Memorandum on the Neivcastle Engine Trials. 
C77 
tensions T, and at its ends, the friction exerted on it by the wheel and by- 
its own weifrht. This gives, taliing- moments about 0 — • 
l\n = T , OM + F, a'+ moment of weight of A BC. 
Considering the portions A D in tlie same way, 
T3 0 N = T, a + F./i' — moment of weight of A D. 
Adding these two equations, we get 
T, a + T., ON = T, OM + T,rt + (F^ +F,)«'+ diflerence of moments of 
weights ABO and A D. 
But the moment of weight of ABO = moment of weiglit of A D because 
the strap is accurately balanced. 
.-. (T, - TJ a = T„ O M - T, 0 N + F a'. 
Now 0 ]\I = O 0 sineO 0 M = (d - b) sine O C M 
and 0 N = O D sine 0 D N = d sine 0 D N 
and Ti - = AV. 
Substituting these values in the above equation we get 
. W rt = T. {d - b) sine 0 0 M - dsma OD N + F «' 
= d [T, sine O 0 ]\I - T, sine 0 DN] - b T,, sine O 0 M + F a' 
But, because the lever is in equilibrium, considering the forces at right angles 
to it, 
T., sine 0 0 M = T + T, sine 0 D N 
or T = T„ sine 0 0 ]M - T3 sine 0 D N 
And by taking moments about D of all the forces acting on the levers, 
D E X P = 0 D sine 0 0 M. 
ov{d- c)V = 6T, sineOOM. 
Substituting these two relations in the above equation we get 
W« = dF - (d - c)V + Fa' 
W rt = c P -•- F«' 
or W - IP = '?'f. 
a a 
That is to say, in order to get the effective value of "\T, the pull at E diminished 
in the ratio of c to a must be deducted. 
This result agrees with the principle that the external forces acting on the 
system should balance. Since it is at rest and the tensions are internal forces, 
the Load, the Pull at E, and the Friction are the only external forces that have 
to be considered, as the point of support is in the centre of gravity of the strap. 
This gives, at once, by taking moments about O 
a^N = cP + Fa' 
as before. Also because 
p ^ 6T, sine OCM 
d — c 
it follows that P depends upon the tension of the strap and upon the pro- 
portion which 0 D bears to the whole length of the lever. Now the tension 
of the strap depends upon the lubrication, hence the more efficient, that is, 
the greater, will be the inaccuracy of the brake. 
It is evident that in order to determine the probable amount 
of error in the Cardiff and Newcastle trials, the pnll upon the 
upper ends of the levers must be ascertained when the brakes 
are running under exactly the same conditions as to power, 
speed, temperature of air, and lubrication. It would be impos- 
sible to secure all these conditions, and I have consequently 
