CITS3007 lab 1 (week 2) – Development environment – solutions
Laptop and SDE requirement
When attending lab classes, you will need access to a laptop from which you can access the CITS3007 standard development environment (SDE), which is based on Ubuntu 20.04, running on version 5.4.0 of the Linux kernel on an x86-64 processor.
The CITS3007 SDE will be used for the unit project, later in semester: all submissions are expected to compile and run correctly in this environment (though you may find it useful to test your code in other environments, as well).
We may also refer to the SDE in tests or quizzes – you might be asked to write code which will compile in this environment, for instance.
In the SDE, you are able to run commands as root
(by
using the sudo
command), and to alter the parameters of the running kernel (using
the sysctl
command). Being able to run sudo
is important for many
of the labs, so you’ll want to make sure it functions correctly for you.
Being able to run the sysctl
command is of lesser
importance – you will likely only need to use it if you want to complete
the extension tasks for lab 4 (on buffer overflows) and lab 8 (on race
conditions).
The preferred way of accessing the SDE is by running VirtualBox and Vagrant on your laptop, as outlined in this lab sheet. (Vagrant is widely used in industry to provide sandard development environments.) However, if you run into difficulties, there are a few other options, outlined below.
Note that UWA provides financial support via the “SOS IT Equipment Scheme” to students who are unable to purchase a laptop due to financial hardship.
tl;dr: Click on the box below to see a flowchart to guide you through the process.
To access the CITS3007 standard development environment, the preferred option is:
Install two open source tools (VirtualBox and Vagrant) on your Windows or Linux laptop. See VirtualBox and Vagrant, below.
You will need about 15 GB of disk space and a minimum of 4 GB of RAM on your laptop. (Note that 4 GB of RAM is likely to result in your VM running very slowly – 8 GB or more is preferable.)
However, VirtualBox is not available for M-series (Apple Silicon) mac laptops – in that case, you might like to try:
This involves installing UTM, virtualization software for the macOS operating system. See Using UTM on M-series Mac laptops. As explained on that page, you’ll need to pick one or more Linux virtual machine images. If compiling code for the project or the lab 4 and 8 extension tasks, you’ll need to make sure you are using an appropriate virtual machine.
The teaching staff for CITS3007 do not have an M-series MacOS testing environment in which we can debug issues with UTM, so our ability to assist you with the software may be limited. If you do run into problems, it’s a good idea to post on the CITS3007 discussion forum (on Moodle), as other students using Macs may be able to assist.
Virtualbox also may not function properly on Windows laptops where you are already using the Windows subsystem for Linux (WSL).
In that case, you might wish to:
In this case, we assume you are already familiar with how to install and access Ubuntu distributions using the WSL.
In general, the facilitators and unit coordinator won’t be able to assist you if you run into problems using the WSL, but you can find general instructions on using it here.
If you use the WSL, you will be able to run commands as root
using sudo
, but may not be able to alter kernel parameters
using sysctl
.
If none of the above options work for you, a remaining (temporary) option is:
GitHub Codespaces provides web-based access to development environments hosted in the cloud, and provides a quota of free hours each month (which most students will probably not exceed).
We provide instructions on how to use GitHub Codespaces here.
If using GitHub Codespaces, you will be able to run commands
as root using sudo
, but won’t be able to alter kernel
parameters using sysctl
.
You’ll also have to find your a way to of getting files you need (or want to keep) into and out of the Codespaces environment – your lab facilitator might have some suggestions.
Using CodeSpaces is a reasonable temporary way of accessing a Linux environment, but very limited, so you’ll want to find a way of running Linux on your own laptop.
What are VirtualBox and Vagrant?
VirtualBox is a type of virtualization software which allows you to run other operating systems on your computer – even operating systems designed for completely different hardware (such as mobile phones, for instance). It allows precise control of what OS kernel is run. (Other technologies for running Linux do exist – for instance, Docker and Windows Subsystem for Linux, or WSL – but they do not allow the precise control over kernel version that VirtualBox does.)
Vagrant is a tool for managing virtual environments. It can manage environments created using VirtualBox, Docker, VMWare, WSL, and many more. It handles tasks such as
It’s widely used in industry to provide developers with a Standard Development Environment (SDE) for their team or organization, so it’s hoped that experience with Vagrant will prove useful beyond your university studies.
