270 
Si’s Answer to P. 
[Sept. 
being made radius. In his ascent the man raises himself through the same height; 
this therefore balances half the water. The other half of the water may lie consi- 
dered as the useful effect of the force expended in descending the inclined plane, and 
in making the progressive motion in the ascent. The proportion which the force 
necessary to make horizontal, hears to that engaged in perpendicular motion is, by 
Coulomb’s table, 1 : 17. Therefore the force required to move along the beam horizon- 
tally is the same as would raise the man’s weight through T ’ T of its length. The force 
required to descend the inclined plane being assumed to lie the same, the two will be 
equivalent to raising the man’s weight through J of its length But the sine of 12* 
is (roughly) Wherefore the man’s weight of water is raised through j of the whole 
length of the beam, by an exertion which we have just found is only equivalent, to 
raising him through J. Here then, if our data are correct, is an actual gain of effect 
over power. 
This is a paradox, however, which I am not prepared to maintain. The reader will 
in fact see that it turns on our supposing an equal force exerted, when weights are 
transferred by a man’s daily labour horizontally or vertically. To this, which is evi- 
dently a paralogism , and not to my under-rating the force required to walk down an 
inclined plane as compared with that exerted in horizontal progression, are wc to 
attribute the above conclusion. But to waive every thing that might appear like 
begging the question, we will assume that the force required to move down the de- 
clivity of the beam, inclined at an angle of 12°, and along it in a horizontal position, 
is in reality equal to the force required to ascend through one-fifth of the beam's 
length. In this case it is evident, that, the whole force exerted is productive of useful 
effect. This force being by the table in your preceding number, represented by 
1800 maunds, raised 10 ft. high per diem, gives a result equal to the work of four 
B engalees with their baling ladles, — a result which, if less striking than my former 
one, is yet sufficiently so to deserve consideration, from all those who have any inter- 
est in the question. When it is considered too, that I have obtained it by adopting 
P.’s own statements, your readers will perhaps have more confidence in it. The 
comparison will be still more favourable, if we take the work of the six Bengallecs as 
in my first letter, 2500 maunds ; giving only 410 instead of 450 as the performance 
of each. So that 40 Bengalees with their scoops could only raise as much water 
as one Parisian labourer working with this pump. I may add, that the proportion it 
bears to the ordinary pump is that of 2 : 1. and to the method of pom-unit, the ordi- 
nary one in Upper Hindustan 5:1. 1 shall be happy if my statements should induce 
any of our indigo planters to give it a fair trial. I am convinced they would 
find their account in it. It is particularly applicable in works situated on a steep 
bank of the river, where there is deep water : for it requires, and this is the only objec- 
tion against its general adoption, that the water from which the supply is drawn 
should have a depth equal to the height to which the water is to be raised*. 
Though in this attempt to estimate the performance of this pump, 1 have been 
contented to assume Coulomb’s valuation of the man’s exertions in mountingstairs, 
yet I must remark, that there is a peculiarity in the application of the man’s labour 
to the working of this pump which is not unimportant. This is the alternation of 
going up and down an inclined plane having so easy a declivity as 12“. This Is one 
of the considerations to which I alluded at the commencement of my letter, as per- 
haps sufficient to account for the great discrepancy between the two estimates. To 
which I may add, that the declivity being less than that which gives a maximum 
ascent, assimilates the work more to that of walking along a level plane. Now, as 
before remarked, we do not know what is the proportion between ihese two kinds 
of forces ; nor would it he easy to determine it, except indeed, from the results of this 
very experiment ; so that we must consent to resolve the question directly bv trial, there 
being no means of arriving at an indirect solution. And when that is done, I shall 
not, for one, be surprised to find this kind of exertion give a higher value than that 
derived from experiments on mounting stairs. At all events I have, I think, made it 
pretty clear, that the performance of this pump, however exaggerated by Professor 
Kobison, is superior to every other method of raising water, giving a result which is 
T bLwhf circumstance would have prevented its application to the particular case, 
Lnvenknri 'uil 1 !" y brst ,etter > emi had !t >>“» otherwise recommended by 
= eD o e b„l' Vhere the , c l u , antit y of water to be raised is not considerable, the 
S “ e .Y ,tlc,1,1 y preferable lor its simplicity, and its independence of 
? f ' Cated apparatus, the frequent removal of which would of 
rn „!L,to7J r r bleSO : Ue - My comparison was not so much intended to apply 
to the question of the applicability of the two methods to any particular case, as to 
their performance mppoany them applied. * 1 
