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Updated: May 22, 2025
But it is not merely the sun which was observed to vary in the speed of its orbital progress; the moon and the planets also show curious accelerations and retardations of motion. The moon in particular received most careful attention from Hipparchus.
If he divides the interval into infinitely small parts by considering the differential dt, he thereby expresses merely the fact that he will consider accelerations and velocities that is to say, numbers which denote tendencies and enable him to calculate the state of the system at a given moment. But he is always speaking of a given moment a static moment, that is and not of flowing time.
Each has doubtless its own period, since each has most likely suffered retardations or accelerations special to itself, which, though trifling in amount, would avail materially to alter the length of the major axis, while leaving the remaining elements of the common orbit virtually unchanged. A fifth member was added to the family in 1887.
The Captain was quite as busy, but in a different way. Pulling out his tablets, he reviewed his calculations regarding the motion of projectiles, their velocities, ranges and paths, their retardations and their accelerations, jotting down the figures with a rapidity wonderful to behold.
When she reached her room, she lit a candle, holding it up before the mirror on the dressing-table and gazing at her face in its reflection. "My God!" she whispered. Truly, in the light of that one candle, she hardly recognized herself. Violent sensations, deep emotions, these are the accelerations of time.
Cruisers don’t clean their tubes more’n once in ten accelerations. The commander is just thinking up dirty work for us to do, like I said." "Never mind," Rip told him. "Let’s find our squadroom and get settled, then draw some protective clothing and equipment. We’ll clean his tubes for him. Our turn will come later." He remembered the last thing Joe Barris had said, only a few hours before.
In the power room, a hastily arranged motor generator set was arranged, making it possible to run the entire ship from the batteries. Scarcely had these been battened down to prevent sliding under the accelerations necessary, than Arcot and Morey were off. The entire operation had required but fifteen minutes. "How are you going to catch him, Arcot?" "I'll overtake him going west.
Cruisers don't clean their tubes more'n once in ten accelerations. The commander is just thinking up dirty work for us to do, like I said." "Never mind," Rip told him. "Let's find our squad room and get settled, then draw some protective clothing and equipment. We'll clean his tubes for him. Our turn will come later." He remembered the last thing Joe Barris had said, only a few hours before.
With the help of the definition of force as the product of mass and acceleration it seems possible, indeed, to derive the parallelogram of forces from that of accelerations in a purely logical manner. For it is necessary only to extend all sides of an a parallelogram by means of the same factor m in order to turn it into an F parallelogram.
It is in this way that present-day scientific thought keeps itself convinced that the parallelogram of forces follows with logical evidence from the parallelogram of accelerations, and that the discovery of the former is therefore due to a purely mental process.
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