THE MECHANICAL EQUIVALENT OF HEAT. 
389 
(2.) The Balance of the Brahe .—(Part I., par. 9.) 
29. If a pair of trials are run, the one with a heavy indicated load, and the 
other with a lighter one, Mg, and if m be the moment carried by the brake on account 
of its initial want of balance, then the works done in the two trials are 
= 27rN^ (Mj d* m) 
Uo = 27rN3 (Mg + m) 
where ISI^ and Ng are the revolutions in the two cases. 
The difference of the work done 
= 277 [NgMi - NgMg + (N; - Ng)] 
and the relative error involved in writing for this 
277(NiMi - N.gMg), 
which has been done in these experiments, is 
m (N^ — N.2) 
Ni.Mi - NgMg 
, very nearly. 
This error is 0 when Nj = Ng. 
The speed of the engine was therefore always regulated to the end that the 
number of revolutions in each of a pair of trials which were afterwards to be 
compared together should be approximately the same. As a general rule, this 
object was very nearly attained. 
The maximum value of N^^ — Ng was about 300, the values of N^ and Ng being 
approximately 18,000. 
Under these circumstances, in trials carrying loads of 1200 and 600 ft.-lbs. 
respectively, the above error amounts to 
300 
18000 X 600 
< 0‘003 per cent, per ft.-lb. of error in the balance of the brake. 
ooOOO ^ ^ 
The method pursued to determine the want of balance was as follows :— 
The lever was freed from all extraneous loads. 
The brake and its pipe connections were then all filled with water, so as to be in 
the same condition as during the progress of a trial. 
The lever was then lifted till its end was in its mean position opposite a pointer at 
a fixed height from the ground. A load was then gradually added to the front side 
of the brake till the friction of the bearings was overcome, and the lever fell. An 
observation of the moment required to cause the motion was then made. A series of 
