136 On promoting the early Puberty of Apple and Pear Trees 
angles were measured exactly. The error arising from this se- 
cond cause, in the last angle of intersection, is by the formule 
of the second Supplement before mentioned, proportional to the 
exponential c~”’, in expressing this error by < or, which in the 
present case becomes 6”,8997.7. Hence it follows that the li- 
mits, within which it may be wagered one to one that the error 
falls, are +3”,2908. If the azimuthal observations were made 
with very great precision, the probability that they indicate an 
ellipticity in the terrestrial parallels might be determined by this 
formula. 
The relative accuracy of the instruments made use of in geo- 
desic operations, may be appreciated, by the value of <’ deduced 
from a great number of triangles. This value, found from the 
‘ sia 4  44B0ON7 
107 triangles of the meridian, ts 
duced from 43 triangles employed by Lacondamine, in his mea- 
- The same value de- 
1718 
Wg 3 OF nearly ten 
times greater than the preceding value. The errors equally pro- 
bable, relative to the instruments employed in these two opera- 
tions, are proportional to the square roots of the values of «’. Hence 
it follows that the limits +8™,0937, between which we have just 
seen that it is equally probable that the error of the are measured 
from Perpignan to Formentera falls, would have been +25™,022 
with the instruments employed by Lacondamine. These limits 
would have exceeded + 40 metres, with the instruments used by 
La Caille and Cassini in their measurement of the meridian. Thus 
it is obvious how advantageous the introduction of the repeating 
circle has been in geodesic operations. 
surement of 3 degrees of the equator, is 
A.M. 
** I shall feel obliged to any of your correspondents who will communi- 
cate the relative accuracy of philosophical instruments, particularly those 
used for observing angles, accompanying the statement with a description 
of the instruments sufficient to ascertain the kind to which that statement 
will apply ——Why is the repeating circle, which is the favourite of our 
scientific neighbours, so little used, and by many held cheap in England? 
What magnifying power ‘in telescopes is sufficient for a given fineness 
of division in theodolites, sextants, and circles?—TraNnsuaTor. 
XXXI. On promoting the early Puberty of Apple and Pear 
Trees when raised from Seed. By J. Wituiams, Esq.* 
Mansy persons inclined to become experimentalists in raising 
fruit-trees from seed, with a view of obtaining new, improved, 
* From New Monthly Magazine, vol, iii. No. 8. 
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