The radius vector / iu;iy also be expressed in term- of the mean ano- 

 maly, supposing the mean distance 1. 



cos. 2m - ea - 



cos. 3 



f ~ e* -f -| e 



cos. 4 iw 



In the case of the sun, e being small (viz. '016814) its powers above the 

 3d. may be neglected, and in this case y (1. 55". 26", 35) sin. m -f- 

 (!'. 12", 68) sin. 2 m + (1". 05) sin. 3 M. 



And r = 1 + i e* e cos. in | e* cos. 2 m. 



When m is computed from the apogee instead of the perigee, the signs 

 of the terms involving the odd multiples of m must be changed. 



ARCHES, Equilibrium of.f Whewell, Play fair.) 



1. In an arch which is in equilibrium, the weights of the voussoirs are 

 as the differences of the tangents of the angles which their joints make 

 with the vertical. 



Hence if O T be in the line of the joint 

 P Q or parallel to it, O T, parallel to 



P Q, &c., and T T, be horizontal, the 

 weights of the voussoirs C, C &c. will 

 be as the portions T T, T T &c. 



1 J 2 



Cor. 1. If the arch is a circle, the 

 weights of the voussoirs are as the dif- 

 ferences of the tangents of the arches, 

 reckoned from the crown. This is 

 nothing more than the general propo- 

 sition above, applied to a particular 

 case. 



Note.As the stones themselves can- 

 not always be made in the proportion 



thus required ; the wedges, of which they make parts, are supposed to 

 be extended upward by courses of masonry. The whole mass included 

 between the planes of the joints produced, as far as that masonry ex^ 

 tends, is understood to make up the weight of the voussoirs. 

 22 



