Landolt and others, made it at first appear that the change in weight, if there is any, consequent on a chemical change can rarely exceed one-millionth of the weight of the reacting substances, and that it must often be much less.
The amount of the sun's heat has been estimated, but we receive on the earth less than one two-thousand-millionth part of the whole radiation.
The imperfections of the thermopile, with which he began his work, led him, about 1880, to the invention of the bolometer, an instrument of extraordinary delicacy, which in its most refined form is believed to be capable of detecting a change of temperature amounting to less than one-hundred-millionth of a degree Centigrade.
Discussing the theory of capillary attractions, Young' found that at a rough estimate " the extent of the cohesive force must be limited to about the 250-millionth of an inch " (=10 8 cms.), and then argues that " within similar limits of uncertainty we may obtain something like a conjectural estimate of the mutual distance of the particles of vapours, and even of the actual magnitude of the elementary atoms of liquids..
It appears tolerably safe to conclude that, whatever errors 'may have affected the determination, the diameter or distance of the particles of water is between the two thousand and the ten thousand millionth of an inch " (= between 125 X I o 8 and 025 X 10 -8 cms.).
That is to say, the metre might be redetermined or restored as to its length within one ten-millionth part, by reference to, e.g., 1553163.5 wave-lengths of the red ray of the spectrum of cadmium, in air at 15° C. and 760 mm.
The small ratio, or ratiuncula, is in fact that of the millionth root of to to unity, and if we denote it by the ratio of a to 1, then the ratio of 2 to I will be nearly the same as that of a301'°30 to i, and so on; or, in other words, if a denotes the millionth root of 10, then 2 will be nearly equal to a 301,030, 3 will be nearly equal to a477,1u, and so on.
So I saw, in real dollars, the cost of computer memory fall to one one-millionth of what it was thirty years ago.
No one can say in how far it is possible for man to advance in this way toward an understanding of the laws of history; but it is evident that only along that path does the possibility of discovering the laws of history lie, and that as yet not a millionth part as much mental effort has been applied in this direction by historians as has been devoted to describing the actions of various kings, commanders, and ministers and propounding the historians' own reflections concerning these actions.