APPLIED MECHANICS LECORNU. 275 



I have stated that the number of cylinders of the Gnome motor is 

 odd. The same statement is true of many motors in use for aviation, 

 and we may well ask wh3^ The reply is given through the formula 

 which I had the occasion to prove, and which may be stated as follows : 

 n= K {n-\-j>~'-^) where n is the number of cylinders, K, the number 

 of cranks, and p the order in which the sparking occurs ; that is after 

 having sparked the first cylinder, then the one of rank, ^ + 1, is 

 sparked, then 2 p + 1, and so on until the first one is reached again. 

 In order that all the cylinders may be s})arked in turn it is necessary 

 and sufficient that p is prime with n. That granted, it follows that, 

 if one crank is emplo3'ed in order to simplify and make the motor as 

 Ught as possible, Jc must equal 1 and when p = 2, n mlist be odd. 



III. RAILROADS. 



The development of our industries requires the use every day of 

 more and more powerful locomotives. Since the gauge is fixed, and 

 so prevents an increase in their wddth, any increase has to occur in 

 then* length. When we pass a certain limit precautions are neces- 

 sary for permitting their passage around curves. This has led to the 

 construction of long articulated locomotives of the Mallet ty])e. The 

 driving mechanism is here distributed between two trucks, the rear 

 one of which only is rigid with the boiler. The fore truck, movable 

 with respect to the rear one, carries the low-pressure cylinders which 

 receive and discharge the steam through flexible tubes. 



The Americans have gone yet further. The excessive length, of the 

 new boilers renders their management difficult, so that they divide it 

 into two parts bolted together. The two parts may then be se})nrated 

 at the workshop for inspection and repair. Then they have recog- 

 nized the advantage of making the joint flexible in order to diminish 

 in going siround curves the overhanging of the ends of the engine 

 beyond the tracks. They thus obtain without an increase of crew a 

 flexibility equal to that of coupled locomoiives. With engines thus 

 coupled there are hauled between ('hicago and the Pacific coast 

 freight trains carrying the enormous loads of 2,200 tons. The 

 results have been excellent and it is only a matter of extending iho 

 process or, what accomplishes the same purpose, of maldng new 

 engines by coupling together older ones. 



In order to increase the traction, the Americans have transformed 

 in turn the tendei into a kind of an auxiliary engine provided with two 

 cylinders connected by flexible tubes for furnishing the low-pressure 

 steam coming from the locomotive. There is thus ol>tained almost 

 a rolling manufactory provided wath 12 axle motors, S of which are 

 under the locomotive and 4 under the tender. There are besides 

 trucks at the front end of the locomotive and under the rear end of 

 the tender. May I ask how one engineer and ojie fireman can be 

 sufficient to control the boiler of such an engine ? 



