^94) Mr Harvey on the Method of Minimum Squares, 
found and difficult nature, has not met with the wide circulation 
which has distinguished his Elements of Geometry ; but for nice 
analytical skill, for elegance, for beautiful and varied invention, 
and all the qualities which distinguish the higher and more re- 
fined walks of analytical inquiry, it is unquestionably unrival- 
led. 
In any investigation ‘relating to the subject of minimum 
squares, the name of Cotes must not be forgotten. With this 
distinguished man the subject may be said to have originated, 
since he was the first who allowed each observation to have an 
influence on the object of inquiry, dependent on its known va- 
lue. In this, as indeed in many other instances, the fine origi- 
nality of Cotes’ mind was clearly displayed. His merit must 
have, indeed, been great, when Newton said of him, ‘‘ If Cotea 
had hved, we had known something.” 
On the Method Minimum Squares, 
In most of those investigations whose object is to deduce from 
experimental observations, the most accurate results they are ca- 
pable of affording, we are generally conducted to a system of 
equations of the form 
E a -|- hoc -j- cy -}- ^ % -j- &c., 
in which a, 5, &c. are known coefficients, varying from one 
equation to the other, and a*, z, &c. unknown quantities, 
whose values it is necessary to determine by the condition, that 
the value of E is reduced either to Zero, or to a very small 
quantity in each equation. 
If we had as many equations as unknown quantities a?, y^ Zy 
&c., there would be no difficulty in determining the values of the 
latter, in such a manner as to render the errors denoted by E, 
absolutely null. But it most frequently happens, that the num- 
ber of equations exceed that of the unknown quantities ; and 
hence it becomes impossible to annihilate all the errors connect- 
ed with the investigation. 
As this is a condition which appertmns to the greater part of 
those physical and astronomical problems, whose object is the de- 
termination of some important elements, it is necessary to exer- 
cise some discretion in the distribution of the errors, and not to 
expect that all the hypotheses employed should conduct precise- 
ly to the same results ; and, above all, we must endeavour to 
