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XXIV. On Spherical Motion. By the Rev. Charles Wildborc ; 
communicated by Earl Stanhope, F. R. S. 
Read June 24, 1790. 
T HIS Paper, which has coft me much pains in patient 
inveftigation, is occalioned by that of Mr. Landen, in 
the Philofophical Tranfadions, Vol. LXXV. Part II. I am 
no ftranger to this gentleman’s great judgement and abilities in 
thefe abftrufe {peculations, but have a very high opinion of 
both ; yet I could not but think it ftrange, that two fuch ma- 
thematician^ as M. d’Alembert and M. L. Euler Ihould 
both follow one another on the fame fubjed, both agree, and 
Rill not be right. I therefore refolved to try to dive to the 
bottom of their folutions, which thofe who are acquainted with 
the fubject know to be no light talk ; and, if poffible, to give 
the folution, independent of the perplexing confideration of a 
momentary axis changing its place both in the body and in 
abfolute fpace every inftant ; and which I look upon as not ab- 
folutely effential to the determination of the body’s motion. 
But finding that I could not thus fo readily Ihew the agree- 
ment or difagreement of my conclufions with thofe of the gen- 
tlemen who have preceded me in this enquiry; I have alfo 
added the inveftigation of the properties of this axis. And I 
fuppole it will be found, that 1 have added many properties 
unknown before, or at leaft unnoticed by any of them. 
M. Landen’s 
