352 Mr. G. H. Bryan on the Equations of 



impulse then necessary to hold the solid at rest. This is in 

 agreement with Prof. Lamb's investigation, which Mr. Bryan 

 has quoted. 



More generally, if the solid is in motion, and the liquid is 

 also circulating, we may suppose the instantaneous motion to 

 have been set up from rest by an immaterial mechanism con- 

 necting the barriers with the solid at the same time that the 

 requisite external impulses act on the solid. The resultant of 

 these last is, as before, the impulse of the whole motion, and 

 is identical with that found by supposing the barriers actuated 

 by impulses from without, and compounding with these the 

 impulse then necessary to give to the solid its instantaneous 

 motion. 



The same point may be further illustrated by supposing the 

 circulations k to vary continuously during the motion. To 

 effect this variation we may suppose finite uniform pressures, 

 P x . . . P m , to be exerted over certain ideal surfaces which 

 occupy the positions of barriers. The rate of variation k of 

 any circulation is given by T = kp, and in order that it may 

 take place without the direct operation of external forces and 

 couples we may conceive the pressure P to be due, as before, 

 to some highly idealized mechanism attached to the solid. As 

 before, the only forces capable of modifying the impulse are 

 the external forces acting on the solid ; and the equations of 

 motion are therefore still to be found by equating the 

 impressed force- and couple-components to the corresponding 

 variations of the " impulse."" Since we know the expressions 

 for the impulse-components corresponding to a given instan- 

 taneous motion of the solid and given circulations, we have 

 only to remember that in these expressions the «'s are 

 functions of the time, and, just as before, the equations 

 of motion are directly deducible from Hay ward's formulse. 

 Equations (19) (20) of Mr. Bryan's paper will thus be 

 applicable to the present case, provided that in the value of H 

 given by (27) the /e's are allowed to vary. 



An investigation proceeding from a consideration of the 

 impulse of the whole motion is not so entirely satisfactory, I 

 think, as the direct method given by Mr. Bryan ; but, at the 

 same time, this brief attempt to interpret the impulse of the 

 cyclic motion may not be without interest. — C. V. Bukton. 



Note added by the Author. 



Dr. Burton's note is of much value as showing more 

 exactly what is meant by the " impulse " of the motion in the 



