( 42 ) 
Art. VII . — On the Diminution of the Obliquity of the Eclip- 
tic. 
HP 
i HE many different opinions which have for the last century 
prevailed concerning the quantity of the secular diminution of 
the obliquity of the ecliptic, and the great variety which appears 
in the result of modern observations, renders this subject pecu- 
liarly interesting. M. Delambre (see the Preface to the last 
Solar Tables) makes it upwards of 52", according to the calcu- 
lations of Laplace. Lalande, in his Tables, used 50", but re- 
marks that 53" appeared to make most of the observations he 
had examined agree ; while, on the other hand, Mr Pond very 
justly asserts, that it is little more than 40", ( Nautical Almanack, 
1818). After examining all the observations registered in the 
various works of Long, Lalande and Delambre, 42". 697 appear- 
ed to reconcile most of the modern observations, though it is con- 
siderably smaller than what those of Pythagoras, Eratosthenes 
and Ptolemy would appear to sanction. But then it must be 
considered how liable these observations were to error. They 
generally adjusted their instruments, by comparing them with 
the meridian altitude of the sun at the vernal equinox, from 
which time, till the solstice, they stood exposed to ail accidents. 
Their sinking, and the inaccuracies resulting from the badness 
of the divisions, made their observations susceptible of very little 
accuracy. 
From a slight modification of Laplace’s formula, we have the 
following theorem for finding the mean obliquity at any time. 
Mean Obliquity = 23° 28' 18".349 — - 1950". 6 sin 2 j 1 6".973 j 
— 2740".347 sin 1 1 32".] 1575 } . 
where t is the time from 1750; it is negative before, but posi- 
tive after this epoch. 
The following Table is constructed from this formula, and is 
-accompanied with a comparison of the results which it gives 
with those of modern observations : 
