
TRANSACTIONS OF THE SECTIONS. 5 
the function assumed in the arbitrary integral by means of which the elliptic integral 
is compared. 
If we want to compare the elliptic function with another elliptic function of the 
same kind but a different modulus, the function in the arbitrary integral will be the 
same radical which enters in the elliptic integral; but if the object be to compare 
the elliptic function with any other integral of a different form, the function in the 
arbitrary integral will be fixed, and depend upon the form of the integral thus used. 
Various rational forms have been given to this arbitrary integral, with a view to 
compare the elliptic functions with functions that can be integrated, and amongst 
them one has been found to answer the conditions of the functional equation, and 
also to be integrable by means of logarithms and circular arcs. 
On the Oscillations of Floating Bodies. By Roserr Rawson. 
This paper had for its object the description of a course of experiments made at 
Portsmouth Dockyard by Mr. John Fincham, the master shipwright, and the author, 
with a view to confirm several important formule discovered by Professor Moseley 
relative to the rolling and pitching motion of vessels. All the experiments, which 
were made by Admiralty order, confirm the formule for determining the amount of 
force or work done to deflect a floating body in a state of equilibrium through a 
given angle, and also another formula which determines whether the vessel thus 
deflected will move slowly or otherwise. 
The importance of these questions to naval architecture is obvious; and all the 
experiments we have made show what we believe to be an important practical fact, 
viz. that when a sudden gust of wind is applied to the sails of a vessel, or any cause 
which acts constantly during one oscillation, the ultimate amplitude of deflection 
will be double the amplitude which the gust of wind will permanently deflect the 
vessel. 
In the next part, several experiments were made on models of vessels, some of 
which have been built with a view to ascertain the best form of midship section 
which will give the easiest rolling motion. 

Description of a Binocular Camera. 
By Sir. Davin Brewster, K.H., D.C.L., F.R.S., & V.P.RS. Edin. 
This instrgment affords to amateurs and artists a ready mode of obtaining double 
_ drawings both of colossal statues and of living bodies or of fixed structures, for the 
purpose of having them exhibited as solids by the stereoscope. As the camera re- 
quired for this purpose must have two lenses of exactly the same focal length, in 
order to form by the Daguerreotype or Talbotype processes the two pictures required, 
with mathematical precision, Sir David has constructed his double camera by di- 
yiding a suitable lens, either single or achromatic, into two semi-lenses, each of which 
will form an image exactly like that which the entire lens would have formed, though 
with less light. These senii-lenses, placed at the proper distance from each other 
and from the object, give the two pictures as required for producing the effect of 
relief when seen by each eye at once in a stereoscope. 


" Improvement on the Photographic Camera. 
By Sir Davin Brewster, K.H., D.C.L., F.RS. & V.P.RS. Edin. 
Sir David Brewster gave an account of an improvement which he had made and 
used on the Photographic Camera. In order to observe when the picture was most 
distinct on the paper or metal, he views the picture with a single or a compound 
eye-piece, either when the picture is received on the ground-glass plate, or in the 
air when the ground-glass is removed. In this last case the camera becomes an 
excellent telescope, by which the satellites of J upiter as well as other astronomical 
phenomena may be easily seen. The ground-glass may be wholly dispensed with, 
‘or it may be permanently connected with the eye-piece, and drawn back when it is 
outofuse. Ifthe ground-glass is retained, a hole opposite the eye may be made in 
it, or that part of the glass may be left unground. This construction of the Camera, 
by which the focus can be adjusted with the greatest accuracy, has been adopted and 
_ successfully by Mr. Beickle of Peterborough, who has executed some of the finest 
] Talbotype we have seen. 
