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162 MERRIMAN—LEAST WORK IN MECHANICS. [April 2, 
THE PRINCIPLE OF LEAST WORK IN MECHANICS AND 
ITS USE IN INVESTIGATIONS REGARDING 
THE ETHER OF SPACE. 
BY MANSFIELD MERRIMAN. 
(Read April 2, 1903.) 
The principle of least work has been extensively used in applied 
mechanics since 1879, when it was first formally stated and estab- 
lished by Castigliano. Previous to that time, various authors had 
discussed the principles of least action, of least constraint, and of 
least resistance, and had applied them in the solution of special 
problems. The principle of least work, however, is capable of 
more definite statement and demonstration than the other mini- 
mum laws, and its range of application in statical investigations on 
elastic structures is wide, while it has been found to be of great 
practical value to civil engineers. 
When a structure like a bridge truss contains members sufficient 
to prevent distortion of its panels and no more, the stresses in these 
members due to given loads can be readily computed by the prin- 
ciples of rigid statics, the members in this case being called 
necessary ones. If there be superfluous members, however, rigid 
statics cannot determine the stresses, since the number of unknown 
stresses is greater than the number of statical conditions. In this 
case the structure is said to be statically indeterminate, and the 
principle of least work must be applied. This principle asserts that 
the stresses under consideration have such values that the potential 
stress energy stored in all the members of the structure shall be a 
minimum. If there be # stresses under consideration and m 
statical conditions, the remaining 7 — conditions are expressed by 
n—m equations, which are deduced by equating to zero the deriva- 
tives of the expression for the total stored energy, these being the 
conditions that render this energy a minimum. 
Asa simple example the case of a rectangular table with four legs 
may be considered, it being required to find the stresses in these 
legs due to single load placed on the table in a given position. 
This is a statically indeterminate problem, since rigid statics furnishes 
but three conditions, and the solution cannot be made if the legs 
are rigid. The legs are, however, really elastic and each one is 
shortened in supporting the load, the stress in each leg multiplied 
by the amount of shortening being proportional to the stored 
