282 Researches in the Theory and Calculus of Operations 



impulsions or velocities inflicted with such intensities : the 

 mass 1, under the velocity 3, describes in the unit of time 

 three times the distance due to the velocity 1 in the same 

 time, etc. 



Item 3 of figure 21 stands as representative of the water 

 type : By substituting a negative or positive semiatom for 

 one of the hydrogene semiatoms, an acid or base is obtained; 

 or replacing one hydrogene semiatom by a negative and 

 the other by a positive semiatom, the result is a salt. Simi- 

 larly item 4 represents the ammonia type : The substituting 

 of one negative semiatom gives an amide; of one positive 

 semiatom, gives an amine; of one positive and one negative 

 semiatom for two semiatoms of hydrogen, yields an alka- 

 lamide. The hypothetical radical ammonium (and perhaps 

 other hypotheticals), may be explained as a semiatom, which 

 cannot exist by itself, but only in combination. Item 2 ap- 

 plies to the chlorine compounds, and item 5 to the carbon 

 compounds. 



It must be understood that these pictured waves are not 

 intended to represent actual vibrations, but merely the num- 

 ber and relative position, or the atomicity of the combining 

 semiatomic forces as in fig. 21; while in fig. 22, the com- 

 plete dichotomised atoms are similarly imaged, the upper 

 lefthand section of each pair regarded as the advancing 

 phase. A volumnar admeasurement is delineated in the ac- 

 companying figure, and explained in the marginal notations. 

 Each elementary parallelogram, as ab, a'6', a"b', a"b" or 

 be, b'& etc. stands for the measure of a half-volume or semi- 

 atomic gaseous volume, when the entire volume is called 

 unity. Whence ac, a'c' contains one atomic volume, and ac, 

 a n c" contains two atomic volumes; and to this measure of 

 two gaseous volumes by the chemical combination of ac, 

 a'c 1 respectively with a'c', a"c", or a'c', de or a'c', aV or a'c', 

 d"e" are reduced (molecular volume : Frankland, Barker, 

 &c). 



