448 



SCIENCE. 



mical text books for nearly half a century. Witness also 

 those mathematical tables " independently computed for 

 this work " containing errors identical with older tables. 

 The definitions given by a professional teacher, whose 

 knowledge is gained from and chiefly confined to text 

 books, will therefore be found to differ from those of a 

 mathematician, astronomer or physicist, whose concep- 

 tions are drawn from memoirs and documents differing 

 radically from text books. If a mathematician, not a 

 teacher, should write an algebra he would probably reflect 

 usage of mathematical terms by mathematicians better 

 than the teacher ; at the same time the teacher might ex- 

 press himsslf with more clear conciseness and in a 

 manner better adapted to the class room. 



The differences pointed out above are illustrated in the 

 work before us. A co-efficient is defined as a known 

 factor, in accordance with the usual custom of defining 

 it ; it is certain that this restriction is not kept up even in 

 algebraic text-books, as they speak of indeterminate 

 (meaning undetermined) co-efficients. That the leading 

 letters of the alphabet usually stand for known quantities 

 is some:hing which the student has to z/«learn as soon as 

 he gets out of the elements, and often before, as is the 

 case in this work when Interest, Annuities, etc., is 

 reached. The statement (p. 27) that " it is usual to prefix 

 to the parenthesis the sign of the first term that is to be 

 enclosed within it," may be questioned. 



" An equation " according 10 this book " is a statement 

 that two expressions are equal." Suppose we make this 

 statement: "One pound is equal to sixteen ounces," 

 will not this conform to the definition and at the same time 

 will it not fail to rtpresent the algebraist's conception of 

 an equation ? According to the definition of " Equation 



of Condition " x * = my is not an equation of condition. 

 " To solve an equation is, to find the value of the un- 

 known quantity," thus implying that there is but one 

 value that will satisfy the equation, an impression that 

 will subsequently require correction. The terms cancel 

 and reduce so much used are not defined. The usage 

 of the first is in accordance with general use but not in 

 accordance with the usual definition. In fact no defini- 

 tion of it in any algebra (I am ready to be corrected) 

 conforms to mathematical usage. 



The definition of fraction is purely the arithmetical one 

 in which the numerator and denominator are supposed to 

 be integers and hence fails as a general definition, just 

 as the definition of index or exponent fails through too 

 great limitation or from tacitly assuming that a general 

 symbol will only have special values. 



In spite, however, of the points to which we have 

 called attention above we consider this algebra a useful 

 one. The numerous examples afford the student ample 

 resources for getting practically familiar with algebraic 

 manipulation, and the conspicuous absence of set rules 

 compels the work to be done thoughtfully rather than by 

 rule of thumb. Factoring, that important branch of alge- 

 bra is fully treated, though the same can hardly be said of 

 radicals. The chapter on logarithms is well done, much 

 better than is common, and to our mind is decidedly the 

 best chapter in the book. The book is well printed and 

 attractive in appearance in spite of the lines at the top of 

 the page and is very free from typographical errors. We 

 have only noticed one, p. 349, Ex. 20, where $10 should 

 read $5. Marcus Baker. 



U. S. Coast and Geodetic Survey Office, 

 Washington, D. C, August 11, 1881. 



METEOROLOGICAL REPORT FOR NEW YORK CITY FOR THE WEEK ENDING SEPT. 10, 1881. 



Latitude 40 45' 58' N.; Longitude 73 57' 58" W.; height of instruments above the ground, 53 feet ; above the sea, 97 



feet ; by self-recording instruments. 



BAROMETER. 



THERMOMETERS. 



SEPTEMBER. 



MEAN FOR 

 THE DAY. 



MAXIMUM. 



MINIMUM. 



MEAN. 



MAXIMUM. 



MINIMUM. 



maxi'm 



Reduced 

 to 



Freezing. 



Reduced 

 to 



Freezing. 



Time. 



Reduced 

 to 



Freezing. 



Time. 



Dry 

 Bulb. 



Wet 

 Bulb. 



Dry 

 Bulb. 



Time. 



Wet 

 Bulb. 



Time. 



Dry 

 Bulb. 



Time. 



Wet 

 Bulb. 



Time. 



In Sun. 



Sunday, 4.. 

 Monday, 5.. 

 Tuesday, 6.. 

 Wednesday, 7 . 

 Thursday, 8.. 

 Friday, 9-. 

 Saturday, 10.. 



30.008 

 30.051 

 30.007 

 =9-934 

 30.031 

 30.003 

 29-933 



30.032 

 30.096 

 30.042 

 29.992 

 30.088 

 30.082 

 29.994 



12 p. m. 

