Formula for calculating Expansion of Liquids. 235 



under the pole-star itself, from whence it spread both ways into the 

 north-east and north-west.'' 



About the time that this aurora appeared, the variation at Lon- 

 don, the place of observation, was about 18° westward; and, conse- 

 quently, neither the two steaks of light, nor the crepusculum in the 

 north, had any relation to the magnetic meridian. The nubecula 

 seen by Dr Halley, seems to have been of the same character as the 

 flashes or waves of luminous vapour, seen at Prestwich during the 

 aurorse of November 21st and December 17th last; they were ob- 

 viously at no very great altitude, certainly within the range of 

 aqueous vapour ; the colour of these waves was that of a dim silvery 

 whiteness. 



I perfectly agree with Halley, Hansteen, Brewster, and many 

 other eminent philosophers, in the belief of a magnetic element or 

 effluvium, pervading the atmosphere, and perhaps all space ; but the 

 principles of Electro-magnetism do not allow of electric currents 

 traversing the magnetic lines of force in the direction of their 

 length, unless constrained by other influences than any known to 

 exist in the regions of the aurora borealis. It is possible, however, 

 that the theoretical views which I have here advanced may be open 

 to objections that I do not myself perceive, and may require the cor- 

 rections of a more diligent observer, and a sounder reasoner on the 

 facts observed. 



On a Formula for calculating the Expansion of Liquids by 

 Heat. By WiLLIAM JoiiN MACQUORIf E.ANKINE, Esq., 

 Civil Engineer. Communicated by the Author. 



Having been lately much engaged in researches involving 

 the comparative volumes of liquids at various temperatures, 

 I have found the following formula very useful : 



c 



LogV=Bt+ — A 



Log V represents the common logarithm of the volume of 

 a given mass of liquid, as compared with its volvune at a cer- 

 tain standard temperatui'c, which, for water, is the tempera- 

 ture of its maximum density, or 4°1 centigrade, and for other 

 liquids 0° centigrade. 



