He makes a passing mention of the fourth aim of life in some verses
PART-1
Chapter 2 : On the acquisition of Dharma, Artha and Kama MAN, the period of whose life is one hundred years, should practise Dharma, Artha and Kama at different times and in such a manner that they may harmonize together and not clash in any way. Any action which conduces to the practice of Dharma, Artha and Kama together, or of any two, or even one of them, should be performed, but an action which conduces to the practice of one of them at the expense of the remaining two should not be performed. Sacrifices such as those made for the destruction of enemies, or for the fall of rain, are seen to bear fruit. Holy Writ, which ordains the practice of Dharma, does not admit of a doubt. It is, further, the protection of what is acquired, and the increase of what is protected. Artha should be learnt from the king’s officers, and from merchants who may be versed in the ways of commerce.Kama is the enjoyment of appropriate objects by the five senses of hearing, feeling, seeing, tasting and smelling, assisted by the mind together with the soul.
