DIFFERENTIAL EQUATIONS OF DYNAMICS. 
215 
In making the observation the telescope would be set on the 
desired star before the meridian ; the HA observer would give the 
signal when the plate should be uncovered and then record on the 
chronograph the time that each division of the circle passed the 
microscope. When done he would give the signal for covering the 
plate and its reversal, and then repeat the observation in that position 
as before. Now, since the graduated circle would move steadily on 
without the slightest vibration even under the high power microscone, 
he would be able to determine the HA with much greater accuracy 
than is possible in the ordinary transit circle, and that motion being 
always at the same rate, even for stars close to the pole, the observer 
would be able to record the HA with extreme accuracy for stars in all 
declinations. 
I have, I think, said sufficient to place before you a fair outline 
of the instrument and the method of using it ; to make this complete 
in every detail would require a small volume, and is not necessary. 
If I have demonstrated the principles involved, and I think I have 
done so, my present purpose will he served, and if my estimate of the 
quality of the work which would be done with this instrument is 
correct, the design for it will be all the better for discussion. 
I would only add that the photographic field might be two 
degrees, and that there would be two images of any stars, save the 
guide star, that might be in the photographic field, and their positions 
relative to the guide star would be determined with the needful 
accuracy by measurement. With the 131 inches objectives used for 
the star chart we can easily get a hard round image of an eleventh mag- 
nitude star in one minute with increased experience in manufacture ; 
and with J ena glass it is fair to assume that star images would he 
smaller and better defined, and measurement more accurate than it is 
now, and even now they can be made good enough to justify the 
making of the photographic transit circle here described. 
4— ON A FORM OF THE DIFFERENTIAL EQUATIONS OF 
DYNAMICS. 
By Sir ROBERT BALL , LL.D ., F.R.S . , Lowndean Professor of Astronomy and 
Geometry at Cambridge . 
I refer to a series of memoirs in the Royal Irish Academy’s 
Transactions for the explanation of the terms and notation employed 
in this paper. 
Euler’s well-known equations for the rotation of a rigid body 
about a fixed point are but a particular case of a much more general 
theorem, which applies to any dynamical system whatever. 
I shall take, as the screw-chains of reference, the n principal 
screw-chains of inertia, the material system being of any type whatever 
and having n degrees of freedom. 
Ret f, . . f n he the components of the acting forces expressed as 
wrench-chains on the n wrench-chains of reference. 
Let p l} . . p n be the pitches of the chains of reference. 
