COMPARISONS OF Sp, RS, K, ETC. 769 
Whence V-\-p'—p appears to weigh as much as ^ in air (thermometer^^', 
barometer = 6'). 
In calculating the densities of Sp, K, Sb, Professor Schumacher adopted the for- 
mulae and constants given in Bessel’s paper on the reduction of weighings, in the 
Astronornische Nachrichten, B. vii. S. 373. It will therefore be proper to use his 
tables in reducing the weighings of 1844, even though the values of some of the con- 
stants, according to recent and more accurate observations, differ slightly from those 
employed by Bessel. 
Let vP be the volume of the weight P at the temperature of melting snow, the unit 
of volume being the volume of one grain of water at its maximum density; p the 
weight in grains of the air displaced by P; ^ the temperature of the air in degrees of 
Fahrenheit’s scale ; and b the height of the mercury in the barometer in English 
inches reduced to the temperature of melting snow. Then 
log p = log h-\- log ^;P-l- log from Table A.-j-log from Table B. or P., according as the 
weight is of brass or platinum, t being the argument in each of the tables. 
Of the following tables, copied as far as they are wanted from the Philosophical 
Transactions for 1836, p. 486, A contains the logarithm of the ratio of the density of 
air temperature t, and under the pressure of one inch of mercury at the temperature 
of melting snow, to the maximum density of water. B and P contain the logarithms 
of the ratio of the density of brass and platinum, respectively, at the temperature of 
melting snow, to the density at the temperature t of Fahrenheit’s scale. 
if. 
.4. 
t. 
B. 
if. 
P. 
6l 
5-61177 
61 
0-000394 
61 
0-000189 
62 
5-61092 
62 
0-000408 
62 
0-000195 
63 
5-61007 
63 
0-000421 
63 
0-000202 
64 
5-60922 
64 
0-000435 
64 
0-000209 
65 
5-60837 
65 
0-000449 
65 
0-000215 
66 
5-60752 
66 
0-000462 
66 
0-000222 
67 
5-60668 
67 
0-000476 
67 
0-000228 
Let A prehxed to the symbol by which any weight is designated denote the 
ratio of the density of the weight at the temperature of nielting ice to the maxi- 
mum density of water. Then (Philosophical Transactions for 1836, pp. 490-493), 
ASp=21'1874, ARS = 21'1874, AK=7'994, ASb = 8'228. The density of U is un- 
known. Let it be assumed equal to a mean between the densities of K and Sb, or 
AU=:8‘111. The platinum weights contain about 5759‘5 grains, the brass weights 
about 5760 grains each. Hence log uSp = 2‘43430, log i;RS = 2'43430, log wK = 
2-85766, logySb = 2-84513, logt;U=2-85135. 
The temperature and pressure to which it will be most convenient to reduce the 
weighings, is the mean of the temperatures and pressures observed during the com- 
parisons of Sp and RS with U. This, taking into account the number of observa- 
tions in the two cases, is, — thermometer =65-66 Fahrenheit, barometer =29*75 
English inches. When both the weights are of brass, or both of platinum, the 
reduction is so small as to be insensible. 
