November 11, 1898.] 



SCIENCE. 



677 



gines. It is a practitioner's and student's 

 text-booli in that system, as Wood's Thermody- 

 namics is the representative for the same classes 

 of readers of tlie Kankinian method. 



In the new book a considerable addition has 

 been made to the discussion of the gas-engines, 

 which includes the latest information regarding 

 producer-gas and the oil-engines, and closes 

 with a discussion of the Diesel motor, now at- 

 tracting, deservedly, much attention among 

 members of the engineering profession as hav- 

 ing attained unusual results by an exception- 

 ally successful attempt to reproduce ideal ther- 

 modynamic conditions in an approximation to 

 the Carnot cycle. Its best work is reported at 223 

 grms. of petroleum per hour for 19.2 horse- 

 power, equal to three-fourths of a pound of coal 

 per horse-power-hour. The best steam-engines, 

 even of many times this power, consume seldom 

 less than double this figure. The latter half of 

 book is devoted mainly to the subjects of steam- 

 engine testing, compound and other multiple- 

 cylinder engines, the influence of the cooling 

 effect of cylinder-walls and steam-engine econ- 

 omy generally. Considerable new matter ap- 

 pears in these sections. The latest investiga- 

 tions, as those of Hall, and of Callendar and 

 Nicholson, are detailed, with admirable success 

 in condensation. Recent and notable reports 

 on steam-engine trials, as of the famous engines 

 of Leavitt and of Sulzer, of Schmidt and of 

 Kockwood, and of the steam-turbines, are sum- 

 marized and the data are tabulated. The more 

 elaborate scientific tests of the ' experimental 

 engines ' of the Massachusetts Institute of Tech- 

 nology and of Sibley College at Cornell Univer- 

 sity are presented in their essential details, 

 while the discussions exhibiting the ideal and 

 the real eflects of the operations of compound- 

 ing, of superheating and of jacketing, as in- 

 fluencing efficiency and economy of steam, heat 

 and fuel, are most instructive and valuable. 

 The final chapters are devoted to brief discus- 

 sions of compressed-air machines and apparatus 

 of refrigeration. 



This book is a rarely good work and is ex- 

 cellently published. It is one which no member 

 of the engineering profession dealing with the 

 heat-engines can safely leave out of the list of 

 his working library, and no student desiring 



more than a superficial knowledge of its subject 

 should fail to read with special care. 



R. H. Thurston. 



Prismoidal Formulie and Earthwork. By Thomas 

 U. Taylor, Professor of Applied Mathe- 

 matics in the University of Texas. New 

 York, John Wiley & Sons. 8vo. Pp. 102 and 

 one plate. Price, $1.50. 



The historical and theoretical discussions of 

 this volume will be of especial interest and value 

 to civil engineers on account of the extensive 

 use of the prismoidal formula made by them in 

 earthwork calculations and because the engi- 

 neering handbooks generally avoid such dis- 

 cussions. There are probably few engineers 

 who know that the prismoidal formula is ap- 

 plicable to the volume of a sphere, or to any 

 segment of a sphere, as also to ellipsoids and 

 paraboloids. The author shows that its appli- 

 cation is wider even than this, and that the 

 volume of any prismoid whose sectional area 

 can be expressed by a cubic function of its dis- 

 tance from any reference section is found by 

 adding the areas of the two bases to four times 

 the area of the mid-section and multiplying 

 this sum by one-sixth of the length. He also 

 gives demonstrations of the two-term prismoidal 

 formulas of Koppe, Hirsch and Echols, and 

 discusses their limitations and uses in a very 

 interesting manner. Although these two-term 

 formulas involve but two sections instead of 

 three, it does not appear that they are more 

 convenient in practice than the common 

 formula. 



The author attributes to Newton the honor of 

 the discovery of the prismoidal formula, and 

 states that it is given in the Methodus Differen- 

 tialis, 1711. An examination of this paper of 

 Newton fails, however, to substantiate this state- 

 ment, and it is to be regretted that the author 

 did not quote the words in which he claims that 

 the theorem was announced. His reference to 

 Simpson is also unsatisfactory, although he 

 points out that Simpson's rule for the quadra- 

 ture of a curve from three ordinates is the same 

 in form as the prismoidal formula. With these 

 exceptions the historical matter of the volume 

 is more complete than can be easily found else- 

 where. Over one-half of the book is devoted 



