Lancaster daily intelligencer. [volume] (Lancaster, Pa.) 1864-1928, 1886-10-30
this. 1t is sin PBA=
There, however,

is developed later on and is placed equal to
this 1t is sin PBA=-- There, however,
getting that sin PBA should have been used
to 10 or the value We assume for r. Since
and Z are in general different, sin PBA, even
If the formulas were correct, would be differ
ent quantities in the two formulas, and can
not be substituted one for the other since the
radii to them are different Ina word, there
Is no evidence in the work anywhere, and in
deed much evidence to the contrary, that r
is to be regarded as fundamental rad ius
The method OF preserving the K In such an
investigation Is At best very uncommon and
is not practised by good writer's
Passing this by for the moment let US go
on to the last formula H. r arc sin
PBA, and follow up the complaint little
more closely in this connection. Here we
supposed he meant sin PSA, but in the re-
ply the author claims to mean sin PBA.
Take il so, for he has the right to define his
Quantities and choose his own place for max
ing his mistakes, Therefore, sector PSA=
Hl}f arc sin PBA. In applying the
test of numbers to verify the formula 1t is
very evident that the factor required by y T
sin PBA is always equal 10 I the radius yec
tor. This 1t is claimed We should have sup
piled. IL so, when r~ 10, IL, II, l3, II and so
on, we should supply an additional 10, IL, L.
IL, Ia and so on. That is, he wants US TO sup
ply r, variable, every time we use r sin
PBA. That is, we should have corrected the
formulas first and then applied the test of
numbers and tried to verify them. This sin
PBA=!I to radius is now carried back
and substituted for siu PBA to radius r. This
is inconsistent and shows precisely what we
claim that no attention Is paid to K, a. the
fundamental radius and If we 20 and do
likewise we get the scoldng.
But apart from this the formula sector
PSAz= =HEsl3 arc sin PBA is wrong in
at least three particulars. The expression
y sin PBA needs at least three changes to
make II correct expression consistent with
the assumption we are required to make for
the first proportion. 1t ought TO be y r. sin
PISA by LOOMS treatise on astronomy, page
66, section ia. If the fundamental radius OF
sin PBA Is K, consistent with the claims of
the first proportion, it ought to be D sin PISA.
This brings us back to that marvellous nut
which the school boy critic was too dull of
comprehension TO see. Here we evidently
gave the theorem credit for at least a partly
correct formula when In reality the reply in.
slsts upon a different Interpretation and a
wrong formula The area OF sector PSA=II
T sin PSA, and not u r. sin PBA, much less
y sin PBA, sine being taken to radius
unity. This Is strictly in accordance with
the reference TO Loomis given above That
Is, the approximate area of a sector is one
half the square of the radius Vector by the
sine OF the included angle II sine be re.
quired to radius r then it is 4 r. 2-I : - 21I'
For this last expression we can give no refer
ence since as we stated before TO preserve
X in the way the theorem claims to do, but
really only does in one instance, IN not prac-
tised in such Investigations even If they are
In elementary trigonometries, although even