172 



CALCULATING MACHINE. 



he commenced preaching in Troy as a stated 

 supply, and on the organization of the United 

 Presbyterian congregation in that city in 1834, 

 became its pastor, and remained in that connec- 

 tion until 1852, when he resigned and visited 

 Europe. On his return he resided for some 

 time in New York, where, in the summer of 

 1853, his wife died. In December of that 

 year, having returned to Troy, he was again in- 

 stalled as pastor of the United Presbyterian 

 congregation, and continued in the pastorate 

 till his death. He was an able preacher, ad- 

 hering firmly to his own views, yet wholly free 

 from bigotry or intolerance; a iiseful and effi- 

 cient pastor, greatly beloved by his people. 

 As a teacher he was highly successful, alike 

 from his exact and critical knowledge of the 

 classics, and the thoroughness and strictness 

 with which he trained and instructed his pupils. 

 He prepared at different times during his long 

 career as a teacher, a very complete series of 

 text-books for classical instruction, which ex- 



hibited his familiarity with the Greek and Latin 

 authors and his indomitable industry. These 

 works have come into very extensive use, and 

 have received the sanction and approval of many 

 eminent scholars and instructors. The follow- 

 ing are the principal works published by him : 

 " Practical Lessons in English Grammar and 

 Composition;" "Principles of English Gram- 

 mar;" "Introduction to Analytical English 

 Grammar ; " " Analytical and Practical English 

 Grammar ; " " Progressive Exercises in Analy- 

 sis and Parsing ; " " Principles of Latin Gram- 

 mar ; " " Latin Reader ; " "Exercises in Latin 

 Composition, and Key ; " " Cesar's Commenta 

 ries, with Notes and References ; " " Sallust, 

 with Notes and References ; " " Cicero's Ora- 

 tions, with Notes and References ; " " Latin- 

 English Dictionary, with Synonyms ; " " First 

 Lessons in Greek ; " " Principles of Greek 

 Grammar;" "Greek Reader, with Introduc- 

 tion on Greek Idioms, Greek Lexicon, &c. ; " 

 " Memoir of Rev. Alexander Bullions, D. D." 



C 



CALCULATING MACHINE. A machine 

 >f this kind is in use at the Dudley Observatory 

 in Albany. It is the only one ever completed ; 

 and although based on the same mathematical 

 theory as the one contemplated by Mr. Bab- 

 bage, it is yet essentially different in its mech- 

 anism. It is well known that Mr. Charles 

 E. Babbage was the first to attempt the con- 

 struction of a difference engine ; but in conse- 

 quence of some misunderstanding between him- 

 self and the British Government, under whose 

 patronage the work was carried on, it was never 

 completed. About 1834 or 1836 Mr. Scheutz, 

 a printer at Stockholm, heard of Mr. Babbage's 

 machine, and at one conceived the idea of 

 building one himself. This machine is the prod- 

 uct of his labors continued through nearly 

 twenty years, and was purchased for the Ob- 

 servatory in 1856, and put in operation for a 

 short time in 1858. 



Suppose it is desired to tabulate the series of 

 square numbers beginning with unity. Let us 

 first see how these numbers can be produced 

 by means of successive differences. We ar- 

 range them for convenience in the following 

 table : 



Number. Square. 1st Dilf. 2d Diff. 3d Diff. 

 1 1 



3 

 24 2 



5 



89 2 



7 

 4 16 



Now suppose we have three wheels, place 

 one above the other on a vertical (shaft) axis, 

 in each of which is inscribed zero and the nine 



digits, corresponding with a like number of 

 divisions on their surfaces. If the number 1 

 on the upper wheel, 3 on the second wheel, and 

 2 on the third wheel, be brought opposite a 

 fixed or zero point; and the nature of these 

 wheels be such that when set in motion by a 

 lever from right to left, the second wheel adds 

 its number to the upper wheel, and by a motion 

 of the lever from left to right, the third wheel 

 adds its number to the second (being in this 

 case constant and always equal to 2) ; from this 

 arrangement we shall be able to compute a 

 table of square numbers. 



We begin by moving the lever from right to 

 left ; when 3 (the number on the second wheel) 

 will be added to 1 (the number on the upper 

 wheel), making 4, the square of 2. On moving 

 the lever back, 2 on the third wheel is added 

 to 3 on the second wheel, making 5. Moving 

 our lever back again from right to left, 5 is 

 added to 4 on the upper wheel, making 9, the 

 square of 3. Repeating the process, we next 

 get 7 on the second wheel, which, added to 9 

 on the upper, makes 16, the square of 4. 



Having given the fundamental principles on 

 which the machine is constructed, we will add 

 a few particulars. This machine can be used 

 to 15 places of figures, of which 8 places are 

 printed, at the time of making the computation. 

 Thirty seconds is the time necessary for a com- 

 plete result. 



Before starting the machine for any compu- 

 tation, it is necessary to set the proper wheels, 

 after which it needs no further attention ; for 

 so long as the last order of differences is con- 

 stant, it will continue to produce the required 

 numbers. Thus for producing a table of squares, 

 it is only necessary to give the macMne threa 



