488 
PROFESSOR SCHUMACHER ON THE LATE 
and the logarithms of these values of Q are given by M. Bessel in the Astron. Nach. 
vol. vii. p. 3/6. 
Ten years later M. Maelstrom resumed the subject, and adding to his experi- 
ments those of MM. Muncke and Stampfer, made since his first determination, 
gave a new Table for the density of pure water in the Vetenskaps Academiens Hand- 
lingar for ar 1833. The whole paper is translated in Poggendorff’s Annalen der 
Physilx, vol. xxxiv. p. 220 etseq. M. Maelstrom finds for the volume of pure water 
between the limits of 0° and -f- 30° of the centigrade thermometer*, 
1 - 0-000057590 t + 0-0000075611 r 2 - 0-000000035100 r 3 
where r denotes degrees of the centigrade thermometer ; and where the volume of 
pure water at the temperature of melting ice is considered as unity. If we call the 
volume v, we obtain hence, for Fahrenheit’s degrees (denoted by t ), the formula 
= 1-0-0000319945 (^-32 o )+0-00000233367(^-32 o ) 2 -0-00000000601848(^-32 o ) 3 , 
which gives the minimum of volume (for t = 39 o- 04 7) = 0-99988832, and conse- 
quently the maximum of density = 1-0001117. Now the density being = we 
obtain 
Q 1 - 
^ ~ 1-0001 117.(1 — 0-00003 1 9945 (t — 32) + 0-0000023 3367 (/ - 32) 2 - 0-0000000060 1 848 (if - 32) 3 )' 
Agreeably to this equation the values of Q, whose logarithms are given in the fol- 
lowing Table, are calculated ; which Table contains also the values of v as above 
stated, as well as of D, together with their logarithms : D being the density of pure 
water at the temperature t (in Fahrenheit degrees), the density at 32° being = 1. 
* There are errors of the press, or oversights in calculation, in the original memoir of M. Hallstrom, re - 
peated in the translation, which I have corrected here. The equation for v should be the arithmetic mean 
(Poggendorff, p. 246.) of the four equations which M. Hallstrom calls I. V. VI. IX. Now we have 
(I.) p. 228. v = 1 - 0-000049976 t + 0-0000062453 r 2 - 0-000000007645 r 3 
(V.) p. 238. v = 1 - 0-000060835 r + 0-0000081037 r 2 — O' 000000048282 r 3 
(VI.) p. 239. v = 1 - 0-000059269 r + 0-0000076816 t- 2 - 0-000000037159 r 3 
(IX.) p. 244. v = 1 - 0-000060280 r + 0‘0000082138 r 2 - 0 000000047313 r 3 
The arithmetic mean of these four equations is 
v = 1 - 0 000057590 r + 0-0000075611 r 2 - 0'000000035100 - 3 , 
as above stated, and not 
v — \— 0-000057577 r + 0-0000075601 t- 2 - 0 000000035091 r 3 , 
as M. Hallstrom has it. The Table (p. 247.) likewise which he has calculated upon his formula for v and D, 
has several inaccuracies. 
