of the Terrestrial Globe. 9A5 



ly, the temperature, which could not undergo variations unless 

 the earth's volume had corresponded to it, has remained sta- 

 tionary. 



These deductions are all most simple, and it is to be hoped 

 they will be apprehended without difficulty. It still remains that 

 we should express, by numbers, the accuracy to which, by pur- 

 suing this theory, we may reach. 



Let us suppose that the mean temperature of each one of the 

 radii of the terrestrial globe had, in 2000 years, diminished 1° 

 (centigrade). Let us assume glass as a standard for the mea- 

 sure of the general dilatability of the materials of which the 

 earth is composed. We shall find this is nearly luu^ono ^^ ^ 

 degree. This diminution of 1° of temperature for each radius, 

 would yield loo^tjou of diminution in the dimensions of the 

 sphere. But, at the beginning of this article, it was shewn how 

 this diminution of the diameter must be followed by an increase 

 of the velocity, and the principles of mechanics permit us to go 

 even farther; they teach us, that for every ^^o^^oo ^^ diminu- 

 tion in the dimensions of the sphere, there should be a corres- 

 ponding acceleration of j^ijjy in the velocity. The sidereal day, 

 then, should have fallen short of 86,400" (the number of seconds 

 of which it is composed), by its being divided by 50,000% that 

 is, by \^j^". But the observations of the moon's movements 

 prove, that, since the time of Hipparcus, the sidereal day has not 

 varied even ^ig of 1"*, a quantity 170 times less than l^u- 



• Perhaps there might be mcredulity as to this astonishing accuracy, if we 

 were to say nothing of the methods by which it is reached. Suppose, that to 

 satisfy ourselves of the invariability of the sidereal day, we take at each epoch, 

 as a standard, the course which the moon pursues during a single one of these 

 days, and that which a single direct observation can supply. To what degree of 

 accuracy can we thus arrive ? By using the best instruments which modem 

 astronomers employ, the arc described by the moon in a sidereal day, could be 

 measured almost to a second of a degree. The moon could not traverse the 

 second of a degree in less than two seconds of sidereal time. Accordingly, 

 if there be an error, for example, in excess, in the determination of the lunar 

 movement of V\ it is as if we made the sidereal day too long by 2^ of time, 

 which is very far from the accuracy assumed in the text. Let us remark, 

 then, that it is not from the observations of a single day, that we deduce the 

 diurnal movement of the moon. 



Suppose now, then, that we measure the arc described by the same lumi- 

 nary in ten days. This arc will be ten times longer than that which corres- 

 ponded to a single day ; but the uncertainty of the experimental conclusion. 



