1894.] Mechanical Equivalent of Heat. 23 



various ages, the corresponding line of Table I will give the informa- 

 tion, while if the smoothed values are wanted, a similar line in the 

 chart of isogens will give them after being smoothed, not in one 

 dimension only but in tivo dimensions. Similarly, as regards the birth- 

 rates for a father of any specified age and for mothers of various ages, 

 by following the vertical columns instead of the horizontal lines. 



In conclusion, I would remark that, though the method of isogens 

 applied to Korosi's tables fully discusses the distribution of mean 

 birth-rates, those tables do not enable us to determine the second 

 postulate of paramount importance, namely, the degree of conformity 

 of individual cases to the means of many cases. We know nothing 

 thus far about the facility of error at the various positions in the 

 chart, whether or no it conforms to the normal law of frequency ; 

 still less, what is its modulus, or whether the modulus is constant 

 throughout the chart or varies in accordance with some definite law. 



The answer to these questions admits of being obtained by a 

 moderate amount of work on the original observations, selecting at 

 first a few squares for exploratory purposes, such as are (1) dis- 

 tributed evenly about the chart, and (2) contain each of them not 

 less than some 300 observations, and (3) whose means accord with 

 the smoothed* isogens that pass over the squares, thereby affording 

 satisfactory centres of reference. 



IV. " Appendix to a Communication entitled ' The Mechanical 

 Equivalent of Heat.' "* By E. H. GRIFFITHS, M.A. Com- 

 municated by R. T. GLAZEBROOK, F.R.S. Received 

 December 7, 1893. 



Section I. 



In a communication which I had the honour of making to the 

 Royal Society in the spring of this year, the following statement 

 occurs (p. 420) : " We are (with the help of Mr. Callendar) now 

 entering on a careful direct comparison of thermometer E OT with a 

 new form of air thermometer, which, there is every reason to believe, 

 will give very accurate results, but we are unable to assign any 

 definite limit to the time that this investigation may take." 



A great number of comparisons have been made during the 

 summer of this year by Mr. Callendar and myself between the mer- 

 cury thermometer E TO used by me for determining the temperature of 

 the calorimeter, the Tonnelot thermometer, No. 11,048, described in 

 the above paper (pp. 426 433), the platinum thermometer N, by 

 which the mercury thermometer E OT had been previously standardised, 



* ' Phil. Trans.,' vol. 184 (1893), A, pp. 361504. 



