Rotatory Motion of Bodies. 13 
method applied to the case of bodies of any figure. A leading 
difference in the results was this: that while according to Euler, 
Dalembert, &c. in an irregular body not acted on by any extra- 
neous forces, the angular velocity about the instantaneous axis is 
variable, as well as the position of the axis itself; Mr. Landen 
found, that the angular velocity is constant, and that the instanta- 
neous axis in changing its place in the body, can assume only a 
series of positions, for all of which the rotatory inertia is the 
same; so that the trace of the instantaneous pole upon a con- 
centric spherical surface would generally be an oval, and its 
projection an ellipse or hyperbola. In the second part of his 
“© Mathematical Memoirs,’ published in 1789, he resumed the 
subject, and having occasion to establish propositions analogous 
to those in Euler’s “ Theorta,” the most regular treatise on the 
subject which had then appeared, he obtains theorems at 
variance with those of that author, and expresses rather 
strongly his astonishment, that Mathematicians so celebrated as 
his opponents, could fall into mistakes so gross. His death, 
which took place shortly afterwards, closed the controversy ; 
but it is said that his opinions remained unaltered. Mr. Wild- 
bore, in the Philosophical Transactions for 1790, re-considered 
the subject in a new point of view, and declared against Landen ; 
and since that time it does not appear that any person has re- 
vived his ideas, and the foreign elementary treatises all proceed 
according to the method which Mr. Landen declared erroneous. 
Perhaps, therefore, it may seem that the question is already 
sufliciently settled, and that there is no farther necessity to prove 
the truth of the conclusions of Euler, Dalembert, Lagrange, &c. 
As, however, the subject is both important and curious, and as 
Mr. Landen’s mathematical talents are deservedly highly esti- 
mated, I may be excused for making an attempt to place in a 
clearer point of view the falsity of his results. The Memoir ef 
