28 
polished surface is rapidly moved, as when a 
wheel with a polished spoke is rapidly rotated. 
Another interesting example in loci of brilliant 
points is that of a circular saw which has been 
polished with emery in a lathe and thus re- 
ceived a great number of concentric circular 
scratches. The locus of the brilliant points of 
this family of scratches was shown in this paper 
to be a curve of the fourth degree. In the 
special case when the point source of light and 
the eye of the observer (the point recipient) are 
in a plane through the axis of the saw, the 
curve degenerates into a circle and two coinci- 
dent straight lines. A photograph of the saw 
curve has been taken in which the optical cen- 
ter of the camera lens is the point recipient. 
Other interesting facts and a number of geo- 
metrical constructions were also given in this 
paper. 
Three persons were elected to active member- 
ship in the Academy. 
WILLIAM TRELEASE, 
Recording Secretary. 
DISCUSSION AND CORRESPONDENCE. 
THE ELECTRICAL THEORY OF GRAVITATION. 
Ir is, perhaps, by the severe but impartial 
criticism of his work that the greatest of all 
possible obligations is laid upon the scientific 
investigator, for thereby his theories are purged 
of what may be incorrect or trivial, and that 
part of them which may be true is compacted 
and separated from what might otherwise hide 
its value, and cause it to be neglected. 
Unfortunately I have been unable to profit 
as much as I felt I had a right to expect from 
Dr. Franklin’s letter, ScrencE, December 7th, 
as he has apparently been unable to find time 
for that careful examination and study which 
the subject, aside from the paper, demands. It 
is a matter of regret, also, in view of Dr. Frank- 
lin’s admirable qualifications for dealing with 
the question, that he should have directed his 
criticism, in every single case, against theories 
which are the exact opposite of those which I 
hold, and which I have explicitly set forth in 
the paper referred to. 
But though Dr. Franklin has with some slight 
lack of courtesy invited his readers to ‘ignore’ 
SCIENCE. 
[N.S. Vou. XIII. No. 314. 
my remarks on the methods by which my theory 
was deduced, I shall not return the compliment 
by ‘ignoring’ his criticism, because it contains 
a number of very serious misstatements which 
should be promptly pointed out, as otherwise 
they may become sources of error. 
To consider, first, his criticism of my paper, 
he says (par. 1): 
‘Professor Fessenden in a recent number 
of SCIENCE discusses the nature and velocity of 
gravitation. There is, no doubt, something of 
value in Professor Fessenden’s suggestions and 
much that is new. However, the explanation 
of gravitation which Professor Fessenden offers 
is by no means so adequate as would appear 
from Professor Fessenden’s discussion.”’ 
On careful perusal we find his reasons for 
making this statement to be three in number. 
In regard to the first he says: 
“Tf we admit that the diminution of volume 
of the ether at each point is proportional to the 
resultant intensity of the electric field, then 
the part of the energy which depends upon 
diminution of volume cannot be separated in 
its effects from the part of the energy which 
depends upon the shearing distortion, inasmuch 
as both are proportional to the square of the 
resultant field intensity. Therefore a diminu- 
tion of volume of the ether could not explain 
gravitation, but would only be involved in the 
explanation of ordinary electrical attraction 
and repulsion.’’ 
But, so far from my theory implying a diminu- 
tion of the density of the ether at each point pro- 
portional to the resultant field intensity, F, I have 
expressly stated that the change of density is pro- 
portional to F?, as witness the following extracts 
from my paper: 
“Whilst the one which is a density must de- 
crease with the second power of the correspond- 
ing intensity.” 
“‘And hence, as my experiments prove, the 
change in density is proportional to the square 
of the electric intensity.’’ 
As a matter of fact, even a cursory exami- 
nation of my paper will show that the whole 
point of my argument rests on the fact that it 
is the second and not the first power which is 
involved. For the qualitative equation is 
ULS= TIL? X MILT, 
