Both the great parties are rallying and cont centrating their forces, that they may uninupon soine candidate, though both are surroudded by serious difficulties which t svill be hard to overeÃ³me. Tlie " Slavery Question" is the source of the difficulty. A larga portion of the Whig and Democratie parties of the North, say, " no more slavo territory, no support of any man who does not avow that. A small part of the South, some three States, affirm that they will oppose whoever does not unequivocally declare "that ncither the people of the territories, nor Congress, have any right to stop aslaveholder frotn goinginto any new territory with his pi-operty." On the Democratie side, Messrs. Polk, Cues, Buchanan, Woodbury and Dallas are spoken of as candidatos for the Presidency ; of these, Mr. Woodbury, at present, seoms to us to unite the largest number of States. On tho Whig, Messrs. Taylor, Clay, McLean and, Scott, are most prominent. Mr. Clay lias published the following circular: [Examiner.] TO THE PUBLIC. The various and conflicting reports whicli have been iti circulation, in regara to my intentions with respect to the next Presidency, appear to me to f'uanish a proper occasion for a ful], frank and explicit exposilion of my feeling, wishes and views upon that subject. This Ã¯t is now my purpose to make. With a strong disinchnation to the use of my name again in connection with tliat office, I laft my residence in December last, lindera determination to announce to the public, in some suitable form, my desire not to be tho't of as a candidatr. During my absonce, I frequently expressed to different gentlemen my unwillingness to be again in that attitude; hut no one was author ized to publish my decisiÃ³n one way or the other, having reserved the right todo so exclusively to myself. On reflection, I thojght it was duo to my friends to consult with thora before I took a final step. Accordingly, n tho course of the last three months, 1 have had many opportunities of conferring fully and freely with them. Many of them have addressed to mo the strongest appeals, and the most earnest entreaties, both verbal and written, to dissuade me from executing my inlended purpois. They have represented to me that the withdrawal of my name would be fatal to the success, and, perhaps, lead to the dissolution, of the party, willi which I have been associated, especial! in the free States; that at noformer period did there ever exist so great a probability of my election, if I would consent to the use of my name ; that the great States of New York and Ohio would u all human probability, cast their votes for me ; that New York would more certainly bestow her suffrage upon me than upon any other candidato, and that Ohio wo'd give her vote to no candidate residing in the slave States but to me; that there is a better prospect than has heretofore al any time exsted, that Pennsyl'nia would unite with them - that no candidate can be elected without the concurredce of two of thoso three States, and none could be defeated upon whom all three of them should be united ; that great numbers of our fellow-citizens, both of native and forÃ¯gn birth, who were deceived and thereiore voted against me at the last election, are now eager for an opportuuity of besto wing upon me their suffrage; and that, whilst there is a strong and decided preference for me, entertained by the great body of the Wliig party throughout the United States, they (the friends to whom 1 refer,) at the same time are con vinced that I am more available than any candidate thal could be presented to the American people. I do not pretend to vouch fur the accuracy of all these representations, althongh I do not entertain a doubt that they have been honestly made, and are sincerely believed. It has been nioreover urged to me that the great obligations under which I have hitherto been placed by a large portion of the peoplo of the United States, the full forcÃ© of which no one can be more sensible of than I am, demand that I should not withliold the use of my name if it bo required. And I have been reininded offaequent declarations which I have made, that while hfe and health remain, a man is bound to renderhis best services upon the calj of his country. Since my return home, I have anxiously deliberated upon my duty to myself, to my principies, to my fnenils, and, above all, to my country. The conflict between my uiiaffected desire to continue in prÃvale iÃe, as most congenial with my feelings and condition, and my wish faitlifully to perform all my public dudes, has been painful and embarrassing. If I refuse the use ofmy name, and those injurious oonsequences should ensue, wliich liave been so confÃdently predicted by ray friends, I sho'J justly incur their reproaches, and the reproaches ofmy own heart. And, if, on the contrarv, I should assent to the use ofmy name, whatr ever the result may be, I shall escape both. I have, therefore, finally decided to leave to the National Convention, wliichis to assembla next June, tho consideration of my name, in connexion with such othecs as may be presented to it, to make a seleclion of a smtable candidate for President of the United States. And whatever may be the issue of its fair and full deliberations, t will meet with my prompt and cheerful acquiescence. It will be seen, from what I have stated, that there was reason to anticÃpate that I woulJ decline giving my consent to the use ofmy name again as a candidale tor the Presiilencv of the United States. Owing, perhaps, to th's, as well as other causes, many of my friends and fellow-citizens have avowed a preference for, and directed their at tention to the distinguished names of othar citizens of the U. States. I take p'.easure in truly declaring, that I have no regrets to express, no complaints, no reproaches to make on account of auy such preferences, which I am fjlly persuaded are generally founded on honest and patriotic eonvictions. H. CLAY. Ashland, April 10, 1848. EiP M. Guizot and family have, as Protestants, joined the French Protestant Presbytcnan church in St. Martin's Ie Grand, London. Madame Guizot, the venerable mothor of th# ex-minister, attends tlie service.