348 Mr. Baspace on the Influence of Signs 
only be resolved approximately, but in proportion to the interest 
thesé questions have excited, the variety and accuracy of the 
approximations have been multiplied. This is strongly exempli- 
fied in the problem of the three bodies, as applied to determining 
the place of the Moon: the great importance of the question has 
caused the approximations to be pushed to such an extent, that 
they have arrived at a degree of inelegance and complexity, which 
would long since have caused them to be rejected from any 
other question on the exact solution of which less important in- 
terests depended. But on this second stage in the solution of 
a question, it is less necessary to add many observations; the 
operations which are concerned in it, and the modes of effecting 
them, being more fully treated of in works of instruction than 
either of the others. 
III. The last of the stages into which the resolution of 
a question has been distributed, has been more neglected than 
any other. It may perhaps appear singular that the answer 
to a question, which is of course* the great object of research, 
should have been passed over without suflicient attention. It is 
not however of any errors in those results which are usually 
arrived at that I complain; but it is, that: sufficient instruction 
is not given in elementary works, as to the full meaning of all 
the different circumstances which are contained in the result that 
analysis has presented. In those questions which lead to alge- 
braic equations, it is not unfrequently the case, that some one 
or perhaps twe roots are taken as the answer, whilst all the 
remaining ones are completely neglected. Now a question can 
never be said to be fully answered until every root of the equation 
to which it has conducted has been discovered, and its signi- 
fication with reference to the data of that question been ex- 
plained. It sometimes happens that superfluous roots have been 
