﻿NATURE OF THE TEMPORARY STAR OF 1572. 313 



infinite velocity. This last supposition itself would only lessen by half the result of 

 our calculations."* 



There is certainly a fallacy in the reasoning of Arago. If a lurainuous body were 

 to dart off from an observer with the velocity of light, it should become instantly 

 invisible, saving only the time required for the light already emitted to reach his 

 eye. This position is advanced on the following grounds : the velocity of the body, 

 being equal to that of light, and in the opposite direction as regards the observer, it 

 should neutralize the motion of the light, and nullify its effect. 



This argument may fail to convince some persons, and they will be assisted by a 

 further elucidation. 



Let us suppose a non-luminous body at rest in space, and in the midst of darkness. 

 Near the body is a being, capable of perceiving the impression of light. Suddenly 

 the body becomes luminous, and darts its rays into space, at the rate of 192,000 miles 

 in a second. At the same instant, the being darts off at the same velocity, but always 

 keeps in advance of the light. Will any one assert that the being will see the light? 

 Certainly he cannot, for he is always beyond the sphere of its visibility. 



Let us now suppose a case in which the motion is changed conversely. When the 

 body becomes luminous, it darts off itself with the velocity of light, leaving the 

 observer at rest. He cannot see the light, for he too is beyond the sphere of its 

 visibility. The light does not advance in his direction, because the centre from which 

 it is eliminated recedes at the same rate as the light leaves it, and the observer 

 must remain in darkness. f 



This case differs from the one proposed by Arago, inasmuch as in the latter the 

 star was not supposed to become suddenly luminous ; and his observer was so distant, 

 that light could only reach him in three years. In that case, the star should be seen 

 for three years, and then be extinguished. 



With regard to the hypotheses advanced by Sir Isaac Newton and de Maupertuis, 



* Astronomie Populaire, vol. i., pp.- 418, and seq. 



t A learned friend, who puts no faith in the corpuscular theory of light, dissents from the doctrine em- 

 bodied in this argument, and agrees with Arago so far as to believe that an undulation of light will be propa- 

 gated through the ether, with a velocity which is absolute with reference to space, and does not respect the 

 motion of the body from which it emanates. By a singularly ingenious mode of reasoning he arrives at a 

 conclusion identical with that which we have reached ourselves. 



The number of undulations to a second in the extreme violet ray is 727,000000,000000 ; in the extreme red ray 

 458,000000,000000. If the luminous body recede from the observer, the number of undulations in a second 

 must diminish in the inverse ratio of the motion of the body, the velocity of light being unity. 



If, therefore, the star recede with the velocity of light, the number of undulations of the extreme violet ray 

 will be reduced to 363,500000,000000, which is below the number of the extreme red. Consequently the star 

 should make no impression upon our visual organs. 



This argument is the more interesting as it is the direct offspring of the undulatory theory of light, the 

 reasoning in the text being more nearly allied to the corpuscular theory. As in many other instances, the 

 two theories lead to like result.-. 



