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and represents the elapsed process time in seconds multiplied by the object-like macro CLK_TCK or CLOCKS_PER_SEC which is set to 1000 for DOS in <time.h>
It is not multiplied, it is divided by..

Actually, for the old DOS enviroment the clock_t is used with the clock() function, and it is divided by the macro TICKS_PER_SEC, not CLOCKS_PER_SEC or CLK_TCK.

The form of TICKS_PER_SEC was:
#define TICKS_PER_SEC 18.2f

As you well said, this value represents the number of interupts that the timer emits per second.The clock() function is exactly the function that gets this number.

If you check it out, you'll see that this macro "works" only for Win 95 and over, nor for DOS.
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The 8253 timer oscillates at 1,193,180 Hz with a built-in divisor of 65,636
The "divisor" is 65536 (not 65636).It is not a coincidence that this number represents 2^16+1, the maximum number of values a WORD can store.