442 
REPORT OF THE ANNUAL MEETING Proc. N. A. S. 
The paper discusses the effect of the neglect of these conditions and a 
more general treatment, as an extension of the original treatment by 
Joukovsky, is then developed for taking care of conditions (1), (2), (3), (4). 
Based on this treatment a further extension is then developed, including 
the influence due to imperfect reflection at the valve end. 
Four different bases for the specification of the amount of reflection 
realized are presented and the treatment is developed to include any of 
these according to choice. 
These four methods are as follows : 
(1) A constant fraction or percentage of complete reflection. 
(2) A fraction or percentage of complete reflection defined as (ai - a) /ai 
where ai = area of full valve opening and a = area of opening at any 
instant during valve movement. 
(3) A fraction or percentage of complete reflection defined as {A~ a) /A 
where A = cross-section area of pipe and a = area of valve opening at 
any instant during valve movement. 
(4) A fraction or percentage of complete reflection defined as {vi - v) /vi 
where for closure Vi = full initial velocity and for opening Vi = full final 
velocity, while v = velocity at any instant during valve movement. 
The treatment throughout the paper includes both closure and opening 
of the valve, either in whole or in part, or in general any amount of valve 
movement either in closure or opening. 
The paper is illustrated with diagrams showing typical numerical cases. 
Of the various conditions thus brought within the scope of a form of 
analytical treatment, the author considers that part of the paper relating 
to No. 5 of more especial interest, representing, so far as he is aware, a 
distinct extension of earlier treatments of the problem and in such manner 
as to bring under some form of analytical control an important condition 
which must always prevail in actual cases of the development of shock 
or water ram in liquid conduits. 
REPORT OF THE ANNUAL MEETING 
PrHparkd by THE) Home Secretary 
The annual meeting of the Academy was held in Washington, April 
26, 27 and 28, 1920, at the Smithsonian Institution. The following 
eighty-eight members were present: C. G. Abbot, BailEy, A. Graham 
BeivL, Boas, Bogert, Bridgman, Bumstead, W. W. Campbell, Carty, 
Castle, Cattell, F. W. Clarke, J. M. Clarke, Conklin, Crew, 
Cross, Curtis, Dall, Davenport, Davis, Day, Dickson, Donaldson, 
Dunn, Durand, Fewkes, Forbes, Frost, Gomberg, Hale, E. H. Hall, 
G. S. Hall, Halsted, Harper, Harrison, Henderson, HillEbrand, 
Holmes, Howard, Howe, Howell, Iddings, Jennings, Jewett, Kas, 
* 
