360 Astronomical and Nautical Collections. 



at the beginning of the century, by modes of reasoning which he 

 has left unexplained ? This is not, indeed, absolutely impossible 

 for a mathematician to whom nothing was impossible in the higher 

 analysis ; but it would be singular that he should have left no 

 trace of the discovery in any other of his immortal writings." So 

 elegant and so important a demonstration could certainly not have 

 been left unrecorded by Newton, if it had occurred to him : but he 

 does not appear to have entered, in the latest period of his life, 

 into any very deep speculations relating to pure mathematics ; nor 

 to have been employed on any physical problem which was likely 

 to lead him to the investigation, having in all probability found it 

 sufficient for the present purpose to follow the steps of Taylor's 

 ingenious researches. 



Theory q/ Simpson and Table of Bradley. 



The greatest practical improvement on Newton's Table was 

 made before the year 1743 by Thomas Simpson, who computed 

 the effects of the atmosphere on a ray of light, upon the supposition 

 of a uniform decrease of the air's refractive force in ascending, and 

 obtained from observations communicated to him by Dr. Bevis, a 

 table which gives 33' 0" for the horizontal refraction, and 53" for 

 the altitude 45°. He computes his refractions by taking -^ of the 

 difference of two arcs of which the sines are as 1 to .9986 : and 

 he observes, that the distribution of heat in the atmosphere is the 

 reason why the computation upon the supposition of an equable 

 temperature is so erroneous : though he exaggerated the error of 

 this hypothesis so much, as to make the horizontal refraction 52': 

 being probably unacquainted with the computations of Taylor and 

 Newton, which had been published twenty or thirty years before. 



The Table of Bradley, which has been so universally admired 

 and employed by the English astronomers and navigators, was ob- 

 tained from that of Simpson, by the very slight modification of 

 adopting } instead of -fj for the multiplier of the difference of 

 the arcs, the correction having of course been obtained from obser- 

 vation only ; but with the fondness for approximative computation 



