In the investigations made by Crampton it was shown that the formula would be more accurate, written as follows:[236]
| δ = | D₀ - D₀ʹ |
| (tʹ - t) × D₀ + D₀ʹ | |
| 2 |
The absolute densities can be calculated from the formula Δ = δ + K, in which Δ represents the coefficient of absolute expansion, δ the apparent coefficient of expansions observed in glass vessels, and K the cubical coefficient of expansion of the glass vessel. The mean absolute coefficient of expansion for fats and oils, for 1° as determined by experiment, is almost exactly 0.0008, and the apparent coefficient of expansion nearly 0.00077.[237]
288. Standard of Comparison.—In expressing specific gravities it is advisable to refer them always to water at 4°. The temperature at which the observation is made should also be given. Thus the expression of the specific gravity of lard, determined at different temperatures, is made as follows:
| 15°.5 | |
| d —— = | 0.89679; |
| 4° | |
| 40° | |
| d —— = | 0.91181; |
| 4° | |
| 100° | |
| and d —— = | 0.85997, |
| 4° | |
indicating the relative weights of the sample under examination at 15°.5, 40°, and 100°, respectively, to water at 4°.
289. Densities of Common Fats and Oils.—It is convenient to have at hand some of the data representing the densities of common fats and oils, and the following numbers are from results of determinations made in this laboratory:[238]
| 15°.5 | 40° | 100° | ||||
|---|---|---|---|---|---|---|
| Temperature. | d = | —. | d = | —. | d = | —. |
| 4° | 4° | 4° | ||||
| Leaf lard | 0.91181 | 0.89679 | 0.85997 | |||
| Lard stearin | 0.90965 | 0.89443 | 0.85750 | |||
| Oleostearin | 0.90714 | 0.89223 | 0.85572 | |||
| Crude cottonseed oil | 0.92016 | 0.90486 | 0.86739 | |||
| Summer ” ” | 0.92055 | 0.90496 | 0.86681 | |||
| Winter ” ” | 0.92179 | 0.90612 | 0.86774 | |||
| Refined ” ” | 0.92150 | 0.90573 | 0.86714 | |||
| Compound lard ” | 0.91515 | 0.90000 | 0.86289 | |||
| Olive oil | 0.91505 | 0.89965 | 0.86168 | |||