346 Mr. Baspace on the Influence of Signs 
to its particular rules, and each liable to its peculiar difficulties. 
The order in which these succeed each other, will prescribe that 
which will be followed in the remarks upon them. 
I. The first stage consists in translating the proposed ques- 
tion into the language of analysis. 
II. The second, comprehends the system of operations 
necessary to be performed, in order to resolve that analytical 
question into which the first stage had transformed the proposed 
one. 
III. The third and last stage consists in retranslating the 
results of the analytical process into ordinary language. 
I. In the first step, which consists in translating the proposed 
question into the language of analysis, much caution is requisite: 
for unless this is correctly done, it is quite manifest that the 
labour bestowed on the remaining stages is useless. It is at this 
point that the principles applicable to the question are employed 
for its solution; in all the succeeding parts they are kept totally 
out of sight: the termination of this stage is usually marked by 
the circumstance of the difficulty being reduced to one or more 
equations*, which is the case in most of those questions that 
arise in the application of analysis to physics: but this however 
does not always happen, since very many questions relating to 
chances are reduced to the finding of the coefficient of a certain 
term in the developement of a given function into a series, and 
although most of these may be reduced to equations of differences, 
yet it is not universally the case. It is of some importance to 
observe, that those errors most difficult to detect and remove, 
* The term equation in this place must be understood to comprehend such expressions 
as A~B> or < C. ; . ; 