Since the purpose of Vagrant is to manage VMs on a computer, vagrant commands need to be run from the host computer (for instance, your laptop), not from within a VM.
To install VirtualBox and Vagrant:
Visit https://www.virtualbox.org/wiki/Downloads, download the appropriate VirtualBox package for your platform (Windows, MacOS or Linux), and install it.
Note, if you are using a Mac: VirtualBox is only available for Macs using x86-64 processors. If you are using a more recent M-series (Apple Silicon) Mac, then it uses an ARM64 processor, and you should be using UTM, as described previously. If you don’t know which yours is: you can go to the ‘Apple’ at the top left of your screen and select ‘About this Mac’, and it will show whether your cpu is Apple silicon (ARM, M1 or M2) or x86/Intel.
.exe
file you can
simply run by double-clicking..dmg
file – double click
on it for instructions..deb
file is provided – we
assume you already know how to install one of these. If you are using a
non-Ubuntu distribution, consult the VirtualBox documentation for
instructions on how to install.If on Linux, once VirtualBox is installed, you should run the command
sudo usermod -aG vboxusers $USER
from a terminal; this
gives you all the permissions needed to run VirtualBox properly. You’ll
then need to log out and log back in again.
Visit https://www.vagrantup.com/downloads, download the appropriate Vagrant package for your platform, and install it.
.msi
file you can run
by double-clicking..dmg
file, or (if
you have Homebrew installed) there are
instructions for adding Vagrant with a brew install
command.Check that Vagrant has been successfully installed.
On Windows, open a “Command Prompt” window. On MacOS or Linux, open a terminal window.
Then type vagrant --version
; Vagrant should display
Vagrant 2.3.7
(Or something similar – any version from 2.2.0 onwards should be fine.)
Test a small virtual machine (VM) image.
On your host machine (i.e. your laptop), create a new
directory (called e.g. vagrant-test
), open a terminal
window and cd
into the directory. (The cd
command works on Linux, Mac and Windows.)
Download a test VM image. Run the command
vagrant box add --provider=virtualbox generic/alpine319
.
Vagrant will then attempt to download a virtual machine image containing
Alpine Linux from
https://vagrantcloud.com/
, a central repository of VM
images.
It may take about a minute to download the image over WiFi; if successful, it should display something similar to the following:
==> box: Loading metadata for box 'generic/alpine319'
box: URL: https://vagrantcloud.com/api/v2/vagrant/generic/alpine319
==> box: Adding box 'generic/alpine319' (v4.3.12) for provider: virtualbox (amd64)
box: Downloading: https://vagrantcloud.com/generic/boxes/alpine319/versions/4.3.12/providers/virtualbox/amd64/vagrant.box
box: Calculating and comparing box checksum...
==> box: Successfully added box 'generic/alpine319' (v4.3.12) for 'virtualbox (amd64)'!
Create a Vagrantfile. Assuming this step was
successful, run the command vagrant init generic/alpine319
.
This creates a file named Vagrantfile
, which can be used to
configure a VM before you run it (for instance, by altering the amount
of RAM allocated to the VM, or the network configuration). You can take
a look at the file contents in any text editor.
Bring up the VM. Run
vagrant up --provider=virtualbox
. Vagrant will then attempt
to configure the VM for use and start it running.
If you type vagrant ssh
, Vagrant will connect to the new
virtual machine using ssh
and present
you with a shell prompt:
$ vagrant ssh
alpine319:~$
Note that the command-line
prompt has now changed from the usual terminal
prompt you see. The prompt alpine319:~$
indicates that
you’re running commands in an Alpine Linux VM. To be able to run
commands from your host machine again, you need to exit from your SSH
session to the VM. (Or alternatively, of course, you can simply open a
new terminal window.)
You can exit your current SSH session by typing exit
or
hitting ctrl-D
.
(It’s not strictly necessary, but it’s good practice to also
halt VMs when you’re not using them – you can do so by issuing
the command vagrant halt
after you’ve exited the SSH
session.)
Vagrant username and password
Normally, you shouldn’t need a username and password to access a
Vagrant-managed virtual machine at all – running
vagrant ssh
should log you into the machine without any
other authentication being needed.
Should you ever need to specify a username and password, though, the
CITS3007 SDE follows the standard Vagrant convention of setting them
both to “vagrant
”.
