110 Mr. Galbralth on the Velocity of Sound. 



0-002083 Fahrenheit, or 0*375 -+- 100 =0'00375 of the centi- 

 grade scale. Proceeding on these principles, the formula fre- 

 quently adopted, particularly by foreigners, is obtained, that 



is, u = c ^ 1 4-0'00375 t; where v denotes the horizontal ve- 

 locity, c a constant determined by observation, commonly as- 

 sumed at 333*4 !• metres, or 109-t English feet, and t the tem- 

 perature by the centigrade thermometer. Hence in this for- 

 mula an allowance was made for temperature, but none for 

 barometric pressure and moisture, which certainly ought not 

 to be omitted, as each has its proper effect. 



Newton's solution may be represented by the following for- 

 mula, in which I denotes the height of the homogeneous atmo- 

 sphere in feet, and g the gravitating force : 



v = vY^i (1) 



But, according to the accurate theory of Laplace, Mr. Ivory in 

 the 63rd volume of the Philosophical Magazine, p. 4-2G, fi*om 

 his investigations on the astronomical refractions shows that 



V = i/gx/x4 (2) 



which agrees pretty well with experiment. 



The quantity |, or 1*3333, has been determined by expe- 

 riments. Those of Clement and Desormes give 1 •3492, and 



those of Gay-Lussac and Welter 1*3748, the 



mean of which is 1*362, a little greater than Mr. Ivory's esti- 

 mate, and may be considered as a close approximation to the 

 truth. 



Now if in equation (2) these be substituted, observing that 

 I = 27818 feet nearly, when the barometer is at 30 inches, 

 and the thermometer at 50° Fahrenheit, and g = 32*2 feet, it 



will become v = \/ 32*2 x 27818 x 1*362 = 1 ]04i feet, agree- 

 ing very well with observation. If we take the specific gra- 

 vity of mercury at 13568, and that of atmospheric air at 1*22, 

 then mercury will be about 11121*3 times heavier than air, 

 in a mean state ; or if the specific gravity of air be taken at 

 1 '2 1 , as there is some uncertainty, the mercury will be 1 1 2 1 3*22 

 times the weight of air. In fact, a slight altei'ation in the spe- 

 cific gravity of either of these fluids makes a considerable 

 difference in their relative weights. Let p = the barometric 



• . , , 11213-2» , . I. 

 pressure m mches, then — - = / m leet. 



/ 32-2 X 1-362 xll213-2'2;, cm-aa J— io\ 



Hence v =v j^ —— 202'44'^^ .... (3) 



If p = 29*7912, the mean of Dr. Gregory's experiments, 



then V = 202-44 / 29*7912 = 1105 feet. This agrees very 



nearlv 



