170 PROCEEDINGS OF THE AMERICAN ACADEMY 



The study of the periodic law has directed attention to the relations 

 between the atomic weights and these properties, muny of wliich were 

 previously treated as functions of the electro-chemical order. 



When the exact atomic weights are all determined with sufficient 

 accuracy, it is natural to infer that the deviations from the regular 

 increase will show a law as significant as the approximate coinci- 

 dence with the serial numbers, and even now we see clear evidences 

 of this law. To make it more apparent, it will first be necessary so 

 to adjust the formula as to reduce these differences to a minimum, and 

 in the low atomic weights to take account of smaller fractions. 



The formula a -\- n d then has the following values for the sev- 

 eral groups of common difference : — 



6.99 + «X 4.02 12.00 + «X 4.01 



70.25 + nX4.85 74.88 + ^x4.12 



107.85 + n X 0.20 105.98 + /i X 6.22 



Table III. shows the deviations, arranged in the groups and series 

 of the periodic law ; the lower division shows the electro-chemical 

 numbers in the same form. 



Neglecting insignificant deviations, we find the positive results, or 

 those where the atomic weight is slightly in excess of the serial num- 

 ber, either near the extremes of the electric series, in elements of 

 maximum atomic volume, etc., or in the very centre of this series. 

 The negative results occur half-way between the centre and the ex- 

 tremes. Of the perissads, 1, 2, — 31, 32, — 57, 59, are positive, and 

 17, 18, 19, 21, — 44, 47, 54, 55, are negative; of the artiads, 7, — 

 46, 51, 53, are positive, and 8, 14, 21, 23, 28, are negative. 



In the periodic arrangement, the first and second groups show posi- 

 tive deviations in the high series of this arrangement; the third, fourth, 

 and fifth, negative in the high series ; the sixth, positive in the high 

 series; and the seventh, jjositive in two terms, and insignificant in 

 two. The seventh and eighth groups are negative in the third series. 

 The deviation of Zn is not included in these calculations, nor is the 

 cause of its deviation yet apparent. Perhaps the perissads of the 

 second group are formed from an artiad nucleus, and the artiads of 

 the second group from a perissad nucleus, thus : * 05, 70, 75, 80, etc., 

 and 03 * 71, 75, 79, etc. The last line shows the algebraic mean of 

 the deviations in each group, which, as might be expected, corre- 

 sponds nearly to the relative atomic volumes. 



To do justice to the bearing of these results on the physical ques- 

 tion of the ultimate nature of " atoms " would involve a mathematical 



