Like another Archimedes, he requested that the logarithmic spiral should be engraven on his tombstone, with these words, Eadem mutata resurgo.
The correction for pressure has also been worked out in a series of tables and the logarithmic factor here corresponds to the ratio p/760, in which p is the observed barometer.
His placinglogarithmic lines on the edges of instrument boxes was outdone in oddity later by Everard who placed them on tobacco-boxes.
Cajori, History of the Logarithmic Slide Rule and Allied Instruments, New York, 1909, pp.
There are graduations on three sides of the rulers, one graduation being the logarithmic line of numbers.
It will be noticed that the description of the instrument at the opening makes no references to logarithmic lines for the trigonometric functions; only the line of numbers is given.
They are divided into four parts, the first and third containing a variety of logarithmic and other tables, for the purpose of facilitating astronomical calculations.
But God hath bestowed upon this humble architect the practical skill of the learned geometrician; and he makes this provision with admirable precision in that curvature of the logarithmic spiral which he gives to the section of the shell.
Why the Mollusks, who inhabit turbinated and discoid shells, should, in the progressive increase of their spiral dwellings, affect the peculiar law of the logarithmic spiral, is easily to be understood.
A relation which is of historical interest connects thelogarithmic function with the quadrature of the hyperbola, for, by considering the equation of the hyperbola in the form xy = const.
The title of Gunter's book, which is very scarce, is Canon triangulorum, and it contains logarithmic sines and tangents for every minute of the quadrant to 7 places of decimals.
The only otherlogarithmic canon to every second that has been published forms the second volume of Shortrede's Logarithmic Tables (1849).
The exponential function, which may still be defined as the inverse of the logarithmic function, is, on the other hand, a uniform function of x, and its fundamental properties may be stated in the same form as for real values of x.
It now remains to notice briefly a few of the more important events in the history of logarithmic tables subsequent to the original calculations.
Such tables can scarcely be said to come under the head of logarithmic tables.
Briggs also gave methods of forming the mean proportionals or square roots by differences; and the general method of constructing logarithmic tables by means of differences is due to him.
Henry Wace gave a simple and clear account of both the logarithmic and antilogarithmic processes, with tables of both Briggian and hyperbolic logarithms of factors of the form 1 [+-] .
The curve is a logarithmic spiral, and the use of the instrument involves no other labor than that of setting it in position.
This last term is defined as the logarithm of the ratio of one swing to the next succeeding swing, and a galvanometer of which the logarithmic decrement is large, is said to be highly damped.
The quality of a galvanometer in this respect is best estimated by taking the logarithmic decrement of the oscillations when the movable system is set swinging.
The student should not lose any opportunity of exercising himself in numerical calculation and particularly in the use of logarithmic tables.
Equations of the two first degrees, with one or more unknown quantities; Logarithms, Logarithmic Equations, Arithmetical and Geometrical Progression, and practice in the application of the various theories.
Edmund Gunter drew a "logarithmic line" on his "Scales" as follows (fig.
Slide rules are instruments for performing logarithmic calculations mechanically, and are extensively used, especially where [Sidenote: Slide rules.
Near the balance a large logarithmic scale is fixed with a slide which has three indices only.
That is, the stream lines will be logarithmic spirals.
An integral possessing such logarithmic infinities is said to be of the third kind.
We have in what precedes shown how to generalize the ordinary rational, algebraic and logarithmic functions, and considered more general cases, of functions expressible by power series in z.
Either this logarithmic law, or a law that lies exceedingly close to it, must be the law of nature.
If, as seems probable, the logarithmic law is the law of nature, there appear to be three elements lighter than hydrogen, which Dr.
The central curve is found on examination to be either a logarithmic curve or some curve lying exceedingly close to it.
Johnstone Stoney’s “Logarithmic Law of Atomic Weights,” a theory recently advanced in a communication to the Royal Society.
The results give equations of the same logarithmic form as those obtained in a somewhat different manner in the theory of concentration cells described above, and have been verified by experiment.
The tabulated logarithmic aid for correcting the apparent distance, and facilitating the reduction of the observations.
As the rarity of the air within the bulb increases the force of this repulsion begins to diminish, like the logarithmic decrement, and when the latter has sunk to one-twentieth the former has fallen off one-half.
Only in the exceptionally perfect vacuum referred to above did this logarithmic decrement sink to about one-twentieth of what it had commenced with.
Elements of Trigonometry and Logarithmic and Other Tables.
By this characteristic we recognize the 'logarithmic spiral.
Cut and polished length-wise, the fossil shows a magnificent logarithmic spiral, the general pattern of the dwelling which was a pearl palace, with numerous chambers traversed by a siphuncular corridor.
Unrelated to the appendix-lacking, corkscrew-twirling Worm, she is nevertheless familiar with the logarithmic spiral.
He improved the differential calculus, solved the isoperimetrical problem and discovered the properties of the logarithmic spiral.
All, down to the common Snail-shell, are constructed according to logarithmic laws.
I prefer that, as an explanation of the logarithmic curve of the Ammonite and the Epeira, to the Worm screwing up the tip of its tail.
To have done with this part of our subject, here is another property of the logarithmic spiral.
The Epeira, therefore, is versed in the geometric secrets of the Ammonite and the Nautilus pompilus; she uses, in a simpler form, the logarithmic line dear to the Snail.
At least one of them, Planorbis vortex, for example, is a marvel of logarithmic whorls.
The logarithmic spiral describes an endless number of circuits around its pole, to which it constantly draws nearer without ever being able to reach it.
The Epeira's construction, therefore, is a series of chords joining the intersections of a logarithmic spiral with a series of radii.
The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine.
Stefanowska has since, in 1904, obtained a logarithmic curve for the early period of the growth of maize, which doubles its weight every ten days, and the subject has since been pursued by Chodat and others.
