1082 
4. By the aid of the above considerations it is possible to represent 
the results of the experiments described in Comm. N°. 151d somewhat 
more systematically. As there are only two infinite series of modes 
of motion, everything may be reduced to the change of two of the 
five elements u, 7, 7,, K and R'). In the first place, seeing that in 
most of the experiments the apparatus remained unchanged (7,, K 
and R thus remaining the same), and only the liquid was changed, 
the most natural procedure is to consider 4 and u as the variables 
and accordingly to reduce equation / of section 3 (Comm. N°. 151d) 
which was found with a modified oscillating system to the same 
values of K and 7, which applied to the equations ato f. Equation 
h itself does not change thereby, considering that @ and z are 
dimensionless numbers; d does not change either and the conditions 
(2) show, that the same equation ought to have been found, if 
the sphere, connected with the aluminium cylinder, had oscillated 
in a liquid for which w= .607 and 74 = .01028. The value of 
PT a 
P= = ~ — (10 would also have remained unaltered. 
It is preferable, however, to reduce everything to one and the 
same liquid, for instance with u =1 and 4 = .01 (water at 20°), 
and allow A and 7, to me *). In that case the adjoining table 
is obtained. 
This table may be utilised for the purpose of deriving the most 
favourable conditions, under which the experiments with a given 
liquid can be conducted; we have only to reduce it to a different 
liquid by multiplying all values of 7’, and A by definite factors. 
As an instance, taking for liquid hydrogen the values: u = .07 
and 74 — .00013, the latter of which was calculated in Comm. N°. 1485 
section 13 by the application of the law of corresponding states, it 
will be seen that for this liquid the values of 7, have to be taken 
about 5 times higher and those of A about 15 times smaller; if we 
wish, therefore, to experiment with liquid hydrogen under condi- 
tions about corresponding to those which existed in the experiments 
with ether, it would be necessary to take K=60 and 7, = 40. 
1) At least, if we use the rough approximation of confining the oscillating body 
to the sphere. Of course it would be possible to extend the theory of similarity 
to the case where the oscillating system is partly in one liquid and partly in 
another; it is easily seen, that in that case the ratios of the densities of the two 
liquids must be equal in all cases. 
2) This was also the method followed in Comm. N°. 148c. The advantage is 
that K and To can be changed over a much wider range than y and g. 
