Mr. landen’s new Theory of 
diameter of the equator of the fpheroid, with the angu- 
lar velocity d y likewife meafnred at the distance r from, 
that diameter. Upon receiving fuch impulfe,the fpheroid 
will take a new axis of motion, which will be a momen- 
tary one; fuppofe fuch new axis to be p c.7t a; . Then the 
particles of the fpheroid being urged (or having a ten- 
dency) to turn about that axis with the angular velocity 
\Jc 2 +d z y (which we will denote by e) their joint centri- 
fugal force will fo urge the fpheroid to turn about that 
diameter of the equator which fhall be at right angles to 
the momentary axis p err, that the accelerative force of 
the point d of the equator to turn it about the faid dia- 
meter according to the order of the letters d q_e will (as 
appears by what is proved in art. i . and in the Appendix 
annexed hereto) be = y x prpj. or ^ x ^ ^ according as 
b is lefs or greater than r: and it follows from hence and 
what is proved in art. 3. and 4, that v, the angular velo- 
city (at the diftance r from c) with which the momen- 
tary pole p will change its place, will accordingly be = 
cd r*—b z cd r-—r 
* K r * + b* ° r t V + *** 
(c) To find the pofition of this axis fee art. 1, by which the fine of the angle 
dr 
oc p (to the radius r) is.found = — . 
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