Mr. G. Boole on the Theory of Probabilities. 313 



sphere the rising of synthermal temperatures appears to be a little 

 inferior to what it is in the northern, if we compare together stations 

 with nearly corresponding latitudes and differences of longitude in 

 both hemispheres. 



From the results tabulated in his synthermal Tables, the author has 

 projected on an equatorial map of the world, the synthermal lines of 

 4 a.m. and 2 p.m. Greenwich time. This map clearly exhibits the 

 risings of the synthermals, and the existence of spaces of maximum 

 temperature. The synthermals in both hemispheres rise towards the 

 poles opposite these spaces, and converge towards the space of mini- 

 mum tropical temperature. In islands circumstanced like the British 

 Isles, the synthermals may be represented by two systems of closed 

 curves, one for the day with an interior space of maximum tempera- 

 ture, and the other for the night with an interior space of minimum 

 temperature. These groups would be connected somewhat in the 

 way of the magnetic curves delineated by Gauss in his Theory of 

 Terrestrial Magnetism (Taylor's Scientific Memoirs, vii.). The 

 shapes of these groups would closely resemble the isothermals already 

 published by the author*, and which, from the small differences of 

 longitude in our islands, may be conceived to represent very closely 

 the synthermals of 9 a.m. and 8 p.m. 



The probable shapes of the lines of equal soil temperature, or syn- 

 geothermals as the author calls them, are next considered ; and it is 

 shown that they must not only present far more remarkable devia- 

 tions from equatorial parallelism than the synaerothermals, but also 

 that their diurnal rising must be very considerable. 



The author points to the connexion between some of his results 

 and the diurnal law of the wind force discovered by Mr. Osier ; and 

 he also shows how the abnormal regressions of temperature in the 

 latter months of spring may be partly explained by the circumstance 

 that, although the isothermals of mean temperature during these 

 months do not deviate widely from equatorial parallelism, the syn- 

 thermals not only swing to a greater extent than during most of the 

 other months of the year, but that they are also more closely crowded 

 together. 



These results are most strikingly developed during themonthof May. 



" On the Differential Coefficients and Determinants of Lines, and 

 their application to Analytical Mechanics." By A. Cohen, Esq. 



"On the Theory of Probabilities." By George Boole, Esq., 

 E.B.S. 



This paper has for its object the investigation of the general analy- 

 tical conditions of a method for the solution of questions in the 

 Theory of Probabilities, which was published in a work entitled " An 

 Investigation of the Laws of Thought, &c. f" 



The application of the method to particular problems has been 



* Proceedings, vol. i\\, and Atlantis, vol. i. 

 f London, Walton and Maberly, 1854. 



