From the London Daily News.

GENOA, Sunday, May 27.

Dispatches have been received from Palermo by the Sardinian Government, which fully confirm not only the victory obtained by GARIBALDI at Calatafimi over the 4,000 Neapolitans led by LANZA, but the more important one, which placed the heights surrounding Palermo in the hands of the Sicilian patriots. The first of these victories is further confirmed in a letter addressed by GARIBALDI himself to ROSALINO PILO, Count of Capace, from Calatafimi, under date of the 16th:

"Yesterday we fought and won. The enemy is flying towards Palermo. The populations are in high spirits, and join my camp by thousands. To-morrow I shall march on Alcamo. Tell the Sicilians that the hour is come to put an end to their slavery, and that we shall do it soon. Every arm is Hood for the brave -- musket, scythe, hatchet, a nail at the top of a stick. Unite with me. Thwart the enemy’s plans as much as possible. Light bonfires upon all the heights which surround the Neapolitan troops. During the night kill as many of the enemies outpost sentries as you can. Intercept the communications. In a word, harass the enemy as much as you are able. I hope to see you soon

Yours, GARIBALDI"

As you see, this laconic letter contains all the necessary instructions for a war to the knife, and war to the knife it will be. To understand how, after the loss sustained by the Neapolitan troops at Calatafimi, the insurgents were able to push their army to the very gate of Palermo, it is necessary to bear in mind that the remains of LANZA’s column were incessantly attacked by the bands of Baron SANT ANNA and Marquis FIERATURA from Montelepre to the Pioppo. The defeat of the Neapolitans was so thorough that only 1,500 out of 4,000 could reach the capital, and even these entered it only by groups of ten or twenty at a time. The cavalry was almost annihilated, field-pieces were abandoned, together with ammunition carts. The routed column as soon as it entered the barracks declared it would never go to meet GARIBALDI again, and the dread under which it was laboring soon spread among the garrison. Works of defence were erected all round the city, but the threatening attitude of the population will render them useless when Palermo is attacked by the patriots. According to an official dispatch received an hour ago, to-day is the day in which GARIBALDI will attack the in trenched camp of the Neapolitan army. Besides these summary pieces of intelligence, partly derived from private telegrams, partly from those sent by Marquis PERSANO, the Sardinian Admiral in the Mediterranean, to his government, the man steam-packet has brought us letters from Palermo, dated May 18, and those of Messina dated May 21, together with the official bulletins of the insurgents.

I had written so far when I heard that the Neapolitan Consul of this city had received a telegram from Count CARAFA, in which it is stated that GARIBALDI was completely routed whilst attempting to get possession of the Neapolitan entrenched camp near Palermo. The Government of his Neapolitan Majesty has always proved so mendacious that I cannot place any faith in the truth of its official information sent to its agent. Let us, therefore, wait for the confirmation of this report from more trustworthy quarters. Till then we have a right to believe that the Sicilians are triumphant, and that the island is almost freed from the ga???ling yoke of FRANCIS II.