78 REPORT—185/7. 
in practical astronomy, it is to be expected that improvements should be 
continually made; and it is of course advisable that the officers charged with 
the responsibility of bringing out the ‘Nautical Almanac’ should be able to 
avail themselves of improved methods. Moreover, the Astronomer Royal, 
who is always one of the most eminent men of science in this country, and 
it may also be said in Europe, is the superintendent-in-chief of the ‘ Nautical 
Almanac.’ The reputation and acknowledged ability of the scientific officers 
concerned in this case are a sufficient guarantee of the accuracy of the 
methods they employ. 
The rule or rules employed for the calculation of tonnage or displacement 
are of a very different nature. As a matter of fact, no real improvement 
has been made in the method, in a scientific point of view, since the days of 
Newton, the rule called Simpson’s or Sterling’s having in reality been invented 
by Newton. The great merits of this rule are, that it is as accurate as any 
rule for the measurement of a figure not strictly geometric can he, and that 
it is simple and easy of application. As applied to obtain internal roomage, 
Stirling’s rule requires only measurements to be taken at certain intervals, 
and these measurements are very easily made. The whole process, after the 
measurements are made, is simply arithmetical. The accuracy of the mea- 
surements can be tested by laying them down to a fixed scale on paper, and 
passing a curve through them; but this curve is not required for the purpose 
of making the calculations. 
Mr. Peake’s method is founded on the very same principle; but, in the 
points wherein it differs, it is, in my opinion, no improvement. First areas 
of sections are calculated as usual; then two sets of calculations are after- 
wards required to complete the operation. The areas of sections are repre- 
sented on paper by lines set off to a certain scale, and an elaborate system of 
exhausting the area so formed is employed. This is evidently a far more 
complex and difficult process than to make simple calculations from ordi- 
nates at once. In taking, also, the greatest distances from various base- 
lines of points in the curved portion, Mr. Peake assumes that he obtains the 
areas more correctly than Sterling’s rule gives them. This is a mere assump- 
tion, founded on no known property of the parabola, which is the curve 
supposed to pass through any three points. 
We know that a parabola may be made to fulfil five conditions; if it pass 
through three points it fulfils three of these—and its having its axis parallel 
to a fixed line, is equivalent to the fulfilment of the other two. We know 
also, that a parabola so drawn, subject to the ordinary conditions under which 
this (Sterling’s method) is applied, is palpably, to the eye, coincident with 
the section of the ship. It is, at all events, impossible to draw a regular curve 
more nearly coincident with it. 
It would be very dangerous, as it would be unnecessary, to leave subordi- 
nate agents to exercise their own discretion in the use of methods for caleu- 
lating tonnage, when a rule so simple and correct as Sterling’s is at their 
command. I conceive, therefore, that no alteration is required, or advisable, 
in the rule now in force under the Merchant Shipping Act of 1854. 
I have the honour to be, Sir, your obedient Servant, 
J. Yates, Esq. os JosEPH WOOLLEY. 
No. 4.—Mr. James Rosert Napier (Member of the Committee). 
Glasgow, March 2, 1857. 
Reply to Tonnage Committee's Circular of 6th November, 1856, by 
James R. Napier. 
1. The objects of registering shipping I believe are,—1st. For the purpose 
a 