Troubleshooting on Linux
Note that on Linux, if you happen to already have
libvirt
installed: libvirt
and VirtualBox
can’t both run at the same time. Ensure that libvirt
isn’t
running by typing sudo systemctl stop libvirtd
.
Download a VM containing the standard CITS3007 development environment. Note that this will likely take around 5–10 minutes, so once you’ve started the process, move onto the next exercise.
On your host machine (i.e. your laptop), create a new
directory (called e.g. cits3007-test
), open a terminal
window and cd
into the directory.
Download the CITS3007 VM image. Run the command
vagrant box add --provider=virtualbox arranstewart/cits3007-ubuntu2004
.
Vagrant should take around 5–10 minutes to download a virtual machine.
The output from Vagrant should look something like the following:
==> box: Loading metadata for box 'arranstewart/cits3007-ubuntu2004'
box: URL: https://vagrantcloud.com/api/v2/vagrant/arranstewart/cits3007-ubuntu2004
==> box: Adding box 'arranstewart/cits3007-ubuntu2004' (v0.1.4) for provider: virtualbox
box: Downloading: https://vagrantcloud.com/arranstewart/boxes/cits3007-ubuntu2004/versions/0.1.4/providers/virtualbox/unknown/vagrant.box
box: Calculating and comparing box checksum...
==> box: Successfully added box 'arranstewart/cits3007-ubuntu2004' (v0.1.4) for 'virtualbox'!
Type vagrant init arranstewart/cits3007-ubuntu2004
to
create a Vagrantfile, then vagrant up --provider=virtualbox
to start the VM. You should see output like the following:
Bringing machine 'default' up with 'virtualbox' provider...
==> default: Importing base box 'arranstewart/cits3007-ubuntu2004'...
==> default: Matching MAC address for NAT networking...
==> default: Checking if box 'arranstewart/cits3007-ubuntu2004' version '0.1.2' is up to date...
==> default: Setting the name of the VM: xxx-cits3007-test_1658816964468_16898
==> default: Clearing any previously set forwarded ports...
==> default: Fixed port collision for 22 => 2222. Now on port 2200.
==> default: Clearing any previously set network interfaces...
==> default: Preparing network interfaces based on configuration...
default: Adapter 1: nat
==> default: Forwarding ports...
default: 22 (guest) => 2200 (host) (adapter 1)
==> default: Booting VM...
==> default: Waiting for machine to boot. This may take a few minutes...
default: SSH address: 127.0.0.1:2200
default: SSH username: vagrant
default: SSH auth method: private key
default: Warning: Connection reset. Retrying...
default: Warning: Remote connection disconnect. Retrying...
default: Warning: Connection reset. Retrying...
default:
default: Vagrant insecure key detected. Vagrant will automatically replace
default: this with a newly generated keypair for better security.
default:
default: Inserting generated public key within guest...
default: Removing insecure key from the guest if it's present...
default: Key inserted! Disconnecting and reconnecting using new SSH key...
==> default: Machine booted and ready!
==> default: Checking for guest additions in VM...
==> default: Setting hostname...
Once it’s done, you can type vagrant ssh
to get shell
access to the new VM:
$ vagrant ssh
vagrant@cits3007-ubuntu2004:~$
Note that again, your terminal prompt has changed – it sould look like this:
vagrant@cits3007-ubuntu2004:~$
(usually in bright green). The prompt indicates the name of the
current user (“vagrant
”)1, and the hostname for
the machine you are connected to
(“cits3007-ubuntu2004
”).
If you want to issue commands on your host machine again (that is, on your laptop), you’ll need to either
exit
or by typing ctrl-D
In particular, trying to run Vagrant commands from within your VM will not work, since Vagrant has not been installed within the VM.
Optional: install VS Code and the “Remote-SSH” extension.
The standard CITS3007 development environment VM comes with the
vim
editor already installed, and for some tasks we do, it
will be necessary to use vim
or another terminal-based
editor.
However, if you already have VS Code installed and are familiar with it, we provide instructions on how to configure it for use with a Vagrant box here.
You can find a useful “cheat sheet” of commands for managing Vagrant VMs here: https://cheatography.com/davbfr/cheat-sheets/vagrant-cheat-sheet/.
If possible, it’s recommended you work on this section in pairs or small groups and compare answers.
