On Concave Gratings for Optical Purposes. 197 
the edge of the plate ; in the two last-mentioned cases, the 
distribution corresponding to a diminution of pressure. 
TTe see from these experiments that the nature of the 
electricity produced is not dependent upon the particular 
method by which a local heating or warming is produced, 
but depends essentially upon the position in the crystal of the 
point where these changes in temperature take place. From 
the result that heating the peripheral portions of the plate and 
heating the central portions produce opposite electrical effects, 
I am disposed to draw a conclusion, which indeed has not yet 
been experimentally demonstrated but which seems to me 
tolerably safe. If we suppose it possible to warm a plate so 
uniformly that no perceptible differences of temperature or 
tensions should be produced, then I believe that this heating 
would produce no electricity or relatively very little, although 
the particles of the plate suffer considerable displacement 
amongst themselves. If, now, we consider that even very 
small displacements of the particles produce very considerable 
quantities of electricity, if these displacements are accompanied 
by changes of tension in the crystal (as is the case, for 
example, with irregular heating of a plate), the assumption 
seems to be justified that change of temperature and position 
of the particles in itself produces no electricity, but that, on the 
other hand, the real cause of the evolution of electricity is to 
be found in changes of tension. 
In what has been described I have made a first attempt to 
explain the electricity produced in cpiartz by change of tem- 
perature as due to stress produced in the crystal. I am well 
aware that the explanation given in the separate cases is here 
and there defective, and that further investigations are neces- 
sary in order to establish the exact connexion between changes 
of temperature and evolution of electricity. 
Giessen, March 20, 1883. 
XXIX. On Concave Gratings for Optical Purposes. By 
Hexet A. Rowland, Professor of Physics, Johns Hopkins 
University, Baltimore* '. 
General Theory. 
HAYIXG- recently completed a very successful machine 
for ruling gratings, my attention was naturally called 
to the effect of irregularity in the form and position of the 
* An abstract of this Paper with some other matter was given at the 
Physical Society of London in ^November last, the Paper being in my 
hand in its present shape at that time. As I wished to make some addi- 
