1 847.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



351 



Hud which will greatly aggravate the difficulties with which the adminis- 

 tration of Lord John Russell is already threatened. A blow once given, 

 we hope the railway interest will not rest till they have swept away every 

 vestige of interference. 



TEMPERATURE OF STEAM. 



Sir — The following empirical formula for determining the temperature of 

 steam is new, accurate, and may be interesting to some of your readers. 



If n = the number of atmospheres, then 



212 + ',2 + 'I + Y. «S:c., till " = the temperature in degrees of Fah. 

 renheit. Thus, for 



Atmospheres. 



2 = 212° 



3 = 212° 



4 = 212° 



5 = 290° 



6 = 304°' 



248 + 'j' 



7 = 316°-4 + 



The following are the results of Dr. Ure's experiments, and those of the 

 Franklin Institute, as far as ten atmospheres, contrasted with the results 

 obtained by this method of calculation : — 



Dublin, October 16, 1847. 



I am. Sir, 



Your obedient servant, 



William T Matieb, 



Civil Engineer. 



MEASUREMENT OF ANGLES. 



How to lay off an Angle of any number of Degrees, Minutes, Sfc, with 

 Compasses only, without the use of Scale or Protractor. 



By Oliver Byrne. 



First allow me to correct a trifling mistake involved in the solution of the 



converse of this proposition, published in the Journal of last month. Page 



313, col. 2, line 10, for " -H 1 or - 2," read " -^ 1 or - 1 ;" and the ex- 



pression (Q) becomes 



nor 



e = . 



mny + y + 1 



The same correction must be made at page 314. 



Let it be required to lay off an angle of 36° 40' = fi. — Take any small 

 opening of the compasses less than one-tenth of the radios, and lay off any 



number of equal small arcs, from A to 1 ; from 1 to 2 ; from 2 to 3 ; &c. 

 (fig. 1), until we have laid otT an arc, A B, g reater than the one required. 



Fig. 1. 



Draw Bb through the centre 0, then will the arc ab •= arc A B, which we 



shall put = 20 (p in this example, and proceed to measure a i as in example 



fig. 5, page 314. Lay off a 4 from 4 to c ; from c to d ; from d to e ; from 



e to/; homftog. Putting ja = A,, then 



108 

 6 X 20(J> -^ A, = 360° = — /3; because 



360° 



21600 



11 

 108 



36° 40' "~ 2200 



Layoff, as before directed, J a, = A j, from a to A, from A to s, and J to /; 



then calling s t, A„, we have 



3A, + A, ^ 20<p; 



and we find that s t is contained 28 times in the arc a 4 ; 



108 

 .-. 120^ -^ ^, = —&; 3^1 ■(■ Aa = 209; and 28Aj = 20?. 



Eliminating A, and A^, we find 



29205 



fl = p = 12-9 times © nearly ; 



2268 f 1 , 



.•. 36° 40' «= Z A N is laid off with as much ease and certainty as by a 



protractor. 



As a second example, let it be required to lay off an angle of 132° 27'. — 



From 180° 0' take 132° 27' = 47° 33', which put = $. 



360° 2400 r , v„ „^„„ 



when put = -, then -B = 360° = tt. 



47" 33' 



317 



Fig. 2. 

 Referring to fig. 2, we have laid off 29 small arcs from A to 29 = €. AB = <ii = 

 ic ~ cd = de =• ef. And a j = S h'^of = A, ; hg = A^. 



