FORMULAE. 117 



&quot;y&quot; is the grade in feet per mile. 



tk x&quot; is the load drawn, including tender, and is expressed in tons. 



Formula? (2) and (4) are simply deductions by transposition from (1) and (3.) 



In formula? (1) and (3) the numerator expresses the effective adhesive weight; that is to say, it 

 expresses the portion of the total adhesive weight which is found by experiment to be really 

 effective in drawing a load in certain states of the rail. Now, since we know by experiment that 

 on a level a force of eight pounds is necessary to draw one ton, if we divide the effective adhesive 

 weight (expressed in pounds) by S, the quotient will be the load due that effective adhesive weight, 



0.2 A 



and formula (1) will read x = . 



8 



On a grade we know that, in addition to the force necessary to overcome the friction, it is also 

 necessary to apply further power to counteract the effect of gravity. 



Taking a load of one ton, and calling &quot;/&quot; the height of the plane, &quot;/&quot; the length, (for the value 

 of which we may, in the slight inclinations given railway grades, substitute the value of the base 

 of the plane, without appreciable error,) we have for the tendency of one ton to move down the 

 2240 xf 2240 x f 



plane , or substituting for Z, 5280, the number of feet in a mile = 0.4242^ &quot;/&quot; 



/ 5280 



being the height in feet of a plane whose base is one mile long. 



This expression (0.4242/) is, then, the measure of the force required to prevent one ton from 

 sliding down the plane, and must be added to the force necessary to overcome the friction of a 

 ton on a level in order to obtain the force required to keep one ton in motion up a grade. 



Dividing, then, by this sum (0.4242y*+ 8) the disposable power of the engine (0.2 A,) we 

 have the number of tons that the engine can draw up any given grade. 



Engines usually weigh from 20 to 24 tons; some as much as 30 tons: it is considered desirable 

 to reduce the weight of engines as much as possible, in order to diminish the wear and tear of 

 the rails. 



Most engines now run with four drivers the front of the engine resting upon a truck with 

 eight small wheels ; some engines, particularly those intended for heavy grades, are placed upon 

 six wheels, all driveis, in order to increase the effective adhesive weight. The objection to mul 

 tiplying the number of drivers consists in the increased number of joints, &c., with the conse 

 quent increase of friction and loss of power. 



A common 8-wheel tender weighs, empty , 14,000 Ibs. 



Water for 25 miles, (12,000 gallons at 8.35 Ibs. per gallon) 10,437 &quot; 



Wood, (1.44 cord, at 3,180 Ibs. per cord) 4,579 &quot; 



4 passenger cars, for 50 passengers each, at 12,000 Ibs. each 48,000 &quot; 



2 baggage cars, at 16,000 Ibs 32,000 &quot; 



200 passengers, at 150 Ibs. each 30,000 &quot; 



Baggage, at 100 Ibs. each passenger 20,000 &quot; 



Add for contingencies 12,224 &quot; 



Total weight of train of 200 passengers 171 ,240 &quot; 



or 76 tons. 



We will now take a 20-ton engine on four drivers and apply the formula. 



The total adhesive weight will be about 28,600 Ibs. 



Its maximum load on a level, over a good track 715 tons. 



Its maximum load on a level, over a track in bad condition, slippery, &c 511 &quot; 



By formula (2) we have for the same engine the maximum grade up which it 



can draw the train of 200 passengers, as given in detail above 159f feet. 



By formula (4) we have for same data a maximum grade of 109 &quot; 



