But there are forms in which the involution is " hyperstrophic," that is to say, the turns of the spire projecting but slightly, the spire, after flattening out gradually, finally becomes re-entrant and transformed into a false umbilicus; at the same time that part which corresponds to the umbilicus of forms with a normal coil projects and constitutes a false spire; the coil thus appears to be sinistral, although the asymmetry remains dextral, and the coil of the operculum (always the opposite to that of the shell) sinistral (e.g.
It results from this that the horn has the appearance of a mass of agglutinated hairs, which, in the newly growing part at the base, readily fray out on destruction of the softer intermediate substance; but the fibres differ from true hairs in growing from a free papilla of the derm, and not within a follicular involution of the same.
From serving primitively as the essential organ of the cleft the tongue-bar may have undergone reduction and modification, becoming a secondary bar in Amphioxus, subordinate to the primary bars in size, vascularity and development; finally, in the craniate vertebrates it would then have completed its involution, the suggestion having been made that the tongue-bars are represented by the thymusprimordia.
Evolution and involution are usually regarded as operations of ordinary algebra; this leads to a notation for powers and roots, and a theory of irrational algebraic quantities analogous to that of irrational numbers.
Ingestion and dissolution of the Trypanosomes by phagocytes has frequently been observed; and it is probable also that the haematopoietic organs secrete some substance which exerts a harmful action on the parasites, and causes them to undergo involution and assume weird-looking " amoeboid " and " plasmodial " forms.
Nothing is known of its natural history outside the body, but on cultivation it is apt to undergo numerous involution forms. Its presence in a patient is regarded as positive diagnostic proof of plague; but failure to find or to identify it does not possess an equal negative value, and should not be too readily accepted, for many instances are recorded in which expert observers have only succeeded in demonstrating its presence after repeated attempts.
The theory of forces in involution has been studied by A.
If, however, the links are in involution, these forces become infinite or indeterminate.
Many of the bacteria exhibit curious involution forms (" bacteroids "), which are finally broken down and their products absorbed by the plant.
This is not only a play within a play, but in part of it there is actually a third involution, one set of characters beholding another set discharging the parts of yet another.
Of N when n and p are given) is involution; the calculation of roots (i.e.
Involution is a direct process, consisting of successive multiplications; the other two are inverse processes.
- Addition, multiplication and involution are direct processes; and, if we start with positive integers, we continue with positive integers throughout.
Desargues has a special claim to fame on account of his beautiful theorem on the involution of a quadrangle inscribed in a conic. Pascal discovered a striking property of a hexagon inscribed in a conic (the hexagrammum mysticum); from this theorem Pascal is said to have deduced over 400 corollaries, including most of the results obtained by earlier geometers.
The principle of involution solves such constructions as: given four tangents and one point, three tangents and two points, &c. If a tangent and its point of contact be given, it is only necessary to remember that a double point on the curve is given.
Logarithms.-Multiplication, division, involution and evolution, when the results cannot be exact, are usually most simply performed, at any rate to a first approximation, by means of a table of logarithms. Thus, to find the square root of 2, we have log A /2 = log (21)=1 log 2.