For each of the following concepts, review the definition given in the lecture slides, and explain it in your own words. If you can, give an example, based on your own experience or from recent news reports:
Sample solutions
Definitions for all these terms are in the week 1 lecture slides: your explanations should be in your own words.
Examples of each could be:
threat: Any source of danger or loss will do. A threat to information security specifically might be: Accidental [or intentional] deletion of records from a server.
vulnerability: A vulnerability rendering (for example) your house susceptible to physical security might be: there are no locks on your doors and windows. (This renders you susceptible to theft.)
A vulnerability of a computer system might be: lack of a firewall. (This allows connections to potentially be made from any remote system to any open port on the computer system.)
confidentiality: An example of confidentiality in the physical world might be: I might have a filing cabinet containing (say) financial records which I don’t wish to be publicly available.
An information security example could be much the same (financial records), except that the records are held on a computer system (e.g. a bank’s servers).
integrity: An example of a (compromise of) information integrity could be the example given above – deletion of records from a server.
A physical security example is similar: suppose business records are kept in hard-copy format (as was not uncommon up until the mid to late twentieth century). If those hard copies are destroyed (or fraudulently altered), there’s been a compromise of integrity.
availability: An example of a (compromise of) availability is when (for instance) a web server goes down.
The server could become unavailable due to (for instance) a natural disaster such as flood or power outage, but also due to a malicious attacker.
How would you describe the relationship between threats, vulnerabilities, and attacks? Give examples to illustrate the relationship.
An example answer:
A threat can be thought of as a source of danger (e.g. a power outage could pose a threat to the integrity of computer records stored on a server). However, not all systems will necessarily be vulnerable (that is, susceptible) to a particular threat. For example, systems with proper backups might not be vulnerable to a loss of integrity due to a power outage. If the power outage were due to natural causes or accident, then this would not be an attack, but rather an “incident”. However, if the power outage was deliberately brought about with the intent of causing data loss, then this would be an attack. (An example of a known cyber attack on a power grid is the “Ukraine power grid hack” of December 2015, in which attackers were able to remotely compromise the computer systems of three power distribution companies in Ukraine, and temporarily disrupted the power supply to consumers.)
Is it possible for a threat and a vulnerability to both exist, without there being an attack? Explain why or why not.
An example answer:
Yes, it is possible.
A threat to (for instance) data integrity might exist (an intern with access to a server), and a vulnerability might exist (files on the server do not have adequate protections and/or are not properly backed up), and the threat might even eventuate (the intern accidentally deletes all files). But if the act wasn’t carried out intentionally, this is not considered an “attack”.
Consider an ATM, which requires users to provide a bank card and a PIN in order to perform transactions. Give examples of confidentiality, integrity and availability requirements associated with the system. How important do you think each requirement is – are they all equally important, or does the importance differ?
An example answer:
An example of a confidentiality requirement might be: when a bank card and a PIN are provided, the ATM doesn’t let a customer view the transactions of other customers.
For integrity: when a bank card and a PIN are provided, the ATM doesn’t let a customer make transactions for other customers (nor does it let records of transactions be deleted).
For availability: the provider of the ATM system might have a
requirement along the lines of “the ATM shall not be unavailable due to
hardware or software system error more than 0.1 percent of the time the
system is operational”. (This would allow, for instance, the system to
be unavailable for no more than about 9 hours each year.)
If the bank, however, suffered a local power outage, that would
not be a failure of the requirement, so the provider of the ATM system
would not be at fault. (The banks customers might be unhappy, though:
perhaps the bank should ensure backup generators are available.)
All of these requirements are fairly important, but most customers would probably rate the “integrity” requirement as being most important, then the confidentiality requirement, and finally the availability requirement.
C language familiarity
Ideally, you should be doing this unit in your third year, and have familiarity with the C programming language.
You need to either
Note that YouTube tutorials will not be sufficient as a C reference for this unit – you will need a textbook (or to make use of the cppreference.com site). The lab facilitators will not be able to assist you if you are using video tutorials instead of a C language reference.
If you are still in the process of purchasing a textbook, the following sites may provide a helpful refresher:
What is the difference between the C literal values
3
, '3'
, "3"
and 3.0
?
What is the type of each?
Answer
The literal value 3
is an integer – it has type
int
(see here).
The literal value '3'
is a character constant – it also
has type int
(see here).
The literal value "3"
is a string literal; it has type
char[1]
(see here).
