Transactions . ndition that bevel wheels be able towork correctly with any others of the same pitch besides their ownfellows. Hence, when this last is the case, a rolling circle may be used up tohalf the virtual number of teeth of each wheel, for its own flanks andthe other wheels faces. And if they are wished to work with other wheels (as afterwardsdescribed) the rolling- circle may still be kept about double of that forspur wheels. This will require separate tables for R and R, from thosefor spur wheels. VIRTUAL NUMBERS OF TEETH AND RADII OF number of teeth, or the factor m, to be
Transactions . ndition that bevel wheels be able towork correctly with any others of the same pitch besides their ownfellows. Hence, when this last is the case, a rolling circle may be used up tohalf the virtual number of teeth of each wheel, for its own flanks andthe other wheels faces. And if they are wished to work with other wheels (as afterwardsdescribed) the rolling- circle may still be kept about double of that forspur wheels. This will require separate tables for R and R, from thosefor spur wheels. VIRTUAL NUMBERS OF TEETH AND RADII OF number of teeth, or the factor m, to be used in the formulae, orto go into the tables, is not the real number of teeth, nor the real radiusof wheel -r- radius rolling- circle, but is to be found thus :— Let the lines A B and B Cbe the diameters of a pair ofbevel wheels, seen in edge view,and D G, D H, the centrelines g_ of their shafts. Draw also B Dand G H at right angles to B D. Then, for the forms of teeth,the virtual radius of wheel ?ieeih E. A B is B G, = B E —^ and of wheel BCisBH = BF BD D F Nfteefh, II The virtual m is the virtual radius The virtual number of teeth, always greater than the real number,is Mx = M ^ and Nx = N |^. CAPABILITY OF WORKING WITH OTHER BEVEL WHEELS. Although each pair of bevel wheels is usually designed to work onlywith each other, and that at right angles; yet, if there be any two pairsof bevel wheels of same pitch, having the dimension B D the same(and of same rolling circle and h), then any of the wheels will workwith any of the others; of course at angles determined by the anglesa and /3 in each case. 282 ON THE TEETH OF WHEELS. It may be said that cases where this is done are rare; but it is some-times wanted, and would likely be much oftener resorted to, if facilitieswere afforded for obtaining wheels to suit. Now, in arranging- sets of bevel wheel patterns, or deciding on exactsize for a pair for a given purpose, it would be a simple matter, whenother conditions did not pr
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