1921.] The Eighth Indian Science Congress. CXVii 
The kinetic theory of solids and the partition of thermal 
energy.— By B. M. Sen 
The kinetic theory of gases has been aaghne nae by many well-known 
physicists, nut little coo has been made on that a8 the solids. 
ntly, however, Nernst and ot thers ce developed the subject on 
Planck’? hypothesis. In i a pags paper the subject 2 teen treated 
on i 
sie 
Atte s ha made to otiials the specific heat of atoms on the 
Satara = the equipartition ‘of energy. Jt is known sa tfor 1°C rise E 
temperature. euges om of most er absorb 4x 10° '® ergs in 
numbers, ach m having six degrees of freedom, oe of the oes 
able energy is sae ml by the pate ieee mo 
[ef. 4 m»®=ae where a=202 x 10- Pad 
while the other on is absorbed by the motion of ro tation. But the 
specific heat of most elements emg gradually with the a 
whereas the degree es 0 nate edo n only increase y leaps. It may be 
noted that t he hypothesis i is fairly precupeead for gas 
n the present paper, fro values of the peat heats and 
compressibility, the peel Bons sof ane ‘molecules pags nt determined an n 
— “he ics cular forces. The gain of energy molecule (for 1°C 
of t ture) is split up into hiss piéetione: Phy that t absorbed by 
the ieetae Genel velocity which increases the ex xternal ns | (2) that ab- 
orbed in doing work against the inter-molecular — ; (3) the third 
portion being absorbed by the pe erg itself and m be explained by 
the absorption by the electrons. Those three portions are calculated 
aud the mathematical analysis is worked out in 
This result is considered oh cobecgy being a direct negation of the 
Principle of Equi-partition of Ener: 
e on the criterion that two samples are samples of the 
same Population.—By P. C. MaHALANOBIS 
12) The a method consists in comparing Mean values 
i aad an’ ‘of the two samples, and finding the probably of the differ- 
ence m-m’ (as pera ured in terms of its probab — ye 
neglects alt together r any difference in the santa aabas of the t 
aca gag ab of f requen: cies. 
earson’s Coefficient of pak ain He The two samples Bi ee 
kg oup by oup, and their independ ence is measured by f 
probability (P ; aE, of x2, a certain defined fanahionl of the two series © 
reque 
If figs Rg- es -s ...total N. 
mn it ‘ rare ae total N’ 
oe series of actually observed frequency group®, 
2 
‘nN—" /N’ 
then x2=NN' S— ew) jee o's (A). 
the above two methods 
icaldata. It is shown 
the more appropriate 
3. In the first part of the present paper, 
are compared, with special reference to anthropolog! 
n 
geared = fferent C acpies. 
ba nou x hi ee Nee a © difficulties a! arise: in applying 
formula (A) " the case ‘of small samples. 
{i) The values of n =. , the up “frequencies, | depend to a 
gro 
considerable panes on the system of grouping adopted. 
