560 Royal Socielt/. 



simple method of approximating to the real roots of numerical equa- 

 tions, which possesses several important advantages. After de- 

 scribing the nature of tlie transformations which are subsequently 

 employed, the author proceeds to develope the process he uses for 

 obtaining one of the roots of a numerical equation. Passing over 

 the difficult question of determining the limits of the roots, he sup- 

 poses the first significant figure (R) of a root to have been ascertained, 

 and transforms the proposed equation into one whose roots are the 



roots of the original, divided by this figure ( or vv ) : O'l^ root of this 



equation lying between 1 and 2, the first significant figure (/•) of the 

 decimal part is obtained, and the equation transformed into another 

 whose roots are those of the former, divided by 1 + this decimal 

 (or 1 +r). This last equation is again similarly transformed ; these 

 transformations being readily effected by the methods first given. 

 Proceeding thus, the root of the original equation is obtained in the 

 form of a continued product. After applying this method to finding 

 a root of an equation of the 4th, and likewise one of the 5th degree, 

 the author aj)plies it to a class of equations to which he considers it 

 peculiarly adapted, namely, those in which several terms are want- 

 ing. One of these is of the 16th degree, having only six terms; 

 and another is of the 622nd degree, having only four terms. 



2. " Additional Note on the Contraction of ^'^oluntary Muscles in 

 the living body." By William Bowman, Esq., F.R.S., Demonstrator 

 of Anatomy in King's College, London, and Assistant Surgeon to 

 King's College Hospital*. 



This communication contains a short account of some recent ex- 

 aminations made bj' the author on the human muscular fibre affected 

 by tetanus. The efi^ect of the violent contractions which character- 

 ize this disease, is to produce, in manj"^ parts of the muscles, con- 

 siderable ecchymosis, which gives the contiguous jiortions a pale 

 and gray aspect. In other places the muscles lose, in a great mea- 

 sure, their fine fibrous character, and exhibit a soft mottled surface, 

 which is easily torn. The primitive fasciculi, when microscopically 

 examined, present indications of strong contraction, appearing 

 swollen into a fusiform shaj)e, and having their transverse striae in 

 some parts much more closely approximated, and in others separated 

 to much greater distances than in the natural state, or even altogether 

 obliterated, in consequence of the whole texture being broken up 

 into those primitive elements of which the discs are constructed ; and 

 frequently they ai-e l)roken across without a corresponding rupture 

 of the sarcolemma. 



The author is led from his observations to the conclusions, — 1st, 

 that the contraction of a muscle is the essential cause of its rupture ; 

 2ndly, that there is no repellent force between the contractile ele- 

 ments of muscular fibre ; and, lastly, that the contraction of volun- 



[* An abstract of Mr. Bowman's former paper appeared in Phil. Mag. 

 Third Series, vol. xvii. p. 38G.] 



