Note on the formulas used for calculating the weight of the brain in the albino rats / by Shinkishi Hatai.

  • Hatai, Shinkishi.
Date:
1909
Catalogue details

Licence: In copyright

Credit: Note on the formulas used for calculating the weight of the brain in the albino rats / by Shinkishi Hatai. Source: Wellcome Collection.

Provider: This material has been provided by The Royal College of Surgeons of England. The original may be consulted at The Royal College of Surgeons of England.

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    The formula in each case was as follows: Brain weight or y = .509 log (x— 8.7)+0.554 (3) Spinal cord weight or y= .585 log (x + 21 )—0.795 (4) Body length ory = 143 log(x + 15 )—134 (5) Although the formulas (4) and (5) are entirely free from theo- retical objections within the interval x = (5 grams, 325 grams), the formula (3), however, has two defects when we apply it to the case of x < 8.7. The first defect, which appears when x, the body weight, is less than 8.7 grams, is due to the fact that the resulting value of (x— 8.7) becomes a negative quantity and the logarithm of such a quantity is necessarily imaginary. The diffi- culty thus presented is, however, merely a theoretical one, since for the purpose of computation the following method may be em- ployed. Let us consider the two cases when x is greater than a and when x is less than a then we have (A) - A = —1?— when x > « dx (x —a) (B) — —-— when x < a dx (a— x) Then integration of (A) leads to the formula (3) which we have already obtained, that is y = A + C log (x — B) = .554 + .569 log (x — 8.7) while the integration of (B) becomes (C) y = A — C log (ft —x) = .554 - .569 log (8.7 —x) The formula (C) thus obtained gives results identical with those obtained when we compute the value of y from the formula (D) y = .554 + .569 log (-C) In this case, of course, with an understanding that log (— C) should be treated as equivalent to — log C. As long as the results obtained by the formula (C) agree with those obtained by the formula (D), the following procedure is justified.