412 Mr, Herapath on the Causes^ Laws, and principal [June, 



warmer. Uranus alone, if future computations should verify the 

 present, exhibits an exception to this rule. This is not indeed 

 impossible, nor repugnant to our formula; it only requires a dif- 

 ferent constitution from the rest of the planets, such, for instance, 

 as minuter particles ; for then by reason of the coldness, they 

 may be more numerous. Another argument in favour of our 

 formula is the very small disposition to disturb that is found in 

 comets.* This might in part arise from a difference of consti- 

 tution, but it hardly seems reasonable to make it the only cause 

 with all of them. 



Granting that attraction and temperature are proportional, it 

 follows that the polar parts of the earth being colder than the 

 equatorial, the attraction of the whole earth, in places about the 

 former, must be less than its attraction in places about the latter; 

 and, therefore, the isochronal pendulum must be shorter under 

 the poles than at the equator. On this account, therefore, if the 

 earth was a sphere, its figure, as indicated by the pendulum, 

 should be a prolate spheroid ; and if the figure be an oblate 

 spheroid, the measures by the pendulum would give either a 

 prolate spheroid, a sphere, or an oblate spheroid of less eccen- 

 tricity than it really is. Now, according to the best observa- 

 tions, the compression of the earth by the pendulum is about 

 ■j^, whereas by Newton, from the theory of gravity, it is 

 .^j-jj-g-, and by most of the admeasurements it lies between the 

 two, or about -j\-^ by Col. Lambton. But the same theory 

 which indicates too small a compression with the pendulum, 

 indicates also too large a one on the supposition of uniform 

 gravity ; for as the gravitation on the Newtonian theory is 



freater at the poles and less at the equator than it ought to be, 

 fewton must, in his computation, have made the polar iiuid 

 canal too short, and the equatorial too long, and consequently 

 the ellipticity of the earth too great. Hence our theory also 

 indicates the cause of those discrepancies in the three methods 

 of determining the figure of the earth, which have so much 

 baifled mathematicians. The intervention of other things, and 

 a want of extensive and correct observations on the mean tem- 

 peratures in different latitudes, prevent me at present from 

 attempting a numerical proof of these ideas. Humboldt's 

 collection of experiments on the temperatures of different places, 

 lately published, and the experiments made by Dr. John Davy in 

 his voyage to Ceylon, with some others that have lately 

 appeared, have indeed enabled me to fix very nearly f the law of 



« " II a plusieure raUons (says M. Laplace) de croire que les masses des cometes 

 sont tres-petites, et qu' ainsileur action est insensible." 



+ The formula for accurately expressing the mean annual temperature of different 

 latitudes would be one of very great complexity, and, perhaps, in the present state of 

 science, would surpass the powers of analysis to exhibit in a finite equation. Assuming 

 the temperatures of the polar and equatorial regions at (P and S I i° of Fahrenheit, my 

 formula will seldom differ more than a degree or two of Fahrenheit's scale from that 

 lately given by Dr. Brewster, namely, temperature = 8 1 4° x cos. latitude. 



