Spherical Motion . 5° 9 
the variation of A but are denoted by the fame quantities, 
whether e be conftant or variable ; which conclufion, and alfo 
the values of the forces themfelves, is perfedtly agreeable to 
what is brought out by Mr Landen, by a method fo very 
different, in the Philofophical Tranlaetions for 1777. 
But it is here carefully to be noted, that thefe are not motive 
forces, but accelerative ones ; for no notice whatever is yet 
taken of the internal ftructure of the revolving globe ; but the 
expreffions hold true, be that ftruaure what it will : if it be 
fuch that one and the fame quantity, drawn into each accele- 
rating force, will give the correfpondent motive one, then are 
the motive forces proportional to the accelerative ones, but 
otherwife not. It may here alfo be obferved, that it is quite 
conformable to nature, that thefe accelerating forces fhouid be 
exprefied by the fame quantities whether e be conftant or va- 
riable ; for thefe forces, adding at the pole of the natural axis, 
cannot poffibly have any effeft upon the velocity round it. But 
it is not hence by any means to be concluded, that the velo- 
city about the axis is therefore conftant ; becaufe thefe are not, 
in general, the only accelerating forces that add upon the body, 
but there is alfo a third accelerating force whofe value Is 
arifing from the different variability of x, y, and z, and 
which cannot vanifh except @x + yy + $z = o, it therefoie can 
only vanifh in particular cafes. 
If the equation e~ @x + yy + $z be fquared, there will 
thence arife after due ordering e z = x +f + z‘ - e X 
( yl Q - where the member which is 
drawn into e keeps its form whether e be conftant or variable, 
but by no means will x z +y+z\ after due fubftitution, do fo 
2 too. 
D 
