Ei. B, Hunt on the Nature of Forces. — 241 
—rdzr 

and dr= » also y:dy::«r2:2(r+dr)?—zr?. Hence by re- 
duction and by neglecting dr? as an infinitely small quantity of 
—2ydr —2yde —2y'dr 
Lin dc pjt@mee. s Sapiee 
which is the expresssion above found as the differential of a New- 
tonian force. The signs of dz, dy and dr depend on the direc- 
tion of the motion of the receptive surface. 
It will be seen by inspecting the above, that not only is New- 
ton’s law derived from this consideration of ray-reception, but 
that the differential equation of that law expresses simply the 
telation between the differential of distance and that of ray recep- 
_ ton, is law also involves the two assumptions which for all 
appreciable distances are entirely admissible, though not at all so 
for extremely small distances: first, that the effect of ray ob- 
liquity for the same receiving disc may be neglected, and second, 
that the diffusion over the disc may be regarded as uniform. By 
substituting spherical atoms for the disc, we at once obtain the 
case of nature, when the question is of actions between sensible 
masses, 


the second order, we obtain dy= 
f 
If we construct the curve of the equation y=% we find that 
the differentials of force and distance are always equal in con- 
struction. The law of the increment is only satisfied by that 
cutve which cuts the line through the origin making an angle of 
45° With the two axes, in the point whose ordinate equals the 
tadius of disc. Thus the radius of the receptive disc or ato 
determines the particular characteristic curve of relation between 
orce and distance: a curve which is the same for a homogene- 
°us sphere of atoms as for a single component atom. 
i y : 
Passing to the more general function y=". and differentia 
—ny'dx 
seta? in which if we substitute y for < 
ting, we obtain dy = 

Y. If we suppose now that all the curves 
xv 
Corresponding to any particular value of n are duly constructed, 
and if a ase line rama the origin make the angle z with the 
We obtain dy=—ndz 
; y 
"xis of x then “— tang, a= a constant; or in dy=—ndz"» we 
Stcoxp Sates, Vol XVII, No. 53—Sept., 1854. 31 
