The contracts for the first ten miles of the western road are completed, with but few exceptions, those of little importance, and such as are common on work of this kind. The contractors are paid, except a small sum reserved from each, sufficient to ensure the final completion next spring. The road is open, and used daily by travellers. On the second letting, comprising nearly eleven miles in addition, the contractors (for the time) have made considerable progress, and are now at work, each with a considerable number of hands, and there is every probability the contracts will be completed within the time provided, viz: the first of November next. It is now sufficiently ascertained that the estimates heretofore made, viz: $150,000, will be sufficient for the completion of the first twenty-one miles, embracing every expense, probably a small surplus of from three to five thousand dollars. The next ten miles it is expected will cost, on an average, nearly the same as the preceding; a small sum in addition may be required, on account of several large bridges which will be wanting. If it be desirable that the work should progress with more expedition, ten miles or more might be let the ensuing spring; it would be well, at all events, to contract for four or five miles more on account of building a bridge across the Little Youghiogheny river, as it must be a considerable building, and, to lessen expense, it would be necessary to take advantage of low-water, and the spring season, for procuring sawed timber, as there is but one sawmill convenient, and that during three-fourths of the year unemployed for want of water. It is expected the Legislature of this State will pass a law, authorizing the President to receive toll, for the purpose of repairing the road, and likewise against abuses which are common on all roads of the kind, to prevent which laws have been found necessary.

The first ten miles of the western road is finally completed. The banks and sideways are dressed, and the whole of the accounts settled and paid.

The second letting, eleven miles, has not been finished, as was expected and provided for by contract the 1st of November last; four miles thereof are now used by travellers, and require but little dressing to the sideways to be complete, four more are nearly so, and it is confidently expected the whole will be finished next summer.

On the third letting, about eighteen miles, there is but little done; the time fixed by contract for its completion is the 1st of November next. Judging from the little progress made, it will not he finished within that time; but as the contractors are making great exertions to procure laborers, and a number of persons, from the evident utility of the work, have become anxious for its speedy progress, and are giving their aid to procure hands, and the contractors having in view to employ slaves, it is quite possible this letting may be completed within the time.

Provisions for keeping the road in repair, and for the prevention of abuses to the work, similar to that of other turnpikes, are every day becoming more necessary.

The distance from the end of the last letting to Uniontown is about twenty-one miles. A sum of from one hundred and fifty to one hundred and sixty thousand dollars it is thought would be sufficient to make the road to the latter place.

In my last report of the progress of the Western road I informed you that the first ten miles were completed, since which the side roads, banks, &c. have been repaired.

The second letting, four sections, about eleven miles in length, is now generally used by the traveller. The pavement is complete, except from a half to three-fourths of a mile, and the side roads are much in the same state of forwardness. This part of the road would have been entirely completed early this fall but for the very uncommon rainy and wet summer we have had, which has impeded the progress of the work very considerably.

On the third letting there is nine sections about eighteen miles in length. On the two first, ninth, and tenth, containing about four and three quarter miles, little progress is made. On the 11th, about one and three quarter miles, nearly the whole of the leveling is done, and the greater part stoned. The twelfth, thirteenth, and fourteenth sections, containing about five and three quarter miles, are in a state of great forwardness, nearly the whole of the leveling done, and at least two-thirds of the paving is completed. On the remaining three sections, containing about six miles, but little is done. Taking this part of the work into view, it may be understood that about eight miles is in great forwardness and nearly completed, and on ten but little progress is made, except the mason work, which is nearly finished. Adding the whole of the work done together, it may be considered about twenty-eight miles, and eleven yet to be made, which will complete the whole of the work contracted for. The eleven miles are unequally divided between three contractors: one of them, it is expected, will complete his work early next spring; another, early in the fall, and the third may not complete his before late next season. With a view to show that some of the contractors will be thrown idle, if more work is not let early next season, I have been induced to be thus particular in stating the situation of the work at present, and the probable state it will be in early next summer.

I had nearly completed a location from the end of the work contracted for, to Uniontown, about twenty-one miles, and should have reported the work; but as the contractors did not proceed with that speed I expected, I thought it prudent to defer this report, and take time to re-examine the ground. As much time, pains, and care is necessary in fixing on the best ground, and shortest distance through this mountainous country, I will have the notes ready early next spring, when more work can be let, if thought advisable; we shall cross the present travelled road about eleven miles from the end of the present work. This distance would give us another year's work, or we might contract to the west foot of Laurel Hill, about eighteen miles; the old road, and the location, will not be more than thirty to forty perches apart at this point, and the ground quite level and firm between them.

Thirty-nine miles is the end of the work now contracted for, and places us on the east bank of the big Youghiogheny River, which must be bridged, and ought to be commenced as early next season as the weather and the water will admit. This work has been put off with a view to ascertain with what success we should succeed in building the bridge of eighty feet span across the little Youghiogeny River, which we have now so far completed, that no doubt exists as to our ability to build bridges of any size that may be thought necessary on this road. The cost of a stone bridge (which I prefer on roads much travelled) across the big Youghiogheny, will be about $40,000; of wood it may be built for the one-half of this sum; but, as it is probable all the bridges to the Monongahela will be of stone, and permanently built, I would advise building this bridge likewise of stone, unless it should be found that the necessary materials cannot be had.

