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XVI. Intelligence and Miscellaneous Articles. 



THE ADAMS PRIZE, CAMBRIDGE UNIVERSITY. 



(St. John's College Lodge, May 7, 1887.) 



rpiIE Examiners give notice that the following is the subject for 

 ■*- the Adams Prize to be adjudged in 1889 : — 



On the Criterion of the Stability and Instability of the Motion 

 of a Viscous Fluid. 



It appears from experiment (see Phil. Trans, for 1883, p. 935) 

 that the steady motion in a tube is stable or unstable, according 

 as the velocity is less or greater than a certain amount ; and it is 

 inferred from theory, confirmed by experiment, that in two geome- 

 trically similar systems the motion is stable or unstable according 

 as /.</(OcU is greater or less than a certain numerical quantity n; 

 c, U being a length and a velocity which define the linear scale and 

 the scale of velocity in the system, and p, \x the density and coeffi- 

 cient of viscosity of the fluid ; but the quantity n has not hitherto 

 been obtained even m a simple case except by experiment. 



It is required either to determine generally the mathematical 

 criterion of stability, or to find from theory the value of n in some 

 simple case or cases. Eor instance, the case mighj be taken of 

 steady motion in two dimensions between two fixed planes, or 

 that of a simple shear between two planes, one at rest and one 

 in motion. 



Should the investigation not be found practicable for even a 

 simple case of the motion of a viscous fluid, some substantial 

 advance might be made in what has been done for a perfect fluid 

 (see Proceedings of the Mathematical Society, vol. xi. p. 57), the 

 title of the Essay being modified accordingly. 



The Prize is open to the competition of all persons who have at 

 any time been admitted to a Degree in this University. 



Each Essay should be accompanied by a full and careful abstract 

 pointing out the parts which the author considers to be new, and 

 indicating the parts which are to be regarded as of more im- 

 portance than the rest. 



The Essays must be sent in to the Vice-Chancellor on or before 

 the sixteenth day of December, 1888, privately. Each is to have 

 some motto prefixed, and to be accompanied by a paper sealed up 

 with the same motto and the words Adams Prize on the outside, 

 and the Candidate's full name with his College and Degree written 

 within. 



The papers containing the names of those Candidates who may 

 not succeed will be destroyed unopened. 



Any Candidate is at liberty to send in his Essay either written 

 (but not in his own hand) or printed or lithographed. 



The successful Candidate receives about £170. He is required 



