Report of the Select Committee on Steam-Boats. 167 
P.S. In my former communication for April, when stating 
the equation which has (although improperly) been made the 
principle and derivation of the common rule for equating of 
payments, I purposely withheld the following note, with some 
additional observations, but which circumstances have not ren- 
dered necessary :—still however the insertion of the note is essen- 
tial, as affording perhaps a more simple and decisive confirmation 
of the truth of the above rule. 
Since (4.7.2) is the whole accretion derived by A. for the term 
(4), so collaterally will (a.r.¢) be that derived by 5. in the like in- 
terva!. Now these objects being jointlyeffected by the rule (as they 
ought to be), we need only conceive x. to have such a value that 
br.(t—x) the gain of B in (¢—a) time shall equal (a.r.x) his 
loss by the detention of the sum (a) for the time 2. Yet on the 
other hand it may be urged, that (a.7.c), the gain on @ in .x. time 
is equal br.(¢—a) the loss on b. for (¢—x); and therefore (U.r.2) 
the whole interest must be actually made in such time. Now thus 
equating interest with interest in place of discount certainly seems 
erroneous ; but discard the restriction imposed or applied in this 
ease [that of (a+) instead of (a+ art yi being the sum in 
l+rt 
hand at the end of the first term], the difficulty then vanishes, 
and the thing appears, what it really is, simply a deduction or 
corollary from the general expression and indicating an equality 
between those quantities, but which can have no absolute rela- 
tion to or dependence on the conditions constituting the right 
and interest which A has in the question. 
XXVI. Report of the Select Committee appointed to consider of 
the Means of preventing the Mischief of Explosion from hap- 
pening on board Steam- Boats, to the Danger or Destruciion 
of His Majesty’s Subjects on board such Boats. 
[Continued from p. 100.] 
Mr. Witittam CHarman’s Evidence, 
Waar is your profession, and place of abode >—My profession 
is civil-engineer; my general place of abode is Newcastle-upon- 
Tyne. 
Have you, as engineer, turned your attention to the construc- 
tion of steam-engines for steam-boats?—As to steam-boats I 
have not particularly; but I have been concerned in steam-en- 
gines of every description, from being connected with the col- 
lieries, where we have many engines. 
Have you any steam-boats upon the Tyne ?—We have, 
Have you seen those steam-boats ?>—Yes; 1 have. 
* L 4 How 