The literal value 3.0
is a floating constant; it has
type double
(you could force a type of float
by writing 3.0f
. See here).
Consider the following C code:
const char * str = "test";
char c = str[0];
if (c >= 65 && c <= 90) {
("high\n");
printf} else if (c >= 97 && c <=122) {
("low\n");
printf} else {
("other\n");
printf}
If this code is executed, what will be printed to the terminal?
Answer
Assuming the code is part of some function which is executed, then
the text “low
” will be printed to the terminal. This is
because the first element of the string str
is the char
't'
, which can also be interpreted as the integral value
116. Since 116 is between 97 and 122 (inclusive), the string
"low\n"
will get printed.
What is the output of the question (b) code if we change the
string "test"
to "TEST"
?
Answer
The first element of str
in this case is
'T'
, which can also be interpreted as the integral value
84. Since 84 is between 65 and 90 (inclusive), the string
"high\n"
will get printed.
What is the output of the question (b) code if we change the
string "test"
to "???"
?
Answer
The first element of str
in this case is
'?'
, which can also be interpreted as the integral value
63. The first two “if
” conditions in the code evaluate to
false, so the last else
branch is executed, and the text
“other
” is printed.
In
Download the lab-01-code.zip
file from the “Labs”
section of the CITS3007 Resources
page.
The best way to do so is from within your CITS3007 development environment (i.e. from within the virtual machine).
You can do so by running
$ wget https://cits3007.arranstewart.io/labs/lab-01-code.zip
Navigating the command-line and building C programs
In this unit, we assume you understand how to navigate a Unix-like
operating system2 using the command-line, how to
perform basic file operations, and how to run commands like
wget
and unzip
.
If not, visit the resources page on the CITS3007 website, where you’ll find recommendations of guides and tutorials on using the Linux command-line (e.g. William Shotts’ online guide The Linux Command Line).
Ideally, you should also have completed CITS2002 Systems Programming,
and be familiar with how to build C projects using gcc
and GNU Make. If not, you
should consult your C textbook and the CITS2002
materials (look for the material on “Developing C programs in
multiple files”) for basic usage guides for those tools.
Unzip the zip file into a directory of your choosing, using the
unzip
command. (See man unzip
if you need
details of how to use the unzip
command.)
Build the test_leap
program by typing
make
, then try running it with various different
command-line arguments:
$ ./test_leap 1901
$ ./test_leap 1900
$ ./test_leap 2000
$ ./test_leap -1
$ ./test_leap -0
$ ./test_leap 9223372036854775807
$ ./test_leap 9223372036854775808
$ ./test_leap foo
$ ./test_leap foo bar
What results do you get? Take a look at the code in
test_leap.c
, read the documentation for the
strtol
function (by running man strtol
), and
explain what is happening in each case.
A copy of the code with line numbers printed is included below.
#include <stdlib.h>
#include <stdio.h>
#include <errno.h>
/* return 0 (false) or 1 (true), depending on whether
* `year` is a leap year or not.
*/
int is_leap(long year) {
if (year % 4 != 0) {
return 0;
}
if (year % 100 == 0) {
return 1;
}
return 0;
}
int main(int argc, char **argv) {
argc--;
argv++;
if (argc != 1) {
fprintf(stderr, "Error: expected 1 command-line argument (a YEAR), but got %d\n", argc);
exit(1);
}
char *end;
// clear errno so we can check whether strtol fails
errno = 0;
long year = strtol(argv[0], &end, 10);
int res_errno = errno;
if (end == argv[0]) {
fprintf(stderr, "Error: couldn't interpret '%s' as a number\n", argv[0]);
exit(1);
} else if (res_errno == ERANGE) {
fprintf(stderr, "Error: '%s' is outside the range of numbers we can handle\n", argv[0]);
exit(1);
} else {
if (is_leap(year)) {
printf("%ld is a leap year\n", year);
} else {
printf("%ld is not a leap year\n", year);
}
}
}
Answer
The results observed should be as follows:
return 0;
) of is_leap
gets executed, and
"1901 is not a leap year"
is printed.return 0;
) of is_leap
gets executed, and
"1900 is a leap year"
is printed. (This is incorrect,
though – 1900 is not in fact a leap year.)"2000 is a leap year"
is printed. (And this is correct,
2000 is a leap year.)"-1 is a leap year"
is printed. (This is correct, if we use
the “proleptic
Gregorian calendar”; that is, we imagine the Gregorian calendar is
extended backwards before the year in which it was actually introduced,
namely 1582 for most of Europe, and 1752 in Britain and its colonies.3)strtol
