58 [April 10, 



order) each involve in their numerator the term sin cos 0, which 

 vanishes at both the limits and 90 degrees. It is this feature 

 which gives success to the method. 



In a second section I have given with some detail the mode of 

 effecting the actual computation of elliptic functions by this means. 

 I have given several formulae for using trigonometrical tables with the 

 exactness which these calculations require, and I think they will be 

 found handier for the purpose than those usually given in the books ; 

 at all events I find them so myself. Some of them are my own, and 

 some are taken, with more or less modification, from Legendre. 



In a third section I have stated what has been done with a view 

 to the extension of the method to radicals of a higher index than the 

 square, and to a certain class of differential equations. 



It should be understood that these processes only enable us to find 

 the integral from the amplitude. They do not enable us to find the 

 amplitude, modulus, or parameter from a given value of the integral. 



April 10, 1862. 

 Major-General SABINE, President, in the Chair. 



The BAKERIAN LECTURE was delivered by WARREN DE 

 LA RUE, Esq., F.R.S., " On the Total Solar Eclipse of July 

 18th, 1860, observed at Rivabellosa, near Miranda de Ebro, in 

 Spain." 



The Lecturer gave an account of the more interesting phenomena 

 of the eclipse, and of the methods employed in observing and 

 recording them ; the details of his observations being given in an 

 elaborate Paper bearing the above title. The Lecture was illustrated 

 by a great number of diagrams and models. The photographic 

 images of the eclipse were projected on a screen by means of the 

 electric lamp, and some of the more striking phenomena were imi- 

 tated by apparatus contrived for that purpose. 



The following is an abstract of the Paper : 



The author, for some time previous to the organization of the 

 Astronomer Royal's expedition to Spain, had contemplated making 

 an attempt to photograph the phenomena of the total eclipse of 



