we can declare the constructor private  ,it is called
private constructor.

When you declare a Constructor with Private access modifier 
then it is called Private Constructor.

If you declare a Constructor as private then it don't allow 
to create object for its derived class,i.e you loose 
inhirect facility for that class.
Ex:
Class A
{
// some code
 Private Void A()
 {
 //Private Constructor
 }
}

Class B:A
{
//code
}

B obj = new B();// will give Compilation Error

Because Class A construcor declared as private hence its 
accessbility limit is to that class only ,Class B can't 
access. As i explained the heirarchy of Constructors in the 
previous qn, when we create a object for Class B that 
constructor will call constructor A but class B have no 
rights to access the Class A constructor hence we will get 
compilation error.

When we want to control the object instantiation 
or trying to implement singleton pattern

private constructor access only that class. we can't access 
in other class.we can use the private constructor in 
singleton patteren.

In singleton pattern the constructor is not private but
protected.

Go for private constructor when your class has methods which
do not require object creation. ex. (Math class in c#).
Like If your class has all static method, you need not to
create an object in that case go for private constructor.