function interprets -0
the
same as 0
, and the same path through the code is executed
as for 1900, and "0 is a leap year"
is printed. (Which is
correct, if we use the proleptic Gregorian calendar.)"9223372036854775807 is not a leap year"
is printed.long int
. The behaviour of
strtol
in this case (run man strtol
to read
the documentation for the function) is that the global variable
errno
is set to the constant ERANGE
; the
condition on line 41 (res_errno == ERANGE
) evaluates to
true, and
"9223372036854775808 is outside the range of numbers we can handle"
is printed.strtol
cannot interpret this as a number at all;
it sets its parameter &end
to be the same as
argv[0]
. (end
is set to store the address of
the “first invalid character” in argv[0]
. Since there are
no valid characters in argv[0]
, it therefore ends
up pointing to the start of that string. As a result, the condition on
line 38 (end == argv[0]
) evaluates to true, and
Error: couldn't interpret 'foo' as a number
is
printed.argc != 1
) evaluates to true, and
Error: expected 1 command-line argument (a YEAR), but got 2
is printed.The code in test_leap.c
contains an error. The
correct algorithm for determining whether a year is a leap year is
outlined at https://en.wikipedia.org/wiki/Leap_year#Algorithm, but
the code in test_leap.c
incorrectly reports that (for
instance) 1900 is a leap year, when it is not. (Can you spot any other
errors? Feel free to post in the CITS3007 discussion forum, on Moodle, if you can.)
Fix the code in test_leap.c
and test your changes by
trying the values from step 3 again.
Compare your changes with another student’s – are there any differences between how you fixed the program?
For upcoming quizzes and tests, we’ll be using the CSSE Moodle server, available at https://quiz.jinhong.org.
Moodle also hosts the forum used for unit announcements, so it’s important you register properly on Moodle and subscribe to the forum.
There is currently one Moodle quiz available – it is not assessed, but you should attempt it, as the material covered is examinable later. You can use that quiz to revise or refresh your knowledge of C.
Visit https://quiz.jinhong.org and sign up with your UWA email address – see here for further instructions – then attempt the quiz in your own time, if you don’t finish it in the lab.
Moodle assessments
Make sure you have signed up for Moodle, and added yourself to the CITS3007 section of Moodle, well before the first assessment (in Week 4).
Late in week 3, teaching staff will remove students from the CITS3007 section of Moodle if they are not currently enrolled in CITS3007 (as only currently enrolled students are permitted to take the assessments), and the self-registration will be locked.
Conventionally, all Vagrant VMs have a user account
named “vagrant” on them, with the password for the account also set to
“vagrant”. This makes it very easy to log into them. Normally, using a
well-known, easy-to-guess, hard-coded user ID and password would be a poor
security practice.
But in this case: the VM is only being used for development purposes,
rather than deployed in production; it should only be possible to
connect to the VM from your local computer; and the VM is unlikely to
contain any confidential data of yours. This being so, the use of
default credentials is usually an acceptable risk.↩︎
Unix refers to an operating system originally
developed at AT&T’s Bell Labs;
to the family of operating systems descended from that original
operating system; and to modern operating systems which are licensed to
use the name by the industry consortium The Open Group, which is the
owner of the “Unix” trademark.
Unix-like systems are ones which adopt the same design
principles, and typically share similar commands, but are not
necessarily officially licensed to use the Unix trademark.
Linux is a prime example of a Unix-like operating system – the
design is heavily inspired by Unix, but it was not derived from the
original Unix source code and is not licensed to use the Unix trademark.
MacOS, on the other hand, was developed from a specific version of Unix
(BSD, the Berkeley Software Distribution), and has been officially
certified as a Unix by The Open Group.
In this course, when we refer to Unix (e.g. “the Unix access control
system”), we typically mean Unix-like operating systems, rather
than just those licensed to use the Unix trademark.↩︎
In Britain in 1752, the British calendar differed from the Gregorian calendar by 11 days. During the changeover, those 11 days “disappeared” – the day after 2 September 1752 was 14 September 1752.↩︎