103 
EXPLANATORY NOTES ON PROF. A. G. GREENHILL’S PAPER 
“ON THE ROTATION REQUIRED FOR THE STABILITY OF 
AN ELONGATED PROJECTILE.” 
BY 
CAPTAIN J. P. CUNDILL, R.A. 
The valuable and interesting paper published by Prof. G-reenhill in 
the R.A. Institution “ Proceedings ” for September, 1879 (Yol. X., 
No. 7), has attracted much attention. 
It has occurred to me that, seeing the intricacy of the subject, and 
the high nature of the mathematical reasoning involved in its solution, 
without attempting to go into the more recondite parts of the rea¬ 
soning, it might be useful to give a few explanatory notes pointing 
out the hypotheses assumed, the problem to be investigated, and 
the conclusions arrived at. The notes have been submitted to 
Prof. Greenhill, and, indeed, are in great part given in his own words, 
noted down by himself on an occasion of our going through his article 
together, with a view to the production of this short paper. 
First, then, as to the hypotheses assumed. A body having the 
form of a prolafe spheroid is supposed to move in a frictionless and 
homogeneous (i.e. incompressible) medium in the direction of its 
longer axis. Gravity is neglected, and hence the curvature of the 
trajectory and the “ drift ” do not enter into the scope of the paper. 
In the earlier parts of the reasoning the body is supposed to be solid, 
but suitable adaptations are subsequently made which allow the special 
cases of hollow bodies, or shells, to be considered, and numerical cal¬ 
culations to be made for them. It is necessary to assume that the 
body has a spheroidal form, and that the medium is frictionless and 
incompressible; as hitherto mathematicians have succeeded in solving 
the problem of discovering the “ stream lines,” and the consequent 
state of motion of the surrounding medium, only in the case of an 
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