I have seen people pouring milk on the Shivling.
What is the significance of this?
Image taken from shivmandirsarthali.com
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From shivmandirsarthali.com: (emphasis mine)
Abhishek is a Sanskrit term denoting a devotional activity of giving Holy bath to a deity. It literally means “to cleanse.” Before starting the ritual, a devotee washes his hands and pours water over the Ling. However, this practice is not to cleanse the Ling, as God doesn’t need any cleansing. He is the purest—but it is an implication of cleaning oneself. Later milk is poured on the Shiv Ling, which is a connotation of purifying one’s life and washing all the sins from oneself.
The practice is not to clean the Ling but the person itself. It washes all the sins from oneself and purify one's life.
Milk is used for Shiva-Linga Abhisekam beacuse it is one of the thing which can be used for Linga Abhisekam. For eg. Kamika Aagama (which is one of the 28 principle Shaiva Aagama) state:
वर्णभूत शरावैस्तु वज्राद्यैर्गोमयोद्भवैः|
पैष्टिकैर्वा सुरचितैः राजिका लवणेन च|| ४०६
पयोधति घृतक्षौद्र शर्कराद्यैः स्वशक्तितः|| ४०७
खण्डाभावादिक्षुसारो मध्वभावे घृतं भवेत्|| ४०८
जलधूपान्तरैः कार्योऽभिषेको विभवे सति|
नालिकेर फलाम्बोभिः अन्यैर्वा रसवद्रसैः|| ४०९
अभिषेकं ततः कुर्यान् न कुर्याच्छुन्यमस्तकम्||
Keeping the well-ground flour of rice and other grains, black mustard and salt in one or five shallow earthen plates or in the vajra-like plate made of cow-dung or in such other vessels, the Guru should besmear these over the Linga and then perform the ablution with warm water, perfumed water and unguents. Milk, curd, clarified butter, honey, candied sugar and such other substances may be used for ablution, according to his capacity. These may be with a measure of on kudupa (approximately, a quarter of a liter) to four kudupas(adhaka), increasing the measure by one kudupa each time. If candied sugar is not available, the juice of sugarcane may be used; if honey is not available, ghee may be used. If the resources are abundant, ablution may be done with the water collected from various sacred places and with various kinds of fumigation. Then the ablution should be done with tender coconut water , juices of various succulent fruits, flowered water, water deposited with gold or gold ornaments, water deposited with gems, and the water mixed with sandal paste. Ablution should not be done when the top of the Linga is bereft of flower or leaf.
Shiva Purana also states Sukra worshipping Vishweshwara Linga of Kashi with Panchamrita (Milk, Sugar, Honey, Yoghurt, Ghee) Abhisekam while obtaining Mrita Sanjivani Vidya:
स्थापयामास तत्रैव लिंगं शम्भो परात्मनः ।
कूपं चकार सद्रम्यं वेदव्यास तदग्रतः ।।
पञ्चामृतैर्द्रोणमितैर्लक्षकृत्वः प्रयत्नतः ।
स्रापयामास देवेशं सुगन्धस्रपनैर्बहु ।।
सहस्रकृत्वो देवेशं चन्दनैर्यक्षकर्दमै ।
समालिलिम्प सुप्रित्या सुगन्धोद्वर्त्तनान्यनु ।। (Shiva Purana Rudra Samhita chapter 50)
O! Vedavyasa he dug a pleasant well and consecrated an auspicious Linga of high souled Shiva (lodged at Kashi). He bathed Shiva a lakh of times assiduously with Panchamrita using a Drona measure each time. He also used fragnant materials with them for ablutions. He also applied Sandala paste as well as the paste of Yakshadharma to Shiva.- the lord of Gods a thousand times. Thereafter he applied the fragnant ointment over the Lord.
Thus, it is just a ritualistic method to worship Lord Shiva. And as already told above milk isn't necessarily required to do Abhisekam. It can just be used also. One can do Abhisekam using water only also.
Pouring milk on the Shivling is process of Abhishek. Abhishek is the process of bathing the deity. According to Shiv Aagam (Poojaa rules) Abhishekam is considered as one part of the Shodashopachaar Poojaa. Shiv will be pleased by the process of bathing. If you pour a drop of water on the ‘Ling form’ you will the blessings of Shiv. Since Shiv is widely worshiped in the form of the Shiv Ling as well as presiding deity, Annaabhishekam will be performed only to Shiv Ling.
Shiv Ling Abhishek is done with the prescribed 11 ingredients:
Siva is fond of Abhisheka." In Siva temples, a pot made up of copper or brass with a hole in the centre is kept hanging over the image or Linga of Siva, and water is falling on the image throughout day and night. Pouring over the Linga, water, milk, ghee, curd, honey, cocoanut water, Panchamrita, etc., is Abhisheka. Abhisheka is done for Lord Siva. Rudra is chanted along with the Abhisheka. Lord Siva is propitiated by Abhisheka. Lord Siva drank the poison that emanated from the ocean and wore the Ganga and moon on His head to cool His head. He has the fiery third eye. Constant Abhisheka cools this eye. The greatest and the highest Abhisheka is to pour the waters of pure love on the Atmalinga of the lotus of the heart. The external Abhisheka with various objects will help the growth of devotion and adoration for Lord Siva and eventually lead to internal Abhisheka with pure abundant flow of love.
Shiv lingam is mystical mesonic structure and cosmic pillar of enery. It represents Shiva who is manifestation of endless supreme power and enery . Enery flows contineously around , shiv linga can absorb and can focalize and then desipers enery with vibrations around. We can recieve this and inculcate in auro which affect our karma and dashas. To turn it in positive way , we pour milk from which these vibrations are absorbs in positive manner.
Water coming from clouds, rivers.. and it is we who neglect but water is divine (marjana mantra of sandhya vandana). Remembering it and thus remembering Him after looking at just anything is even more important. Everything is valuable and divine. This is the ultimate meaning of abhisheka you get if you start contemplating on the mantra.