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Updated: May 2, 2025
In doing so, let us note first of all that our images understanding the word "image" in its broadest sense may be divided into two distinct groups: Concrete images, earliest to be received, being representations of greatest power, residues of our perceptions, with which they have a direct and immediate relation.
“M. Arago, having suspended a magnetic needle by a silk thread, and set it in vibration, observed, that it came much sooner to a state of rest when suspended over a plate of copper, than when no such plate was beneath it. Now, in both cases there were two veræ causæ (antecedents known to exist) “why it should come at length to rest, viz. the resistance of the air, which opposes, and at length destroys, all motions performed in it; and the want of perfect mobility in the silk thread. But the effect of these causes being exactly known by the observation made in the absence of the copper, and being thus allowed for and subducted, a residual phenomenon appeared, in the fact that a retarding influence was exerted by the copper itself; and this fact, once ascertained, speedily led to the knowledge of an entirely new and unexpected class of relations." This example belongs, however, not to the Method of Residues but to the Method of Difference, the law being ascertained by a direct comparison of the results of two experiments, which differed in nothing but the presence or absence of the plate of copper. To have made it exemplify the Method of Residues, the effect of the resistance of the air and that of the rigidity of the silk should have been calculated
He entered the dark doorway with a sort of terror, climbed the winding staircase which seemed to smell of the residues of life, hastened the disrobing with eager hands, as if he had no time to waste, as if he was afraid of dying before he realized his desire, and all at once the poor women who looked askance at his feverish silence and the savage hunger which shone in his eyes, were tempted to laugh, seeing him drop dejectedly into a chair in silence, unmindful of the brutal words which they in their astonishment hurled at him; without paying any attention to their gestures and invitations, not coming out of his stupor till the woman, cold and somewhat offended, started to put on her clothes.
He seized all sorts of things and swallowed them. He drank every fluid in the laboratory. I tried to explain to him that he must take nothing that he could not digest and assimilate completely; but of course he could not understand me. He assimilated a little of what he swallowed; but the process left horrible residues which he had no means of getting rid of.
The white residues gleamed beneath the moon, from every smoke stack poured smoke: the dragon breathed. Then the great white cyanide tanks were like bosses on the beast; the train stopped, and the battery roared. That night, for it was a silent and windless night, I heard forty miles of batteries beating on the beach of my mind like a great sea. And men laboured in the bowels of the earth for gold.
The organic remains were all recent; not a trace of an extinct fossil occurred, but an abundance of the residues of burnt bricks and pottery. In their examination from Essouan to Cairo, the French estimated the mud deposit to be five inches for each century. From an examination of the results at Heliopolis, Mr. Horner makes it 3·18 inches.
And thus again the apparent proper motions of the stars are the observed residues of their apparent movements outstanding and unaccounted for by strict calculation of the effects of precession, nutation, and aberration.
Subtracting the sum of these effects from the total phenomenon, there remains c, which now, without any fresh experiments, we may know to be the effect of C. This Method of Residues is in truth a peculiar modification of the Method of Difference.
But as we can never be quite certain of this, the evidence derived from the Method of Residues is not complete unless we can obtain C artificially and try it separately, or unless its agency, when once suggested, can be accounted for, and proved deductively, from known laws. Even with these reservations, the Method of Residues is one of the most important among our instruments of discovery.
If we could observe heat under circumstances agreeing in nothing but heat, and therefore not characterized also by the presence of a body, we could ascertain the effects of heat, from an instance of heat with a body and an instance of heat without a body, by the Method of Agreement; or we could determine by the Method of Difference what effect was due to the body, when the remainder which was due to the heat would be given by the Method of Residues.
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