426 Mr. Ivory on the Astronomical Refractions. 



place in the atmosphere. And secondly, the value which I 

 have assigned to the first term of the development of the 

 function expressing the temperature of the atmosphere, is 

 confirmed by the experiments of the French philosophers. 



Another phenomenon lends its aid to confirm the same 

 conclusions. It is the propagation of sound in the atmo- 

 sphere. Nothing can be more curious than to find the velo- 

 city of sound made a deduction from a theory of the astro- 

 nomical refractions. Yet this follows immediately from the 

 foregoing equations by applying the method of accounting for 

 the phenomenon which we owe to the abilities of Laplace. 

 Let I denote the homogeneous atmosphere in feet; then, ac- 

 cording to Newton, sound, in a second of time, moves 

 through a space equal to 



V32$ x r 

 but, according to the accurate theory of Laplace, the ve- 

 locity of sound deduced from the foregoing equations is" equal 



to ^32jTxT~xJ-, 



and this agrees sufficiently well with experiment. 



I have now traced an unexpected connection between many 

 interesting phenomena that seemed to be very little related 

 to one another. There can be no doubt that the whole in- 

 vestigation leads to a simple principle ; by setting out from 

 which, and following a retrograde order, all the phenomena 

 may be deduced. But I do not now touch upon this point. 

 The difficulty and the labour is to arrive at simple and com- 

 prehensive views. So many different facts clearly prove that 

 the element I have introduced in the theory of the refractions, 

 has been rightly determined. The accuracy of the table de- 

 pends upon this circumstance, and is limited by it. 



The horizontal refraction by my formula is greater than 

 that in any Table of refractions except M. Bessel's. It de- 

 pends entirely upon the first term of the development of the 

 function expressing the heat of the atmosphere. Had it 

 agreed exactly with observation, it would have followed that 

 the refractions depend upon that quantity alone, and that the 

 other terms of the development have no sensible effect. But 

 the observations of M. Bessel make the horizontal refraction 

 much greater than it is in my Table. According to the most 

 probable determination that can at present be deduced from 

 the labours of that distinguished astronomer, it is about 36' at 

 50° Fahr., 30 B. It thus appears that the other terms of the 

 development beside the first have a sensible influence on the 

 refractions at very loW altitudes. I apprehend that this is the 

 true reason why my Table fails in accuracy within li° of the 



horizon. 



