117 



munication by describing his mode of examining delicate anatomical 

 structures : He procures a hollow sphere of glass, between two and 

 three inches in diameter, of which one fourth is cut off at the open 

 part, and the edges ground so as to fit upon a plate of glass to which 

 the object is attached and immersed in water ; the sphere is then 

 filled with water, and inverted over the object upon the plate. The 

 whole being withdrawn from the basin the object may be examined, 

 and the portion of the sphere filled with water furnishes a conveni- 

 ent magnifying power. 



A New Method of Solving Numerical Equations of all Orders, by con- 

 tinuous Approximation. By W. G. Horner, Esq. Communicated 

 by Davies Gilbert, Esq. F.R.S. Read July 1, 1819. [Phil. Trans. 

 1819,^. 308.] 



The process which the author endeavours to establish in this 

 essay, being the leading theorem in the calculus of derivations, pre- 

 sented under a new aspect, may, he says, be regarded as an universal 

 instrument of calculations, extending to the composition as well as 

 analysis of functions of every kind, but it promises to be especially 

 useful in the numerical solution of equations. 



Mr. Horner then proceeds to the illustration of his method, and 

 to explain the investigations to which it is applicable, by details 

 which do not admit of explanation. 



An Account of Experiments for Determining the Variation in the 

 Length of the Pendulum Vibrating Seconds, at the principal Stations 

 of the Trigonometrical Survey of Great Britain. By Captain Henry 

 Kater, F.R.S. Read June 24, 1819. [Phil. Trans. 1819, p. 337.] 



In this communication Captain Kater, having noticed the circum- 

 stances to which his researches owe their origin, proceeds to detail 

 his investigations, and to describe the implements and apparatus 

 employed in his various inquiries; the construction of the pendulum 

 and its appendages is minutely explained, as also the rate of its ex- 

 pansion for each thermometric degree, whence is deduced the cor- 

 responding correction to be applied to the number of its vibrations. 

 The operations at each station, with their results, are enumerated at 

 length, and illustrated by numerous tables. The length of the 

 seconds pendulum for the latitude of London is 39*13722 inches in 

 parts of the scale which forms the basis of the trigonometrical 

 survey; for the latitude of Unst 39' 16939 inches, of Portsay 

 39-15952, of Leith Fort 39'15347, of Clifton 39'14393, of Arbury 

 Hill 39-14043, and of Shanklin Farm 39' 13407 inches. The calcu- 

 lation of the latitude of each of these stations is given at length, to 

 afford the opportunity of any further examination desirable on that 

 subject ; but these and the' other details relating to calculation do 

 not admit of abridgement. 



Captain Kater concludes this paper with some observations re- 



