3829 .] 
Si’s Answer to P. 
2 69 
right, I find it difficult to any. I may observe, however, that it does not appear to me 
quite clear whether Coulomb’s estimate of the exertion in mounting stairs compre- 
hends merely the height through which the man rises, or whether a sufficient allow- 
ance is made for the labour expended in the horizontal progress. Thus, supposing 
the steps or stairs to be 18 inches broad and 6 high, it is evident that if the exertion 
of rising through the perpendicular height be represented by 1800 uiaunds, raised 
10 ft. high, the horizontal effort would be equivalent to 1800 maunds carried 30 ft. 
or one-fifth of ft man’s whole power nearly; consequently, 1800 would require to be 
increased to 2130 to representthe total effort per diem, in mountingsuch stairs, — a 
number, however, which still falls short of Professor Robison's extimate. Whether 
some considerations, which I shall notice towards the end of this letter, be sufficient 
to account for the difference still remaining, 1 must leave to the judgment of your 
readers. I should however further remark, that Coulomb, or rather your correspon- 
dent P., does not mention the acclivity of the stairs, which is also an important con- 
sideration ; for it has been determined that if a certain height is to be ascended, it is 
effected with the least effort when the stairs are of the dimensions mentioned above, 
and consequently, supposing the same effort exerted, a greater height will be as- 
cended on these stairs than on such as have different dimensions. 
But though it is difficult todecide between these conflicting authorities, I do not see 
that there is any difficulty in forming an opinion of the value of this pump. That it 
is an ingeniously contrived one, and fully deserving of a fair trial, was and is my 
firm opinion ; and a very few considerations will be sufficient, 1 think, to show that 
this is neither a hasty nor a prejudiced judgme'nt. First, I would observe then, that 
from the table given by your correspondent it appears, that the maximum effect pro- 
duced by the exertion of a man’s force, (the fatigue being the same,) is when he 
mounts stairs unencumbered by any load, and using no other of his muscles, but such 
as are sufficient for his locomotion. Secondly, and in like manner, in moving along 
a horizontal plane, the maximum force exerted is when the man is unencumbered 
by a load, and has no other exertion to make than that of walking. The conclusion 
then is, I think, inevitable, that if we could so contrive matters as to make the whole 
of the effect produced in each of these cases us kill effect, we should obtain more 
work than by any other mode of exertion. 
Professor Robison’s pump secures this desideratum, I may say, completely, and 
has the further advantage of uniting both methods. The man on the beam which 
works the pump rods is employed to walk backwnvds and forwards ; sometimes up 
an inclined plane, sometimes level, sometimes down an inclined plane. He does 
nothing else. By these exertions, the most effectual a man can employ, is the water 
raised. The whole of the force is productive of useful effect. 1 think then that I am 
entitled to draw the conclusion, that this is the most advantageous method yet de- 
vised of raising water, and that with this pump a maximum of water will be raised 
at the expense of the same degree of fatigue to the man. 
To determine the value of this maximum, liowevcT, is not easy for the reasons bc- 
forementiuned, add to which we have no data to fix the expenditure of force required 
to move down an inclined plane. I should be disposed to say, that the fatigue is less 
than is incurred in walking along a horizontal plane. But not to assume any thing 
too favourable to our estimate till fairly established, let us merely suppose that the 
two operations require an equal expenditure of power. Let us also assume, that 
Coulomb's valuation of the effect iu mounting stairs is the full value, and includes 
the horizontal progress, so that in reality on such stairs a man could only raise 
1500 maunds 10 feet high in one day, the extra 300 being the equivalent to 1500 
moved horizontally 30 feet. 
We may easily see by considering the structure of this pump that on the descend- 
ing arm the surplus weight is that of the man, and that the pluuger will descend till 
the loss of weight, by it’s immersion in the water, is equal to the weight of the man’s 
body. This is equal to the mass of water displaced by the plunger, in other words, 
to the water raised. The man now walks up an inclined plane (say of 24°) which 
gradually assumes the horizontal position by the return to equilibrium consequent 
on his change of position. So that in reality the acclivity he has to ascend mav be 
taken as less than 12°. Arrived at the centre of motion lie is now prepared to cause 
the descent of the other cud to an equal depth simply by walking down a plane which 
is varying from horizontal to an inclination of 24®, or, as before, say having an ave- 
rage inclination of 12°. Thus, then, the labour of the man consists in walking up 
and walking dawn an inclined plane the length of the beam, and having an average 
inclination of 12°. The useful effect consists in twice the man’sweight of water 
being raised through the sine of 24® to half the beam as radius , or in other words, (as 
we do not affect extreme precision,) through the sine of 12°, the length of beam 
