulum, which 
was placed edgewise in the middle of the trough, being 
secured at one end by wedges on both sides. The bar was 
supported on small pieces of glass tube, serving as rollers to 
prevent friction, and the trough was of the same depth as 
the width of the bar. 
Two transverse lines were drawn near the extremities of 
the edge of the bar, distant from each other 49,5 inches, $nd 
a third line was subsequently drawn one inch beyond. The 
microscopes were placed over the lines, and left, together 
with a thermometer, for twenty four hours previous to the 
experiment. 
The temperature being then registered, and the micro- 
