322 Professor Haminton on Conjugate Functions, 
0. Hence, by the theory of compound steps, we have expressions of the following 
sort for all the several moments of the equi-distant series (29.) : 
U 
E’—@a+Oa+@Qa+A, 
E =Oa+6a+t+A, 
= 0 e-vA5 (97.) 
=a. As 
SSC Ot eR 
SS Gage am oss 
with corresponding expressions for their several ordinal relations to the one standard 
moment A, or for the acts of transition which are made in passing from a to them, 
namely : 
E’—A=0a+ O0a+ Qa, 
E —aA=O0a+Oa, 
E —Aa=QOa, 
A —A=0; (98.) 
B —A=a, 
B —A>a+t+a, 
Bi —A=a -atia; 
&e. 
' 
The simple or compound step, a, or a +a, &c., from the zero-moment a to any 
positive moment 8B or B’ &c. of the series, may be called a positive step ; and the 
opposite simple or compound step, © a, or 92+6a, &c., from the same zero- 
moment A to any contra-positive moment E or rE’, &c., of the series, may be called a 
contra-positive step ; while the null step 0, from the zero-moment a to itself, may be 
called, by analogy of language, the zero-step. The original step a is supposed to 
be an effective step, and not a null one, since otherwise the whole series of moments 
(97.) would reduce themselves to the one original moment a; but it may be either a 
late-making or an early-making step, according as the (mental) order of progression of 
that series is from earlier to later, or from later to earlier moments. And the whole 
series or system of steps (98.), simple or compound, positive or contra-positive, effec- 
tive or null, which serve to generate the several moments of the equi-distant series 
(29.) or (97.) from the original or standard moment a, may be regarded as a system of 
steps generated from the original step a, by a system of acts of generation which are 
all of one common kind; each step haying therefore a certain relation of its own to 
