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 : one root of this
equation lying between 1 and 2, the first significant figure (r) 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 l + r). This last equation is again similarly transformed ; these transformations being readily eff'ected 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 applies 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.
3. "Additional Note on the Contraction of Voluntary 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 by the author on the human muscular fibre affected by tetanus. The effect of the violent contractions which character- ize this disease, is to produce, in many parts of the muscles, con- siderable ecchymosis, which gives the contiguous portions 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 shape, 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 are broken 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- tary muscle is not a sustained act of the whole congeries of contrac- tile elements composing it, but a rapid series of partial acts, in which all duly share, becoming by turns contracted and relaxed.
The paper is accompanied by drawings cf the microscopic appearances therein described.
