2940, Dr Repsold proposed a method of meridian observing which consists in causing a web to follow the image of a star in transit by motions communicated by the observer's hands alone, whilst electrical contacts on the drum of the micrometer screw register on the chronograph the instants corresponding to known intervals from the line of collimation.
Delisle is chiefly remembered as the author of a method for observing the transits of Venus and Mercury by instants of contacts.
For instance, to take the two solutions to which we have already referred, we have of ions between molecules at the instants of molecular collision only; during the rest of the life of the ions they were regarded as linked to each other to form electrically neutral molecules.
In 1887 Svante Arrhenius, professor of physics at Stockholm, put forward a new theory which supposed that the freedom of the opposite ions from each other was not a mere momentary freedom at the instants of molecular collision, but a more or less permanent freedom, the ions moving independently of each other through the liquid.
If, instead of considering one point in a succession of instants, we consider a succession of points along the line of propagation at the same instant, we evidently have waves of amplitude varying from 2a down to o, and then up to 2a again in distance U/(ni - n2).
Abandoning therefore all a priori theoretical assumption, Bashforth set to work to measure experimentally the velocity of shot and the resistance of the air by means of equidistant electric screens furnished with vertical threads or wire, and by a chronograph which measured the instants of time at which the screens were cut by a shot flying nearly horizontally.
The value of "one revolution of the screw in seconds of arc" can be determined either by observing at transit the difference of zenith distance of two stars of known declination in terms of the micrometer screw, the instrument remaining at rest between their transits; or by measuring at known instants in terms of the screw, the change of zenith distance of a standard star of small polar distance near the time of its greatest elongation.
It we use Roman letters for mere numbers, capitals for instants of time, Greek letters for time-steps, and a parenthesis to denote a couple, the laws assumed by Hamilton as the basis of a system were as follows: (B1, B 2) - (A i, A2) = (Bi - A,, B2A 2) = (a, 13); (a, b) (a, #)= (aa - b(3, ba--+a(3).2 To show how we give, by such assumptions, a real interpretation to the ordinary algebraic imaginary, take the simple case a=o, b= r, and the second of the above formulae gives (o, 1) (a, (3) = (- 1 3, a).
Its gradient represents the acceleration, and the area (Jzidl) included between any two ordinates represents the space described in the fnterval between the corresponding instants (see fig.
Of ii, if we imagine the two configurations of the system then referred to to be those corresponding to the instants 1, l+t Thus ~(m.~) =~(m).~.
It is obvious that the motions of a pair of points may be varied in any manner, whether by direct or by lateral deviation, and yet that their comparative motion may remain constant, in consequence of the deviations taking place in the same proportions, in the same directions and at the same instants for both points.
Tts value at intermediate instants is given by the following equations: let ~,, 4f be the angles respectively made by the central planes of the forks and shafts with the plane OCiC, at a given instant; then cos 0=tan 4~ tan ~,)
When a machine undergoes alternate acceleration and retardation, so that at certain instants of time, occurring at the end of intervals called periods or cycles, it returns to its original speed, then in each of those periods or cycles the alternate excesses of energy and of work neutralize each other; and at the end of each cycle the principle of the equality of energy and work stated in 87, with all, its consequences, is verified exactly as in the case of machines of uniform speed.
At intermediate instants, however, other principles have also to be taken into account, which are deduced from the second law of motion, as applied to direct deviation, or acceleration and retardation.
A few instants after the echo of the reports resounding over the stone- built Kremlin had died away the French heard a strange sound above their head.