I am doing a project where i am to design a constant current source using a 9/10 Volts regulator of a 78xx series regulators.

The problem i encounter with this circuit is that the current is not constant. i have connected 24V at the input of the regulator, then connect the com/grnd to output voltage through my current producing resistor. the com/grnd of regulator is connected to ground of supply( 24V ) through my load. with constant current flowing i am aspiring to measure the voltage across the varying load at constant current. the data sheet says it should work, but it doesn’t.

 

Show your complete circuit.

 

...the data sheet says it should work, but it doesn’t.

What would "it doesn't (work)" mean?

-“When things are acting funny, measure the amount of funny”. (Bob Pease)

(Complete aside: I just followed a link to some of Bob's wisdom and discovered this is NOT his quote, he is quoting production test manager Tom Milligan, and he calls this phrase “Milligan’s Law,” in his honor.)

 

You probably need a cap between the 78XX O/p and Ground Terminals as recommended!

 

Have you ever consider to using LM317?

LM317 datasheet, page 9, the middle of right side, precision current limiter.
http://www.datasheetcatalog.org/datasheet/nationalsemiconductor/DS009063.PDF