And from this, and from the property of a rigid body, already stated in 29, it follows, that the components along a is ne of connection of all the points traversed by that line, whether -in the driver or in the follower, are equal; and consequently, that the velocities of any pair of points traversed by a line of connection are to each other inversely as the cosines, or directly as the secants, of the angles made by the paths of those points with the line of connection.
But the main purport of the treatise was the exposition of an elaborate system of celestial harmonies depending on the various and varying velocities of the several planets, of which the sentient soul animating the sun was the solitary auditor.
Until the hypothesis has been thoroughly tested by an examination of the line-of-sight velocities of stars from the same point of view, this physical interpretation must be received with some degree of caution; but there can be no doubt of the reality of the anomalies in the statistical distribution of proper motions of the stars, and of these it offers a simple and adequate explanation.
Such collisions are inevitable in consequence of the different velocities acquired by the drops under the action of the capillary force, as they break away irregularly from the continuous portion of the jet.
At a time when the Cartesian system of vortices universally prevailed, he found it necessary to investigate that hypothesis, and in the course of his investigations he showed that the velocity of any stratum of the vortex is an arithmetical mean between the velocities of the strata which enclose it; and from this it evidently follows that the velocity of a filament of water moving in a pipe is an arithmetical mean between the velocities of the filaments which surround it.
Dividing the whole number of arcs, 156, whose angular velocities were measured into three numerically equal groups, according to their altitude, the following were the results in minutes of arc per second of time (or degrees per minute of time): - Each group contained auroras which appeared stationary.
His removal of the considerable discrepancy between the actual and Newtonian velocities of sound,' by taking into account the increase of elasticity due to the heat of compression, would alone have sufficed to illustrate a lesser name.
On the theory that the phenomena are wholly due to unequal ionic velocities this result would mean that the cation like the anion moved against the conventional direction of the current.
Per hour, but for greater velocities up to 80 km.
The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.