416 



Mr. J. Buchanan. 



[May 27, 



Their trustworthiness when applied to individual families is shown 

 as strongly in Table IV, whose results are conveniently summarised in 

 Table VI. I have there classified the amounts of error in the several 

 calculations : thus if the estimate in any one family was 3 light- eyed 

 children and the observed number was 4, 1 should count the error as 1°0. 

 I have worked to one place of decimals in this table, in order to bring 

 out the different shades of trustworthiness in the three sets of calcula- 

 tions, which thus become very apparent. It will be seen that the calcu- 

 lations in Ciass III are by far the most precise. In more than one-half 

 of those calculations the error does not exceed 0*5, whereas in I and II 

 more than three-quarters of them are wrong to at least that amount. 

 Only one- quarter of Class III are more than 1*1 in error, but some- 

 where about the half of Classes I and II are wrong to that amount. 

 In comparing I with II, we find I to be slightly, but I think distinctly, 

 the superior estimate. The relative accuracy of III as compared 

 with I and II, is what we should have expected, supposing the basis 

 of the calculations to be true, because the additional knowledge 

 utilised in III, over what is turned to account in I and II, must be 

 an advantage. 



Conclusion. — The general trustworthiness of these calculations of 

 the probable proportion of light-eyed and dark-eyed children in indi- 

 vidual families, whose ancestral eye-colour is more or less known, is 

 comparable with the chance of drawing a white or a black ball out of 

 a bag in which the relative numbers of white and black balls are the 

 same as those given by the calculation. The larger the proportion 

 of data derived from a certain knowledge of ancestral eye-colours, 

 and not from inferences about them, the more true does the com- 

 parison become. My returns are insufficiently numerous and too 

 subject to uncertainty of observation to make it worth while to 

 submit them to a more rigorous analysis, but the broad conclusion to 

 which the present results irresistibly lead, is that the same peculiar 

 hereditary relation that was shown to subsist between a man and 

 each of his ancestors in respect to the quality of stature, also 

 subsists in respect to that of eye-colour. 



II. " A General Theorem in Electrostatic Induction, with Appli- 

 cation of it to the Origin of Electrification by Friction." 

 By John Buchanan, B.Sc, Demonstrator of Physics, 

 University College, London. Communicated by Professor 

 G. Carey Foster, B.A., F.R.S. Received May 13, 1886. 



Part I. 



This paper contains the results of an investigation into the question : 

 If a dielectric be brought into a field of electric force, and there its 



