ee eee 
P. E. Chase— Velocity of Primitive Undulation. 367 
resulting laws of curvilinear motion under combined tangential 
and focal impulses, are all simple corollaries from the hypothe- 
sis of a universally oscillating, perfectly elastic, imponderable, 
material ether, which would necessarily establish special sys- 
tems of centripetal and centrifugal undulations about every 
center of gross inertia. e may, therefore, reasonably see 
for the value of the hypothetical constant velocity, and in 
order that our terms may all be strictly comparable, we will 
look merely at radial action, either toward the sun’s center, or 
toward the central sun. Let 
2F=M=modulus of Newtonian ether=height of a homoge- 
neous ethereal atmosphere, at sun’s surface, which would 
propagate undulations, or motion toward a vacuum, with 
the primitive constant velocity=2x virtual fall, which 
would produce the same velocity. 
2r=diameter of sun at any given time, either actual, or when 
homogeneously expanded or contracted to any point in 
space ; r,=nr, being the present radius, and r, the radial 
~ unit. 
2r,=v,=diameter of sun at which the ethereal and gravitating 
motions would all be equal, and 2F would=2r=v,=v,= 
v,,=v,,,=2f; v, being the limit of possible ethereal ve- 
locity = primitive constant velocity, expressed in the unit 
of time of traversing 2r,. 
1 =Wigr=2, |4— velocity communicated by infinite fall to 
sun’s surface, (present, past or future; actual, expanded 
or contracted). 
2 
Uv, = == mean velocity of grand-central undulation ac- 
wT 
cordant with vp, (vp being superficial equatorial velocity, 
and ¢ being time of solar rotation). 
U,,, = 2f=9f 1? =g = gf =2r , = falling velocity communicated, 
a 
parabolic wave. 
2 v 2 v 3 v 2 . 
= tt sand we have the following geomet- 
o> oF 2 ne 66 
rical series : 
M wr? M, =2r,n* =473800 r, 
— org — =2r ni = O1SS*, 
2r or 27x20 Or yn = ar, 
comer =<Or nit =r, 248: 
v, ore v, =2r.n® =r,+118450 
