About the star :

Described as a deep garnet color, the south pole of the Milky Way, located in the neck of Cetus, the Whale or Sea-Monster, and has been called the constellation's necklace.

This is a very remarkable star, Mira, Stella Mira, and Collum Ceti are all titles for this "Wonderful Star". An eclipsing binary, (two stars that periodically obscure each other and rapidly dim), subject to extreme irregularities. Mira is a long-period variable star with a cycle of about 331 days from one period of maximum brightness to the next. This period is sometimes a little erratic and can be off by as much as 30 days either way. For about five months Mira is invisible, then in the next six months it gradually increases in brilliance, until finally it shines with the beautiful sparkle of a star of the second magnitude. This peak of brilliance lasts for about a fortnight, after which time it again starts slowly to fade. At various times it has not been seen at all with the naked eye for several years consecutively, — and its maxima and minima are even more irregular. While it has been known almost to equal Aldebaran in its light, as it did under Herschel's observations on the 6th of November, 1779, Chandler gives its maximum as from 1.7 to 5, and its minimum from 8 to 9.5. It thus sometimes sends out at its maximum fifteen hundredfold more light than at its minimum. (Allen).

Ancient people believed this pulsating action to represent the beating heart of the monster Cetus.

Influence of the constellaion :

According to Ptolemy this constellation is like Saturn. It is said to cause laziness and idleness, but to confer an emotional and charitable nature, with the ability to command especially in war. Makes one amiable, prudent, happy by sea and land, and helps to recover lost goods. (Robson).  

Influence of the star:

Its nature corresponds to Saturn and Jupiter. Connected well and with a well placed Saturn and linked up well otherwise, this will mean prudence, perseverance, versatility, a progressive spirit and endurance in solving difficult problems. This star in unhelpful connections, will bring as results failures, fiascoes, enmity, especially with Saturn transits and when linked with the Moon, melancholy will then appear. Linked with Mercury, it will mean a lessening of spiritual forces. In critical situations, suicide is indicated. (Ebertin). 

Remember, only the parallel and conjunction are important and the orb must be no more than 1 (one) degree.