1881.] 4b5 [Chase. 



This is equivalent to twice the time of vibration in a simple pendulum 

 of the same height, (cos 0), or to the time of A-ibration in a linear pendulum 

 of four times the height. The requirements of vis viva, synchronism, and 

 the conversion of wave-propagating velocity into velocity of oscillation 

 under central action, are all satisfied, as I have shown in mj'^ discussions of 

 explosive energy (Note 16, et al.), hj combining the ratios of this and 

 the foregoing note, 5^ X f ■ 



78. Standard Temperatures. 



In thermodynamic deductions and comparisons, it is often important to 

 decide what temperature should be taken as the standard. Whenever a 

 sufficient number of kinetic values have been deduced for the natural 

 units, M^, Lo, T„, the introduction of conditioning equations may help us 

 to much accurate and useful knowledge which will lead to greater pre- 

 cision in many details of molecular physics. The present range of uncer- 

 tainty may be estimated by examining the influence of two diflereut possi- 

 ble standards upon the results of Note 16. The combining calories appear 

 to have been observed, in each instance, at the temperature of 15^ C. To 

 reduce the mean to 0°, we have 



H, = 2 X 15 X 3.409 = 102.27 

 O =r 16 X 15 X .2175 = 52.20 



Total deduction =: 154.47 



Leaving 68886 — 154.47 = 68731.53 calories 



1389.6 

 f X i X i X 68731.53 X -5330" = 279.15 miles ^=7^^. 



On the other hand, if we take the mean between the freezing and boiling 

 points, as in Note 75, we find 

 68886 -f ff of 154.47 = 69246.43 calories, representing K — 281.24 miles. 



\ gives in„ = 332,693 m^ ; nr = 92,871,000 miles. 



^2 " TO„ = 328,989 m^ ; nr = 92,525,000 miles. 



Note 75 m^ = 328,438 ■% ; 7ir = 92,472,500 miles. 



79. Factors of Vis Viva. 



Although ordinary kinetic investigations involve considerations both of 

 mass and velocity, the equality of action and reaction furnishes data, in 

 many cases, for dispensing with one of the three kinetic units. For ex- 

 ample, the equation of circular orbital revolution, v = y'gr = '\~, may 



I i/rV' -y/Vd 

 be put in the form -j = — : — =: — 7-, and we may use either of the 



equivalent values without vitiating our results. The meaning of the 

 mass-factor is especially obscure in the "dimensions of electric units," but 

 when we see that m is regarded as the product of electrostatic m- by elec- 

 tromagnetic m-, and when we remember the importance of Ampere's 



