
NOTICES AND ABSTRACTS 
OF 
“MISCELLANEOUS COMMUNICATIONS TO THE SECTIONS. 
MATHEMATICS AND PHYSICS. 
On the Application of Graphical Methods to the Solution of certain Astrono- 
mical Problems, and in particular to the Determination of the Perturba- 
__ tions of Planets and Comets. By J.C. Apams, F.R.S. 
BY 
; 
* 
a 
% Arter briefly pointing out the advantages of graphical methods, the author pro- 
_ ceeded to give some instances of their practical application. It was shown that the 
solution of the transcendental equation which expresses the relation between the 
_ mean and excentric anomalies in an elliptic orbit, is obtained in the most simple 
__ manner by the intersection of a straight line with the curve of sines. Attention 
_ was directed to Mr. Waterston’s graphical method of finding the distance of a comet 
_ from the earth, and an analogous method was given for determining the distance of 
- aplanet, on the supposition that the orbit is a circle in the plane of the ecliptic. 
__. The author then passed on to the more immediate object of his communication, 
the graphical treatment of the problem of perturbations of planets and comets. He 
first showed how to obtain geometrical representations of the disturbing forces, and 
_ then gave simple constructions for determining the changes produced by these forces 
- “in each of the elements of the orbit, in a given small interval of time. Having ob- 
tained the total changes of the elements in any number of such intervals, it was 
shown in the last place how to find their effect on the longitude, radius vector and 
_ latitude of the disturbed body, and thussto effect the complete solution of the pro- 
_ blem of perturbations without calculation. 


On a Model of the Moon's Surface. By HEnry Buunt. 
This model is an accurate representation of a part of the moon’s surface as it 
appears through a Newtonian telescope of seven feet focus and nine inch aperture, 
under a magnifying power of about 250. The large volcanic crater, which forms the 
principal object in the model, has received the name of Eratosthenes. It is about thirty 
miles in diameter and stands at the end of a lofty range of mountains not far from 
the centre of the moon’s disc. A hilly district, rising into two or three lofty peaks, 
runs upwards from Eratosthenes, connecting it with what appears to haye been an 
ancient crater now filled up. Touching the edge of this crater and descending from 
it towards the right, may be seen a long line of minute volcanic cups, which are 
_ nearly the smallest objects visible with the instrument by which the observations 
__ were made. The whole is represented as seen with an inverting eye-piece, and the 
_ model ought to be held in an oblique light in order to view it to advantage. 

. e 



ur On some new Applications of Quaternions to Geometry. 
% By Sir W. Hamitton. 
On the Heat of Vaporization of Water. By J. P. Jouus. 
= 
5 _ The object was to point out the complex nature of the heat hitherto taken for 
_ the latent heat of steam. In the exact experiments of Regnault 965° was found 
to be the quantity of heat evolved in the condensation of steam saturated at 212°; 
_ of this quantity 75° was stated by the author to be the heat due to the vis viva com- 
1 
; 1849. 