 9 a. m. 

 9 a. m. 

 9 a. m. 

 9 p. m. 

 a. m. 

 9 a. m. 



29.950 

 30 008 

 29.988 

 29.894 

 29.928 

 29.950 

 29.900 



a. m 



6 p. m. 



4 p. m. 



5 P- m 

 a. m 



7 P- m 

 12 p. m. 



68.3 

 75-3 

 84.6 

 90.6 

 79.0 



73-3 

 72.0 



64.7 

 70.6 

 76.0 

 76.0 



7i-3 

 68.0 



69-3 



71 

 82 



97 

 101 



*9 

 78 

 75 



3 P' m - 



4 P- m- 

 4 p. m. 



3 P- m - 

 2 p. m. 



4 p. m. 

 9 a. m. 



66 

 75 

 81 

 83 

 78 

 72 

 71 



3 P. m. 



4 P- m- 

 4 P- m. 

 6 p 111. 

 2 p. m. 

 4 p. m. 

 9 a. m. 



65 

 68 

 74 

 79 



69 



68 

 66 



6 a. m. 

 5 a- 



5 a. m. 



6 a. in. 

 12 p. m. 



5 a. m. 

 12 p. m. 



62 

 66 

 72 

 73 

 *3 

 64 



65 



6 a. m. 

 5 a. m. 



5 a. m. 



6 a. m. 

 12 p. m. 



5 a. m. 

 12 p. m. 



ft. 

 132. 

 150. 

 154- 

 133- 



96. 

 117. 



Mean for the week - 29.995 inches. 



Maximum for the week at 9 a. m., Sept. 5th 30 .096 



Minimum " at 5 p. m., Sept. 7th 29.894 



Range 202 



Dry- Wet. 



Mean for the week 77.6 degrees 70.8 degrees. 



Maximum for the week, at 3 pm. 7th 101. " at 6 pin 7th, 83. " 

 Minimum " ifc 6 am. 4th 65. 11 at 6 am 4th, 62. 



Range " " 36. " .'21. " 



WIND. 





DIRECTION. 



VELOCITY 

 IN MILES. 



SEPTEMBER 



7 a. m. 



2 p. m. 



9 P- m - 



Distance 

 for the 

 Day. 



Sunday, 4- 

 Monday, 5. 

 Tuesday, 6. 

 Wednesday, 7. 

 Thursday, 8. 

 Friday, 9. 



s. e. 



s. w. 

 w. s w. 

 w. s. w. 

 n. n. w. 

 e. s. e. 



s. 

 s. 

 n. w. 

 w. n.w. 

 e. n. e. 

 s. s. e. 



s. 



s. s. w. 

 s. w. 

 w. 

 e. 



s. e. 



87 

 158 



8t 

 122 

 r>7 



63 



Saturday, 10. 



s. c. 



n.e. 



n. e. 



104 



FORCE IN 

 LBS. PER 

 SQR. FEET. 



Time. 



y± 11.30 pm 

 ■zYi 0.50am 

 H 5-3° pm 



•2% 2.0opm 



l'i 



3.20 pm 

 4.00 pm 



8.40 pm 



HYGROMETER. 



FORCE OF VAPOR. 



RELATIVE 

 HUMIDITY. 



B 



a 



B 



rt 



p. 



p. 



t-» 





o> 



.516 



572 



■599 



•599 



•717 



•757 



•757 



•74- 



.850 



■717 



■559 



.827 



.690 



.809 



•529 



•529 



.625 



•693 



.706 



.704 



.635 



CLOUDS. 



CLEAR, 

 OVERCAST. 



8 cu. 

 6 cu. 



9 cu. 9 cu. 

 8 cu. 



3 cir. cu. 1 cir.cu 



4 cir. cu. 1 cir. 



8 cu. 



RAIN AND SNOW. 



DEPTH OF RAIN AND SNOW 

 IN INCHES. 



Time 



of 

 Begin- 

 ing. 



io£ am 

 4.40pm 



Time 



of 

 End- 

 ing. 



Du ra- 

 tion, 

 h. m. 



1 1 i am i.oo 

 10 pm 5.20 



Distance traveled during the week 712 



Maximum force 7 



miles, 

 lbs. 



Total amount of water for the week. 

 Duration of rain 



.08 



.09 inch, 

 minutes. 



DANIEL DRAPER, Ph. D. 

 Director Meteorological Observatory of the Department of Public 



. 6 hours, 20 

 Parks, New York. 



