1798.] Mathematical Correfondence—Account of the State Houfe. 333only the want of room that in- ment, to find that arch geome-d.ices them to quit the maternal trically.hive. Next I proceed to fome of the nea; eft fertlements, where I procure proper aftiftance to cutquestion id.down the trees, get all my prey fecureil, and then return home with my prize.’SmT!JL ii V.By A. iLijor, M.iftcr of the Academy InGerman town.nppole a fquare pyramid,each tide of the bale being 40frrit bees i inches, and nernendicular heightI 1 ' ' 1 * O60 ; in the middle of the lide,ever procured were thus round inthe woods, by mere accident ;and at a certain diftance from thefor at that time I had no kind of bale, there is an aup'cr of threer, • , • . t • 11/ - ^ o'inches diameter entered, whichfieri im this method or tracing-othem. The body of the treeco nes out in the middle of thegie with the plane thereofn -ofbeing perfectly found, tney had f 1 de of the bale, forming an lodged themwixcs in the hollowof oneof its principal limbs, which ^0. Required the folid inches I carefully fa wed off, and with that fa idauger will cut our,dif-a good deal of labour and induf- likewife the perpendicularbrought it home, where 1 fixedhup again in the fame petition was entered, in which I found it growing.This was in April ; I had fivetance from the bafe where itX Jilo \V cib 111 a pill * X lKlvl IIV u ^ ^ • • r 1 1 O T 7c , r , . , Description of the or a.tfJiousj:,1 warms that year, and they have J 1, J 1 crc. in rhilaaettcia.been ever lince very profperous. This buiinefs generally takes upf... 11I d i 1 *Ltime everva week of my and to me it is a week of lolitaryeafe and relaxation.”f - • / *; / f, 1 •sc. in i i-itaceipt.ua.Acecmuank'd with an Elevation of thel'ront upon Chchntt-Ocver, taeen iroma c c * i r a r c m t a i’u i c n i c n t /]city-hall of Fhiladel-phi a. commonly called theState-houfeof Penn 1 y 1 vania, com-Mathematical Ccrreft:ndsnce.QUEc\ vVWljprchencimtr the nan nowocnipi-j Cl t •ed by the ConcTefs of the Urn-j oted States, compoi (imply elee a plain butnuncorange orbuildings, occupying theextent on the touch tide of Chef-on cxw holeBy Peter Delamar, now of the TTni-verfuy of IVnnfvlvani.i.Suppofe a ball, let fall from aface of reft into the curve of a mU ltree^ between Fifth andgiven cycloid, whole axis is per- Sixth-Streets. It prefents inpendicular to the plane of the front a centre xvuh two ranges;horizon : It is required to find (geometrically) in what j#?int oflaid curve, the motion will be the fwifteft, towards the horizon ?w inon beincr connected bvlt;- Cl QUESTION id.By John Craig, ?\!af;cr ff the Academy,Cheihut Hill.Given the excels of the tangent of an arch (to a known radius) above that of its complcythetwo ranges of a more mmure eie-1 /ration than the principal piler.The State-houfe properly lo called, occupies the centre and waserected in 1735- It was originally hniihed wiih a lofty fteeplc,which was taken down after ithad ftood feverul years previousCfTO