As I have no knowledge of the sum appropriated, of course cannot say what additional appropriation will be necessary to complete this work to any particular point, and, therefore, recommend calculating the road at about $7,500 per mile for that done, and that yet to be made. This sum, it is expected, will include every expense on an average, when nothing but common bridging is required.

No difficulty, as yet, presented itself requiring legislative aid. except for keeping the road in repair, and to prevent abuses to the work by mischievous persons, and for which immediate provision ought to be made. On reference to a bill, forwarded on the 29th ultimo, my views, and the provisions thought necessary, will be fully explained.

In my last report of the progress of the western road, I stated that twenty-eight miles had been nearly completed. At the same time, we have in a similar situation upwards of thirty-five miles, and on the remaining three miles, (which complete the distance to the Big Youghiogeny river,) the contractor is now engaged. The state of the road is substantially as follows:

The 1st, 2d, 3d, 4th, 5ih, 6th, 7th, 8th, and 11th sections are finished, embracing a distance of twenty-three miles. The 9th, 12th, 13th, and 14th sections, about eight miles in length, are so near completion as to have admitted travellers upon it for some time past. The 10th and 15th sections (about four and a half miles) are in a state of considerable forwardness, and on the 16th and 17th sections (about three and a half miles) the work is progressing. The mason work upon the whole road to the end of the 17th section (Big Youghiogheny river) has been finished, the accounts adjusted and paid. The contractors on that part of the road last let out, to the end of about forty-seven miles from this place, have made considerable progress, and, from present appearances, I conclude they will be enabled to finish the work within the time specified in their contracts, by which time I confidently believe the whole of the turnpike east of the Big Youghiogheny river will be finished, if it be not sooner.

The contractors for the bridge to be built over the Big Youghiogheny river have commenced the undertaking. They have obtained a rock foundation for the west abutment, about fifteen to eighteen feet below the surface of low water, and have raised the abutment to the ordinary height of the water, in the river. This is the chief part of what has been done, except providing materials for recommencing the ensuing season.

The repairs made the past summer upon the first six sections (comprising about sixteen miles) have cost $1,200. These repairs have rendered the road nearly as perfect as when first made. Early next summer a considerable extent of road will be received from the contractors, when the expense of repairs will be much increased, and when it appears to me essential that some regular plan be adopted, as well with a view of keeping the road in perfect order, as to diminish the probable expenditures by the timely application of a remedy.

If this great national undertaking does not progress with a rapidity equal to the wishes of Government or the anxiety of individuals, the cause may be easily traced to their primitive sources, without involving the crimination of any one. The two most prominent of these I shall proceed to name the inefficiency of the existing mode of letting out contracts, and the very inadequate supply of hands. To the last of these causes is mainly chargeable the tardy completion of that which is now finished, and the incomplete state of some of those sections which are of the old letting. A road thus made by contract may and must frequently get into the hands of men without adequate means, but with every disposition lo fulfil their engagements; they are desirous of doing the work, underbid others, and perhaps contract for what will be an eventual loss to them. The consequences are, the retarding the work by the failure of the contractor; the hands lose their wages, and are thus deterred from labor, and in a manner driven from the road. Then, again, contractors, in order to obtain the work, are obliged to do it so low that they cannot offer any advance of price to the laborers, be the demand for them ever so pressing. Thus, men who prefer lighter labor, also prefer the labor of the farm; consequently, the work drags on heavily, and the contractors fail to perform their engagements in the specified time.

I am sensibly alive to the importance of a speedy completion of the road, but have no hope of accomplishing this object under the present system of contracting. If rapidity be desired by Government, a plan more likely to produce that effect, in my estimation, would be to abandon the mode of separate contracts altogether, and substitute day labor. In this way, rapidity of execution would be combined with faithfulness in performance. All inducements to fraud or deception would be done away; and, from my experience in very extensive repairs on other work, in which from two to three hundred men were employed, I do believe the work could be done belter, certainly with more speed, and with a considerable saving of lime, and perhaps of money. The effect of the organization of the whole number of laborers under one efficient head, aided and assisted by the subalterns, may readily be conceived, by making the comparison with a properly organized military force. By this organization, the vigorous and salutary hand of public authority is immediately felt in tho security for the prompt payment of hands, and the certain and speedy means of supplying any want of labor by increasing the per diem. An increase of twenty-five cents per day, or at most fifty cents, I suppose would produce as many men as we could employ. This price, and the security of the Government for its payment, would give us a choice of all the spare labor of the adjacent country. These are mere suggestions of my own, submitted for your consideration, if the idea is properly embraced by my expression, and you approve of the alteration. If any further explanations are required, I shall attend to your request with promptitude and pleasure.

The ground between the end of the last letting (forty-seven miles from this place) and Uniontown, a distance of about thirteen miles, I have examined; but little time would be requisite to prepare the location. This part of the work might be commenced early next spring. A sum of about $90,000, it is believed, will be sufficient to complete it.